Elo rating system - Knowledge

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include: choosing opponents that they know they can beat with a certain strategy; choosing opponents that they think are overrated; or avoiding playing strong players who are rated several hundred points below them, but may hold chess titles such as IM or GM. In the category of choosing overrated opponents, new entrants to the rating system who have played fewer than 50 games are in theory a convenient target as they may be overrated in their provisional rating. The ICC compensates for this issue by assigning a lower K-factor to the established player if they do win against a new rating entrant. The K-factor is actually a function of the number of rated games played by the new entrant.

6335: 10049: 2754:. Likewise, one can leave the rating difference alone and divide by 480 instead of 400. Since the Elo formula is overestimating the stronger player's win probability, stronger players are losing points against weaker players despite playing at their true strength. Likewise, weaker players gain points against stronger players. When the modification is applied, observed win rates deviate by less than 0.1% away from prediction, while traditional Elo can be 4% off the predicted rate. 5992: 7379: 9399:

is likely to make. Consequently, such an engine is more or less guaranteed to score at least 25% even against perfect play. Differences in skill beyond a certain point could only be picked up if one does not begin from the usual starting position, but instead chooses a starting position that is only barely not lost for one side. Because of these factors, ratings depend on pairings and the openings selected. Published engine rating lists such as

9244: 9166: 8496: 116:, many rating points will be transferred. The lower-rated player will also gain a few points from the higher rated player in the event of a draw. This means that this rating system is self-correcting. Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength. 197:, have proposed using more sophisticated statistical machinery to estimate the same variables. On the other hand, the computational simplicity of the Elo system has proven to be one of its greatest assets. With the aid of a pocket calculator, an informed chess competitor can calculate to within one point what their next officially published rating will be, which helps promote a perception that the ratings are fair. 9235:

large Swiss event which is being fiercely contested, with round winners meeting round winners. This approach to pairing certainly maximizes the rating risk of the higher-rated participants, who may face very stiff opposition from players below 3000, for example. This is a separate rating in itself, and is under "1-minute" and "5-minute" rating categories. Maximum ratings achieved over 2500 are exceptionally rare.

6330:{\displaystyle \ell ={\begin{cases}-\log \sigma (r_{\mathsf {A,B}};\kappa )&{\textrm {if}}~{\mathsf {A}}~{\textrm {wins}},\\-\log \sigma (-r_{\mathsf {A,B}};\kappa )&{\textrm {if}}~{\mathsf {B}}~{\textrm {wins}},\\-\log \kappa -{\frac {1}{2}}\log \sigma (r_{\mathsf {A,B}};\kappa )-{\frac {1}{2}}\log \sigma (-r_{\mathsf {A,B}};\kappa )&{\textrm {if}}~{\mathsf {A}}~{\textrm {draw}},\end{cases}}} 4528: 14634: 7046: 8217: 5935: 3860: 1578:

floor. For players with ratings below 2000, winning a cash prize of $ 2,000 or more raises that player's rating floor to the closest 100-point level that would have disqualified the player for participation in the tournament. For example, if a player won $ 4,000 in a 1750-and-under tournament, they would now have a rating floor of 1800.

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of their opponents. The ratings of a player who won more games than expected would be adjusted upward, while those of a player who won fewer than expected would be adjusted downward. Moreover, that adjustment was to be in linear proportion to the number of wins by which the player had exceeded or fallen short of their expected number.

2707:(FICS). However, each organization has taken a different approach to dealing with the uncertainty inherent in the ratings, particularly the ratings of newcomers, and to dealing with the problem of ratings inflation/deflation. New players are assigned provisional ratings, which are adjusted more drastically than established ratings. 2818:-factor coefficient is set too large, there will be too much sensitivity to just a few, recent events, in terms of a large number of points exchanged in each game. And if the K-value is too low, the sensitivity will be minimal, and the system will not respond quickly enough to changes in a player's actual level of performance. 4328: 6534: 1610:

drawing. The probability of drawing, as opposed to having a decisive result, is not specified in the Elo system. Instead, a draw is considered half a win and half a loss. In practice, since the true strength of each player is unknown, the expected scores are calculated using the player's current ratings as follows.

7374:{\displaystyle {\begin{aligned}{\frac {\textrm {d}}{{\textrm {d}}R_{\mathsf {A}}}}\ell &=-{\frac {2\log 10}{s}}\left((S_{\mathsf {A}}+0.5D)-(S_{\mathsf {B}}+0.5D)g(r_{\mathsf {A,B}};\kappa )\right)\\&=-{\frac {2\log 10}{s}}\left(S_{\mathsf {A}}+0.5D-g(r_{\mathsf {A,B}};\kappa )\right),\end{aligned}}} 9954:

writes mathematical formulas for the Elo rating system on Zuckerberg's dormitory room window. Behind the scenes, the movie claims, the Elo system is employed to rank girls by their attractiveness. The equations driving the algorithm are shown briefly, written on the window; however, they are slightly

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becomes very important at the computer level. Beyond some skill threshold, an engine with White should be able to force a draw on demand from the starting position even against perfect play, simply because White begins with too big an advantage to lose compared to the small magnitude of the errors it

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Performance rating or special rating is a hypothetical rating that would result from the games of a single event only. Some chess organizations use the "algorithm of 400" to calculate performance rating. According to this algorithm, performance rating for an event is calculated in the following way:

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The phrase "Elo rating" is often used to mean a player's chess rating as calculated by FIDE. However, this usage may be confusing or misleading because Elo's general ideas have been adopted by many organizations, including the USCF (before FIDE), many other national chess federations, the short-lived

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A player's Elo rating is a number that may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. If the

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when the player reaches 2400. The current system in the United States includes a bonus point scheme which feeds rating points into the system in order to track improving players, and different K-values for different players. Some methods, used in Norway for example, differentiate between juniors and

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Performance is not measured absolutely; it is inferred from wins, losses, and draws against other players. Players' ratings depend on the ratings of their opponents and the results scored against them. The difference in rating between two players determines an estimate for the expected score between

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There are two ways to achieve higher rating floors other than under the standard scheme presented above. If a player has achieved the rating of Original Life Master, their rating floor is set at 2200. The achievement of this title is unique in that no other recognized USCF title will result in a new

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To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model (i.e., the true skill of each player). One could calculate relatively easily from tables how many games players would be expected to win based on comparisons of their ratings to those

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Elo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss. Actually, there is a probability of a draw that is dependent on the performance differential, so this latter is more of a confidence interval than any deterministic frontier. And while

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The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if

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In 1995, the USCF acknowledged that several young scholastic players were improving faster than the rating system was able to track. As a result, established players with stable ratings started to lose rating points to the young and underrated players. Several of the older established players were

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In a pure Elo system, each game ends in an equal transaction of rating points. If the winner gains N rating points, the loser will drop by N rating points. This prevents points from entering or leaving the system when games are played and rated. However, players tend to enter the system as novices

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One possible cause for this inflation was the rating floor, which for a long time was at 2200, and if a player dropped below this they were struck from the rating list. As a consequence, players at a skill level just below the floor would only be on the rating list if they were overrated, and this

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updates its ratings list at the beginning of each month. In contrast, the unofficial "Live ratings" calculate the change in players' ratings after every game. These Live ratings are based on the previously published FIDE ratings, so a player's Live rating is intended to correspond to what the FIDE

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A further assumption is necessary because chess performance in the above sense is still not measurable. One cannot look at a sequence of moves and derive a number to represent that player's skill. Performance can only be inferred from wins, draws, and losses. Therefore, a player who wins a game is

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Because of the significant difference in timing of when inflation and deflation occur, and in order to combat deflation, most implementations of Elo ratings have a mechanism for injecting points into the system in order to maintain relative ratings over time. FIDE has two inflationary mechanisms.

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The ICC has also recently introduced "auto-pairing" ratings which are based on random pairings, but with each win in a row ensuring a statistically much harder opponent who has also won x games in a row. With potentially hundreds of players involved, this creates some of the challenges of a major

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may play a string of different opponents who are all rated over 2700. In over-the-board events, it would only be in very high level all-play-all events that a player would be able to engage that number of 2700+ opponents. In a normal, open, Swiss-paired chess tournament, frequently there would be

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Rating floors in the United States work by guaranteeing that a player will never drop below a certain limit. This also combats deflation, but the chairman of the USCF Ratings Committee has been critical of this method because it does not feed the extra points to the improving players. A possible

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When a player's actual tournament scores exceed their expected scores, the Elo system takes this as evidence that player's rating is too low, and needs to be adjusted upward. Similarly, when a player's actual tournament scores fall short of their expected scores, that player's rating is adjusted

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is their probability of winning plus half their probability of drawing. Thus, an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing. On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of

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The normal probabilities may be taken directly from the standard tables of the areas under the normal curve when the difference in rating is expressed as a z score. Since the standard deviation σ of individual performances is defined as 200 points, the standard deviation σ' of the differences in

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uses the Elo system to rank its TCG organized play competitors. Prizes for the top players in various regions included holidays and world championships invites until the 2011–2012 season, where awards were based on a system of Championship Points, their rationale being the same as the DCI's for

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Analyzing FIDE rating lists over time, Jeff Sonas suggests that inflation may have taken place since about 1985. Sonas looks at the highest-rated players, rather than all rated players, and acknowledges that the changes in the distribution of ratings could have been caused by an increase of the

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The term "inflation", applied to ratings, is meant to suggest that the level of playing strength demonstrated by the rated player is decreasing over time; conversely, "deflation" suggests that the level is advancing. For example, if there is inflation, a modern rating of 2500 means less than a

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A more subtle issue is related to pairing. When players can choose their own opponents, they can choose opponents with minimal risk of losing, and maximum reward for winning. Particular examples of players rated 2800+ choosing opponents with minimal risk and maximum possibility of rating gain

8491:{\displaystyle {\begin{aligned}E&=\Pr\{{\mathsf {A}}~{\text{wins}}\}+0.5\Pr\{{\mathsf {A}}~{\text{draws}}\}\\&=\sigma (r_{\mathsf {A,B}};\kappa )+0.5\kappa {\sqrt {\sigma (r_{\mathsf {A,B}};\kappa )\sigma (-r_{\mathsf {A,B}};\kappa )}}\\&=g(r_{\mathsf {A,B}};\kappa )\end{aligned}}} 1569:

Higher rating floors exist for experienced players who have achieved significant ratings. Such higher rating floors exist, starting at ratings of 1200 in 100-point increments up to 2100 (1200, 1300, 1400, ..., 2100). A rating floor is calculated by taking the player's peak established rating,

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Therefore, Elo ratings online still provide a useful mechanism for providing a rating based on the opponent's rating. Its overall credibility, however, needs to be seen in the context of at least the above two major issues described—engine abuse, and selective pairing of opponents.

174:. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time. Elo thought of a player's true skill as the mean of that player's performance random variable. 3684: 5506: 5685: 1598:

them. Both the average and the spread of ratings can be arbitrarily chosen. The USCF initially aimed for an average club player to have a rating of 1500 and Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an

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The USCF maintains an absolute rating floor of 100 for all ratings. Thus, no member can have a rating below 100, no matter their performance at USCF-sanctioned events. However, players can have higher individual absolute rating floors, calculated using the following formula:

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Elo's system replaced earlier systems of competitive rewards with a system based on statistical estimation. Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. For example, winning an important

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downward. Elo's original suggestion, which is still widely used, was a simple linear adjustment proportional to the amount by which a player over-performed or under-performed their expected score. The maximum possible adjustment per game, called the K-factor, was set at

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was launched, which used the Elo scoring system to rank teams. The initial K-value was 30, but was changed to 5 in January 2007, then changed to 15 in July 2009. The site later went offline in 2013. A similar alternative site was launched in 2016 under the name

31: 4523:{\displaystyle R_{\mathsf {A}}\leftarrow {\begin{cases}R_{\mathsf {A}}+K\sigma (-r_{\mathsf {A,B}})&{\textrm {if}}~{\mathsf {A}}~{\textrm {wins}}\\R_{\mathsf {A}}-K\sigma (r_{\mathsf {A,B}})&{\textrm {if}}~{\mathsf {B}}~{\textrm {wins}},\end{cases}}} 8113: 7650: 9923:

The Elo rating system has also been adopted to evaluate AI models. In 2021, Anthropic utilized the Elo system for ranking AI models in their research. The LMSYS leaderboard briefly employed the Elo rating system to rank AI models before transitioning to

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assumed to have performed at a higher level than the opponent for that game. Conversely, a losing player is assumed to have performed at a lower level. If the game ends in a draw, the two players are assumed to have performed at nearly the same level.

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First, performances below a "ratings floor" are not tracked, so a player with true skill below the floor can only be unrated or overrated, never correctly rated. Second, established and higher-rated players have a lower K-factor. New players have a

9873:, which concerns the identification of individuals using human descriptions. Comparative descriptions were utilized alongside the Elo rating system to provide robust and discriminative 'relative measurements', permitting accurate identification. 9498:

games. However, the DCI abandoned this system in 2012 in favor of a new cumulative system of "Planeswalker Points", chiefly because of the above-noted concern that Elo encourages highly rated players to avoid playing to "protect their rating".

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was only the 8th player in chess history to reach the 2700 mark at that point of time. This increased to 15 players by 1994. 33 players had a 2700+ rating in 2009 and 44 as of September 2012. Only 14 players have ever broken a rating of 2800.

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has a rating of 1613 and plays in a five-round tournament. They lose to a player rated 1609, draw with a player rated 1477, defeat a player rated 1388, defeat a player rated 1586, and lose to a player rated 1720. The player's actual score is

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had a FIDE rating of 2366 and a USCF rating of 2473." The Elo ratings of these various organizations are not always directly comparable, since Elo ratings measure the results within a closed pool of players rather than absolute skill.

224:, as weaker players have greater winning chances than Elo's model predicts. In paired comparison data, there is often very little practical difference in whether it is assumed that the differences in players' strengths are normally or 1908: 1797: 5378: 1991: 5290: 4320: 4242: 7006: 145:

to enable members to track their individual progress in terms other than tournament wins and losses. The Harkness system was reasonably fair, but in some circumstances gave rise to ratings many observers considered inaccurate.

8206: 9445:(FIBS) calculates ratings based on a modified Elo system. New players are assigned a rating of 1500, with the best humans and bots rating over 2000. The same formula has been adopted by several other backgammon sites, such as 5622: 1056: 989: 922: 1240:

Rating changes can be calculated manually by using the FIDE ratings change calculator. All top players have a K-factor of 10, which means that the maximum ratings change from a single game is a little less than 10 points.

1574:, which would be rounded down to 1200. Under this scheme, only Class C players and above are capable of having a higher rating floor than their absolute player rating. All other players would have a floor of at most 150. 3855:{\displaystyle \ell ={\begin{cases}-\log \sigma (r_{\mathsf {A,B}})&{\textrm {if}}~{\mathsf {A}}~{\textrm {wins}},\\-\log \sigma (-r_{\mathsf {A,B}})&{\textrm {if}}~{\mathsf {B}}~{\textrm {wins}},\end{cases}}} 793: 1480: 283:

The normal and logistic distributions are, in a way, arbitrary points in a spectrum of distributions which would work well. In practice, both of these distributions work very well for a number of different games.

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to evaluate moves played in games between rated players, Regan and Haworth analyze sets of games from FIDE-rated tournaments, and draw the conclusion that there had been little or no inflation from 1976 to 2009.

5930:{\displaystyle \Pr\{{\mathsf {A}}~{\textrm {wins}}\}=\sigma (r_{\mathsf {A,B}};0)={\frac {10^{r_{\mathsf {A,B}}/s}}{10^{-r_{\mathsf {A,B}}/s}+10^{r_{\mathsf {A,B}}/s}}}={\frac {1}{1+10^{-r_{\mathsf {A,B}}/s'}}},} 5386: 3519: 9769:

uses the Elo rating system to determine the standings in the various puzzles. This system is also used in FIFA Mobile for the Division Rivals modes. Another recent game to start using the Elo rating system is

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In some cases the rating system can discourage game activity for players who wish to protect their rating. In order to discourage players from sitting on a high rating, a 2012 proposal by British Grandmaster

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To address these difficulties, and to derive the Elo rating in the ternary games, we will define the explicit probabilistic model of the outcomes. Next, we will minimize the log loss via stochastic gradient.

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ratings are difficult to quantify, due to variable factors such as the time control and the hardware the program runs on, and also the fact that chess is not a fair game. The existence and magnitude of the

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historical rating of 2500, while the reverse is true if there is deflation. Using ratings to compare players between different eras is made more difficult when inflation or deflation are present. (See also

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Askell, Amanda; Bai, Yuntao; Chen, Anna; Drain, Dawn; Ganguli, Deep; Henighan, Tom; Jones, Andy; Joseph, Nicholas; Mann, Ben (2021-12-09). "A General Language Assistant as a Laboratory for Alignment".

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In tennis, the Elo-based Universal Tennis Rating (UTR) rates players on a global scale, regardless of age, gender, or nationality. It is the official rating system of major organizations such as the

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is a parameter. Introduction of a free parameter should not be surprising as we have three possible outcomes and thus, an additional degree of freedom should appear in the model. In particular, with

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Despite questions of the appropriateness of using the Elo system to rate games in which luck is a factor, trading-card game manufacturers often use Elo ratings for their organized play efforts. The

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In theory, this might apply equally to online chess players and over-the-board players, since it is more difficult for all players to raise their rating after their rating has become high and their

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with a low rating and retire from the system as experienced players with a high rating. Therefore, in the long run a system with strictly equal transactions tends to result in rating deflation.

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Graphs of probabilities and Elo rating changes (for K=16 and 32) of expected outcome (solid curve) and unexpected outcome (dotted curve) vs initial rating difference. For example, player

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distributed. Mathematically, however, the logistic function is more convenient to work with than the normal distribution. FIDE continues to use the rating difference table as proposed by Elo.

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wins or loses the game. It is, therefore, not immediately clear what is the meaning of the fractional score. Moreover, since we do not specify explicitly the model relating the rating values

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for a player new to the rating list until the completion of events with a total of 30 games, and for all players until their 18th birthday, as long as their rating remains under 2300.

7873: 7503: 3254:-factor consequently reduced. However, when playing online, 2800+ players can more easily raise their rating by simply selecting opponents with high ratings – on the ICC playing site, a 7941: 7805: 1376: 9917: 8005: 7542: 6529:{\displaystyle \ell =-(S_{\mathsf {A}}+{\frac {1}{2}}D)\log \sigma (r_{\mathsf {A,B}};\kappa )-(S_{\mathsf {B}}+{\frac {1}{2}}D)\log \sigma (-r_{\mathsf {A,B}};\kappa )-D\log \kappa } 9569:

publishes team rankings for most American sports, which includes Elo system ratings for college football. The use of rating systems was effectively scrapped with the creation of the

6751: 9537:. In order to be eligible for professional chess boxing, one must have an Elo rating of at least 1600, as well as competing in 50 or more matches of amateur boxing or martial arts. 3559: 2981:-factor based on factors including the number of games played and the player's rating. The K-factor is also reduced for high rated players if the event has shorter time controls. 2662: 5042: 2484: 2453: 1681: 1646: 2679:

had scored two wins, one loss, and two draws, for a total score of three points, that would have been slightly better than expected, and the player's new rating would have been

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players has been developed. The hockey-Elo metric evaluates a player's overall two-way play: scoring AND defense in both even strength and power-play/penalty-kill situations.

4663: 3243:-factor reduces rating change at the top end of the rating range, reducing the possibility for rapid rise or fall of rating for those with a rating high enough to reach a low 1070: 7997: 7535: 7038: 5194: 5165: 4912: 2422: 11104: 12295: 7965: 7897: 7829: 6707: 6657: 6598: 5651: 5136: 4821: 4762: 3308: 2328:. It then follows that for each 400 rating points of advantage over the opponent, the expected score is magnified ten times in comparison to the opponent's expected score. 8923: 8507: 11623: 5977: 4080: 5207:, we should adopt the model which takes their ordinal nature into account, and we use the so-called adjacent categories model which may be traced to the Davidson's work 119:

Elo ratings are comparative only, and are valid only within the rating pool in which they were calculated, rather than being an absolute measure of a player's strength.

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and thus, the Elo-Davidson rating is exactly the same as the Elo rating. However, this is of no help to understand the case when the draws are observed (we cannot use

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subtracting 200 points, and then rounding down to the nearest rating floor. For example, a player who has reached a peak rating of 1464 would have a rating floor of

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From a modern perspective, Elo's simplifying assumptions are not necessary because computing power is inexpensive and widely available. Several people, most notably

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basis. At about the same time, György Karoly and Roger Cook independently developed a system based on the same principles for the New South Wales Chess Association.

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Since the very beginning, the Elo rating has been also used in chess where we observe wins, losses or draws and, to deal with the latter a fractional score value,

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Pörschmann; et al. (2010). "Male reproductive success and its behavioural correlates in a polygynous mammal, the Galápagos sea lion (Zalophus wollebaeki)".

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seniors, and use a larger K-factor for the young players, even boosting the rating progress by 100% for when they score well above their predicted performance.

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The above expressions can be now formally derived by exploiting the link between the Elo rating and the stochastic gradient update in the logistic regression.

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Kiraly, F.; Qian, Z. (2017). "Modelling Competitive Sports: Bradley-Terry-Elo Models for Supervised and On-Line Learning of Paired Competition Outcomes".

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In other sports, individuals maintain rankings based on the Elo algorithm. These are usually unofficial, not endorsed by the sport's governing body. The

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motive for these rating floors is to combat sandbagging, i.e., deliberate lowering of ratings to be eligible for lower rating class sections and prizes.

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Although Live ratings are unofficial, interest arose in Live ratings in August/September 2008 when five different players took the "Live" No. 1 ranking.

11570: 2829:-factor of 24 (for players rated above 2400) may be both more accurate as a predictive tool of future performance and be more sensitive to performance. 13185: 11138: 9296: 5517: 428: 11405: 9319:

would cause them to feed points into the rating pool. In July 2000 the average rating of the top 100 was 2644. By July 2012 it had increased to 2703.

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for players with any published rating of at least 2400 and at least 30 games played in previous events. Thereafter it remains permanently at 10.

1000: 933: 866: 12191: 2766:. They found that this did not accurately represent the actual results achieved, particularly by the lower rated players. Instead they switched to a 11374: 11595: 11520: 850:{\displaystyle {\text{performance rating}}={\frac {{\text{total of opponents' ratings }}+400\times ({\text{wins}}-{\text{losses}})}{\text{games}}}} 12613: 3231:

for players with any published rating of at least 2400 and at least 30 games played in previous events. Thereafter it remains permanently at 10.

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Certain Internet chess sites seem to avoid a three-level K-factor staggering based on rating range. For example, the ICC seems to adopt a global

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model, which the USCF found provided a better fit for the actual results achieved. FIDE also uses an approximation to the logistic distribution.

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A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.

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higher-rated player wins, then only a few rating points will be taken from the lower-rated player. However, if the lower-rated player scores an

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The following analysis of the July 2015 FIDE rating list gives a rough impression of what a given FIDE rating means in terms of world ranking:

11640: 5501:{\displaystyle \Pr\{{\mathsf {A}}~{\textrm {draws}}\}=\kappa {\sqrt {\sigma (r_{\mathsf {A,B}};\kappa )\sigma (-r_{\mathsf {A,B}};\kappa )}},} 11807: 9667:

team and season through the 2014 season. In 2014 FiveThirtyEight created Elo-based ratings and win-projections for the American professional

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form the basis of the Elo rating methodology. Elo made references to the papers of Good, David, Trawinski and David, and Buhlman and Huber.

1393: 12354:; Glickman, Mark E.; Hoxby, Caroline M.; Metrick, Andrew (2013-02-01). "A Revealed Preference Ranking of U.S. Colleges and Universities". 11651: 9835:, Elo ratings are used to record guild rating gained and lost through guild-versus-guild battles. In 1998, an online gaming ladder called 210: 205:

The USCF implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than the

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The Elo rating system has also been used in biology for assessing male dominance hierarchies, and in automation and computer vision for

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times their expected score for the game into a pot, the opposing player does likewise, and the winner collects the full pot of value

12071: 10847: 13971: 12786: 11227: 9552: 7704: 2088: 11923: 11167: 11100: 8665: 2152: 14429: 14389: 12303: 11047: 10447: 10436: 10414: 9746: 11621: 11249: 10749: 8730: 4826: 777:{\displaystyle {\begin{aligned}&{\frac {w+400+x+400+y-400+z-400}{4}}\\&{\frac {w+x+y+z+400(2)-400(2)}{4}}\end{aligned}}} 14669: 14409: 9796: 9548: 9485: 10514: 1311:, in the USCF rating system, can be estimated by dividing 800 by the effective number of games a player's rating is based on ( 122:

While Elo-like systems are widely used in two-player settings, variations have also been applied to multiplayer competitions.

14404: 12781: 12551: 11828: 11482: 10496: 10425: 10386: 9790: 9749:, uses a derivative of the Elo system to rank competitive players with various adjustments made between competitive seasons. 9461:. VogClub sets a new player's rating at 1600. The UK Backgammon Federation uses the FIBS formula for its UK national ratings. 362:

From July 2009 to July 2012, six lists a year were issued, at the start of January, March, May, July, September and November.

13961: 11756: 11023: 10473: 3437:{\displaystyle \Pr\{{\mathsf {A}}~{\textrm {wins}}\}=\sigma (r_{\mathsf {A,B}}),\quad \sigma (r)={\frac {1}{1+10^{-r/s}}},} 2218: 340: 11303: 11282: 2721:, and to games in which the result can also have a quantity (small/big margin) in addition to the quality (win/loss). See 14349: 14212: 14202: 13966: 12606: 11872: 7387: 4043:{\displaystyle R_{\mathsf {B}}\leftarrow R_{\mathsf {B}}-\eta {\frac {{\textrm {d}}\ell }{{\textrm {d}}R_{\mathsf {B}}}}} 3952:{\displaystyle R_{\mathsf {A}}\leftarrow R_{\mathsf {A}}-\eta {\frac {{\textrm {d}}\ell }{{\textrm {d}}R_{\mathsf {A}}}}} 3283: 3279: 2279: 1180:

is simply the number of points scored divided by the number of games played. Note that, in case of a perfect or no score

3259:

many opponents rated less than 2500, reducing the ratings gains possible from a single contest for a high-rated player.

2667:

Note that while two wins, two losses, and one draw may seem like a par score, it is worse than expected for player

14487: 13957: 13952: 12702: 12356: 10716: 10346: 9678:

Association rated teams based on Elo ratings, to determine handicaps for their cup competition for the 2011/12 season.

9619:. The algorithm analyzes more than 8 million match results from over 800,000 tennis players worldwide. On May 8, 2018, 9608: 9187: 13280: 11341: 10533: 14424: 14324: 14217: 14187: 9213: 2722: 317:

Games. Each organization has a unique implementation, and none of them follows Elo's original suggestions precisely.

11969: 11435: 10868: 10249: 9630:, an Elo-based system called Fargo Rate is used to rank players in organized amateur and professional competitions. 9403:

are based on engine-only games on standard hardware configurations and are not directly comparable to FIDE ratings.

9195: 9139:

for choosing qualifiers to the chess world championship included an activity bonus, to be combined with the rating.

14394: 14384: 14302: 14192: 12942: 12937: 11678: 9824: 9800:

are using the Elo system for their Leaderboard and matchmaking, with new players starting at Elo 1000. Competitive

9696: 9520: 9514: 9442: 9378: 2825:-factor estimation was made without the benefit of huge databases and statistical evidence. Sonas indicates that a 1586: 12273: 12247: 8108:{\displaystyle R_{\mathsf {B}}\leftarrow R_{\mathsf {B}}+K({\hat {S}}_{\mathsf {B}}-g(r_{\mathsf {B,A}};\kappa ))} 7834: 7645:{\displaystyle R_{\mathsf {A}}\leftarrow R_{\mathsf {A}}+K({\hat {S}}_{\mathsf {A}}-g(r_{\mathsf {A,B}};\kappa ))} 7508:

Then, the stochastic gradient descent applied to minimize the log loss yields the following update for the rating

7443: 2710:

The principles used in these rating systems can be used for rating other competitions—for instance, international

14379: 14369: 12890: 10085: 9724: 9664: 9642: 9382: 5196:

to the probability of the game outcome, we cannot say what the probability of the win, the loss, or the draw is.

10214: 9823:, an online chess server, the Elo system is outdated, with Glicko-2 now being used by many chess organizations. 7967:

loses. To recognize the origin in the model proposed by Davidson, this update is called an Elo-Davidson rating.

7902: 7766: 1332: 268:

as the areas of the two portions under the curve. These probabilities are rounded to two figures in table 2.11.

14374: 14364: 14359: 13027: 12989: 12599: 10541: 10231: 10190: 9634: 9191: 3664:{\displaystyle \Pr\{{\mathsf {B}}~{\textrm {wins}}\}=1-\sigma (r_{\mathsf {A,B}})=\sigma (-r_{\mathsf {A,B}}).} 2692: 1250: 294: 231:

The development of the Percentage Expectancy Table (table 2.11) is described in more detail by Elo as follows:

138: 11075: 9282:

winning, the unexpected outcome, is 0.09 (intersection of black dotted curve and blue line); if this happens,

8662:

and we obtained practically the same equation as in the Elo rating except that the expected score is given by

14664: 14509: 14419: 14354: 13935: 13697: 13248: 12857: 11894: 11130: 10928: 9909:

and his team used Elo rating system when they let people to vote between digital photos taken with different

9809: 9395: 6715: 359:

From July 2000 to July 2009, four lists a year were issued, at the start of January, April, July and October.

12677: 11397: 220:

Subsequent statistical tests have suggested that chess performance is almost certainly not distributed as a

13773: 13253: 10173: 9270:

winning, the expected outcome, is 0.91 (intersection of black solid curve and blue line); if this happens,

206: 12195: 2633: 1226: 161:

tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.

14523: 14472: 14182: 12667: 12023: 11603: 11370: 9850:

has rated players based on the Elo system. New players start at 2100, with top players rating over 3000.

9306:

The number of people with ratings over 2700 has increased. Around 1979 there was only one active player (

5012: 3866: 2458: 2427: 1655: 1620: 12221: 11516: 9142:

Beyond the chess world, concerns over players avoiding competitive play to protect their ratings caused

14596: 14574: 14482: 14467: 14131: 14083: 14078: 14068: 13736: 13414: 13258: 9577: 8818: 8603: 7658: 6603: 6542: 5082: 5047: 4767: 4708: 2704: 440: 302: 17: 11944: 4625: 2587:

This update can be performed after each game or each tournament, or after any suitable rating period.

1225:

The unofficial live ratings of players over 2700 were published and maintained by Hans Arild Runde at

14528: 14462: 14312: 14207: 14056: 11839: 9854: 9407: 9085:{\displaystyle g(r;2)={\frac {10^{r/s}+1}{10^{-r/s}+2+10^{r/s}}}={\frac {1}{1+10^{-r/s}}}=\sigma (r)} 8589:{\displaystyle R_{\mathsf {A}}\leftarrow R_{\mathsf {A}}+K({\hat {S}}_{\mathsf {A}}-E_{\mathsf {A}})} 7973: 7511: 7014: 5170: 5141: 4888: 2398: 2272:

This means that by studying only the numerators, we find out that the expected score for player

2215:

Note that in the latter case, the same denominator applies to both expressions, and it is plain that

406: 399: 392: 11644: 6007: 4352: 4162:{\displaystyle {\frac {\textrm {d}}{{\textrm {d}}r}}\log \sigma (r)={\frac {\log 10}{s}}\sigma (-r)} 3699: 14504: 14477: 14319: 14041: 13434: 13429: 13386: 13285: 9668: 9600:

simulations of the odds of whether teams will make the playoffs. In 2014, Beyond the Box Score, an

9570: 9556: 9544: 9176: 7946: 7878: 7810: 6688: 6638: 6579: 5630: 5117: 4802: 4743: 3551: 3289: 1061:

This is a simplification, but it offers an easy way to get an estimate of PR (performance rating).

380:

2,869 players had an active rating in the range 2300 to 2399, which is usually associated with the

373:

5,323 players had an active rating in the range 2200 to 2299, which is usually associated with the

13120: 11998: 11803: 6865:{\displaystyle {\frac {\textrm {d}}{{\textrm {d}}r}}\log \sigma (r;\kappa )={\frac {2\log 10}{s}}} 14613: 14143: 13808: 12756: 12712: 12707: 12587:

Mark Glickman's research page, with a number of links to technical papers on chess rating systems

12044: 10806: 10773: 10141: 10128: 9969: 9925: 9335:

frustrated over what they considered an unfair rating decline, and some even quit chess over it.

9180: 2627: 13154: 11655: 14197: 14126: 13424: 13270: 13175: 13020: 12952: 9788:

instituted an Elo system for its new "Comp Queue" mode, effective with the Jun 20, 2017 patch.

9737: 9682: 9430: 9098: 8894: 8868: 8792: 5656: 3271: 320:

Instead one may refer to the organization granting the rating. For example: "As of April 2018,

69: 11456: 3203: 3168: 3132: 3075: 3040: 3005: 2941: 2906: 2871: 2789: 2363: 2335: 14329: 14252: 14138: 13838: 13833: 13520: 13243: 13202: 12984: 12796: 12741: 9585: 3161:

for a player new to the rating list until the completion of events with a total of 30 games.

2843: 2767: 2618:-factor of 32 is used. Equivalently, each game the player can be said to have put an ante of 225: 11782: 9623:—having won 46 consecutive sets in clay court matches—had a near-perfect clay UTR of 16.42. 9477:

has the largest rated population of active members, numbering about 2,000 as of early 2011.

5943: 4993:{\displaystyle R_{\mathsf {B}}\leftarrow R_{\mathsf {B}}+K(S_{\mathsf {B}}-E_{\mathsf {B}})} 4612:{\displaystyle R_{\mathsf {A}}\leftarrow R_{\mathsf {A}}+K(S_{\mathsf {A}}-E_{\mathsf {A}})} 2075:{\displaystyle E_{\mathsf {B}}={\frac {Q_{\mathsf {B}}}{Q_{\mathsf {A}}+Q_{\mathsf {B}}}}~,} 14046: 13983: 13942: 13903: 13685: 13675: 13605: 13419: 13350: 13275: 13160: 12959: 12751: 12646: 12622: 12351: 12144: 11723: 10976:"On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments" 9756: 9581: 9495: 9490: 9148: 9143: 4668: 4057: 3527: 2711: 2577:{\displaystyle R_{\mathsf {A}}'=R_{\mathsf {A}}+K\cdot (S_{\mathsf {A}}-E_{\mathsf {A}})~.} 1903:{\displaystyle E_{\mathsf {B}}={\frac {1}{1+10^{(R_{\mathsf {A}}-R_{\mathsf {B}})/400}}}~.} 1792:{\displaystyle E_{\mathsf {A}}={\frac {1}{1+10^{(R_{\mathsf {B}}-R_{\mathsf {A}})/400}}}~.} 1542: 1515: 1488: 1183: 1116: 471: 388: 101: 73: 9759:

system to team up and compare Arena players, but now uses a system similar to Microsoft's

5373:{\displaystyle \Pr\{{\mathsf {B}}~{\textrm {wins}}\}=\sigma (-r_{\mathsf {A,B}};\kappa ),} 1986:{\displaystyle E_{\mathsf {A}}={\frac {Q_{\mathsf {A}}}{Q_{\mathsf {A}}+Q_{\mathsf {B}}}}} 8: 14494: 14274: 14026: 13913: 13883: 13853: 13825: 13798: 13741: 13642: 13610: 13570: 13525: 13238: 13180: 13055: 13003: 12998: 12925: 12883: 12421: 9898:

The Elo rating system has also been noted in dating apps, such as in the matchmaking app

9653: 9649: 9593: 9469:: National Scrabble organizations compute normally distributed Elo ratings except in the 9286:'s rating increases by 29 (intersection of brown dotted curve and blue line) to 1429 and 6662: 5285:{\displaystyle \Pr\{{\mathsf {A}}~{\textrm {wins}}\}=\sigma (r_{\mathsf {A,B}};\kappa ),} 4315:{\displaystyle {\frac {{\textrm {d}}r_{\mathsf {A,B}}}{{\textrm {d}}R_{\mathsf {B}}}}=-1} 3275: 3255: 2847: 2763: 2700: 1106:{\displaystyle {\text{performance rating}}={\text{average of opponents' ratings}}+d_{p},} 334: 298: 221: 168: 167:

Elo's central assumption was that the chess performance of each player in each game is a

113: 65: 14036: 12148: 11189: 9857:, it is common for players of ranked video games to refer to all matchmaking ratings as 4237:{\displaystyle {\frac {{\textrm {d}}r_{\mathsf {A,B}}}{{\textrm {d}}R_{\mathsf {A}}}}=1} 14601: 14499: 14242: 14051: 13692: 13580: 13543: 13192: 13060: 12692: 12687: 12672: 12444: 12393: 12113: 11219: 11163: 11003: 10956: 10902: 10623: 10588: 10580: 10043: 9938: 9784: 9597: 9274:'s rating decreases by 3 (intersection of brown solid curve and blue line) to 1397 and 4688: 1163: 1143: 450: 183: 11043: 10444: 10433: 10422: 10411: 9152:

tournaments in favour of a system of their own devising called "Planeswalker Points".

7001:{\displaystyle g(r;\kappa )={\frac {10^{r/s}+\kappa /2}{10^{-r/s}+\kappa +10^{r/s}}}.} 387:

1,420 players had an active rating between 2400 and 2499, most of whom had either the

141:(USCF) from its founding in 1939. The USCF used a numerical ratings system devised by 108:

the difference is 200 points, then the expected score for the stronger player is 76%.

14584: 14457: 14269: 14227: 14158: 14110: 14093: 14073: 13925: 13863: 13803: 13778: 13625: 13590: 13585: 13565: 13553: 13396: 13364: 13330: 13310: 13147: 13141: 13102: 12969: 12547: 12105: 12101: 12078:, D.A. Reid and M.S. Nixon, International Joint Conference on Biometrics (IJCB), 2011 12068: 11211: 10995: 10960: 10948: 10741: 10592: 10512:

USCF Glossary Quote:"a player who competes in over 300 games with a rating over 2200"

9877: 9751: 9728: 9695:

Hemaratings.com was started in 2017 and uses a Glicko-2 algorithm to rank individual

9627: 9311: 9262:(brown curves). The blue dash-dot line denotes the initial rating difference of 400 ( 8891:

which would mean that the probability of draw is null). On the other hand, if we use

2743:

demonstrated according to the Elo formula, two players having a rating difference of

89: 77: 12117: 11223: 8201:{\displaystyle r_{\mathsf {B,A}}=R_{\mathsf {B}}-R_{\mathsf {A}}=-r_{\mathsf {A,B}}} 14579: 14452: 14294: 14237: 14148: 14098: 13947: 13893: 13888: 13878: 13793: 13714: 13704: 13680: 13647: 13219: 13133: 12907: 12682: 12568: 12465:"Chatbot Arena Leaderboard Week 8: Introducing MT-Bench and Vicuna-33B | LMSYS Org" 12365: 12160: 12152: 12097: 11201: 10987: 10940: 10687: 10654: 10615: 10572: 10511: 10015: 9992: 9906: 9742: 9612: 9540: 9488:(formerly Duelists' Convocation International) used Elo ratings for tournaments of 1688: 374: 321: 142: 10493: 10379: 9433:

adopted an Elo-based rating system initially pioneered by the Czech Go Federation.

3274:, that is, only a win or a loss can be observed, the problem can be addressed via 14544: 14518: 14339: 14334: 14284: 14222: 14031: 14006: 13991: 13788: 13746: 13729: 13630: 13548: 13510: 13488: 13473: 13404: 13381: 13340: 13335: 13214: 13197: 13037: 12651: 12522: 12156: 12075: 11627: 11599: 11286: 11027: 10537: 10518: 10500: 10451: 10440: 10429: 10418: 9951: 9943: 9870: 9846: 9813: 9688:

Rugbyleagueratings.com uses the Elo rating system to rank international and club

9660: 9386: 5617:{\displaystyle \sigma (r;\kappa )={\frac {10^{r/s}}{10^{-r/s}+\kappa +10^{r/s}}}} 1566:

is the number of events in which the player completed three or more rated games.

1234: 171: 13813: 13724: 12488: 12464: 11748: 11020: 10465: 1051:{\displaystyle {\text{performance rating}}={\frac {1000+400\times (0)}{1}}=1000} 984:{\displaystyle {\text{performance rating}}={\frac {2000+400\times (2)}{2}}=1400} 917:{\displaystyle {\text{performance rating}}={\frac {1000+400\times (1)}{1}}=1400} 14643: 14559: 14307: 14153: 14016: 14011: 13848: 13843: 13709: 13667: 13637: 13466: 13409: 13297: 13265: 13231: 13224: 13209: 13170: 13165: 13092: 13087: 12932: 12876: 12832: 12822: 12636: 11311: 11280: 9801: 9765: 9616: 9509: 9470: 9307: 6574: 1684: 424: 416: 12324: 11868: 11253: 10692: 10675: 10659: 10642: 10313: 9731:

used an Elo rating system prior to the second season of competitive play. The

9633:

One of the few Elo-based rankings endorsed by a sport's governing body is the

9500: 3286:, and the model relating both is probabilistic: the probability of the player 14658: 14618: 14608: 14591: 14264: 14247: 14174: 14063: 14021: 14001: 13783: 13765: 13756: 13719: 13652: 13575: 13560: 13515: 13498: 13493: 13483: 13315: 13077: 13015: 12817: 12296:"Tinder matchmaking is more like Warcraft than you might think – Kill Screen" 11215: 10999: 10952: 2729: 398:

542 players had an active rating between 2500 and 2599, most of whom had the

194: 46: 11349: 11206: 10334: 10298: 10086:"The Proposed USCF Rating System, Its Development, Theory, and Applications" 9782:

used the Elo system in the rerelease of the bounty hunter minigame in 2016.

9659:

In 2015, Nate Silver, editor-in-chief of the statistical commentary website

9303:

standard of play at the highest levels, but looks for other causes as well.

3524:

denotes the difference of the players' ratings, and we use a scaling factor

2671:

because their opponents were lower rated on average. Therefore, player

405:

187 players had an active rating between 2600 and 2699, all of whom had the

14638: 14564: 14549: 14279: 14105: 14088: 13996: 13930: 13873: 13868: 13600: 13595: 13535: 13478: 13369: 13325: 13097: 13082: 13072: 13008: 12974: 12947: 12915: 12842: 12801: 12791: 12736: 12641: 12269: 12243: 12109: 10944: 10530: 9899: 9884: 9689: 9620: 9560: 9534: 9390: 9323: 5204: 2718: 2696: 134: 12417:"When students have choices among top colleges, which one do they choose?" 9829:

is one of the few video games that utilizes the very first Elo system. In

13918: 13908: 13657: 13620: 13503: 13114: 13109: 13067: 12920: 12847: 12837: 12369: 11973: 11699: 11427: 10880: 10807:

FIDE Rating Regulations valid from 1 July 2013 till 1 July 2014

10245: 9589: 2850:) formerly staggered the K-factor according to three main rating ranges: 2814:

value (for players rated above 2400) is inaccurate in Elo's work. If the

1237:, which covers the top 100 players as well as the top 50 female players. 427:

had on the May 2014 list. A list of the highest-rated players ever is at

381: 186:

to their performances, he made a simplifying assumption to the contrary.

12591: 12165: 11670: 11616:

Reuben Fischer-Baum and Nate Silver, "The Complete History of the NBA,"

9887:

sites are also using Elo rating system or its derivatives. For example,

9844:, which also used the Elo scoring system for ranking teams. Since 2005, 9278:'s increases by the same amount to 1803. Conversely, the probability of 2762:

The first mathematical concern addressed by the USCF was the use of the

236:

performances becomes σ√2 or 282.84. The z value of a difference then is

14554: 13615: 13451: 13441: 13374: 13358: 13050: 12852: 12827: 12388: 11007: 10975: 10627: 10584: 10222: 10181: 10093: 9910: 9892: 9831: 9723:

Many video games use modified Elo systems in competitive gameplay. The

9437: 2783: 2740: 2717:

Elo ratings have also been applied to games without the possibility of

150: 93: 85: 13121: 12586: 1475:{\displaystyle AF=\operatorname {min} \{100+4N_{W}+2N_{D}+N_{R},150\}} 14569: 13898: 13858: 13461: 13456: 13345: 13320: 13045: 12717: 12539: 11490: 10706:

Elo 1986, p. 141, ch. 8.4& Logistic probability as a rating basis

9778: 9760: 9700: 9601: 9565: 9425: 9136: 2603:. The expected score, calculated according to the formula above, was 356:

From 1981 to 2000, two lists a year were issued, in January and July.

310: 130: 58: 34: 14447: 10991: 10619: 10576: 9389:

are capable of defeating even the strongest human players. However,

9165: 45:

is a method for calculating the relative skill levels of players in

14257: 13305: 12449: 10907: 10643:"Selection of the Best Treatment in a Paired-Comparison Experiment" 9964: 9947: 9888: 9776:, using Elo ratings for 1v1, 2v2, and 3v3 random/team matchmaking. 9675: 9604:

site, introduced an Elo ranking system for international baseball.

9478: 9465: 9243: 5983: 3675: 3514:{\displaystyle r_{\mathsf {A,B}}=(R_{\mathsf {A}}-R_{\mathsf {B}})} 81: 11915: 10828: 9989:

This is written as "Elo", not "ELO", and is usually pronounced as

149:

On behalf of the USCF, Elo devised a new system with a more sound

12979: 12776: 12329: 12217: 9820: 9819:

Few video games use the original Elo rating system. According to

9772: 9732: 9712: 9121:, the Elo-Davidson rating is exactly the same as the Elo rating. 1322:) plus the number of games the player completed in a tournament ( 306: 97: 54: 9891:

is using a modified version based on normal distribution, while

7011:

Thus, the derivative of the log loss with respect to the rating

1067:, however, calculates performance rating by means of the formula 419:

was rated 2853, and 3 players were rated between 2814 and 2816).

13446: 12489:"Chatbot Arena: New models & Elo system update | LMSYS Org" 10466:"FIDE Chess Rating calculators: Chess Rating change calculator" 9805: 9704: 9446: 9129: 314: 12019: 9998: 2687:

This updating procedure is at the core of the ratings used by

12899: 11194:

Proceedings of the AAAI Conference on Artificial Intelligence

11095: 11093: 11044:"Chess News – The Nunn Plan for the World Chess Championship" 10129:

Elo-MMR: A Rating System for Massive Multiplayer Competitions

9972:(RPI), another system that incorporates strength of opponents 9708: 7756:{\displaystyle {\hat {S}}_{\mathsf {A}}=S_{\mathsf {A}}+0.5D} 2142:{\displaystyle \;Q_{\mathsf {A}}=10^{R_{\mathsf {A}}/400}\;,} 50: 12385:"Why Colleges With a Distinct Focus Have a Hidden Advantage" 11066: 11064: 9637:, based on a simplified version of the Elo algorithm, which 8720:{\displaystyle E_{\mathsf {A}}=g(r_{\mathsf {A,B}};\kappa )} 5004: 2208:{\displaystyle \;Q_{\mathsf {B}}=10^{R_{\mathsf {B}}/400}~.} 12964: 12697: 10843: 10781: 10606:

David, H. A. (1959). "Tournaments and Paired Comparisons".

10342: 10027: 10021: 10004: 9638: 9400: 6323: 4516: 3848: 2688: 1230: 1219:

rating would be if FIDE were to issue a new list that day.

1215: 1064: 346: 182:

he thought it was likely that players might have different

158: 30: 12069:"Using Comparative Human Descriptions for Soft Biometrics" 11252:(in Norwegian). Norwegian Chess Federation. Archived from 11090: 10717:"The Elo rating system – correcting the expectancy tables" 9920:, such as those by the digital credential firm Parchment. 9641:

uses as its official ranking system for national teams in

8779:{\displaystyle E_{\mathsf {A}}=\sigma (r_{\mathsf {A,B}})} 4875:{\displaystyle E_{\mathsf {A}}=\sigma (r_{\mathsf {A,B}})} 1263:

2200–2399 plus 300 games above 2200: Original Life Master

860:

Example: If you beat a player with an Elo rating of 1000,

12350: 11895:"List of the Best Tetris Players in the World (NES NTSC)" 11542: 11061: 9895:

is using another version based on logistic distribution.

9663:, and Reuben Fischer-Baum produced Elo ratings for every 2839:

except when playing against provisionally rated players.

2486:

points. The formula for updating that player's rating is

1244: 14633: 12868: 8501:

and thus, we obtain the rating update may be written as

5679:

we recover the model underlying the logistic regression

1160:, which is then used as the key in a lookup table where 11994: 11948: 10774:

FIDE Rating Regulations effective from 1 July 2014

10531:"Approximating Formulas for the US Chess Rating System" 3262: 2977:

Currently, the USCF uses a formula that calculates the

27:

Method for calculating relative skill levels of players

11671:"Hockey Stats Revolution – How do teams pick players?" 9812:) derives its ratings using a combination of players' 9533:

The Elo rating system is used in the chess portion of

3111:

FIDE used the following ranges before July 2014:

2739:

In 2011 after analyzing 1.5 million FIDE rated games,

2639: 412:

40 players had an active rating between 2700 and 2799.

11869:"Age of Empires II: DE Leaderboards - Age of Empires" 10563:

Good, I.J. (1955). "On the Marking of Chessplayers".

9853:

Despite many video games using different systems for

9596:. Based on this adaptation, both also made Elo-based 9101: 8926: 8897: 8871: 8821: 8795: 8733: 8668: 8606: 8510: 8220: 8125: 8008: 7976: 7949: 7905: 7881: 7837: 7813: 7769: 7707: 7661: 7545: 7514: 7446: 7390: 7049: 7017: 6885: 6762: 6718: 6691: 6665: 6641: 6606: 6582: 6545: 6349: 5995: 5946: 5688: 5659: 5633: 5520: 5389: 5301: 5216: 5173: 5144: 5120: 5114:

are merely indicators to the events when the player

5085: 5050: 5015: 4923: 4891: 4829: 4805: 4770: 4746: 4711: 4691: 4671: 4628: 4542: 4331: 4250: 4175: 4083: 4060: 3969: 3878: 3687: 3562: 3530: 3456: 3319: 3292: 3206: 3171: 3135: 3078: 3043: 3008: 2944: 2909: 2874: 2792: 2636: 2495: 2461: 2430: 2401: 2366: 2338: 2282: 2265:{\displaystyle \;E_{\mathsf {A}}+E_{\mathsf {B}}=1~.} 2221: 2155: 2091: 2005: 1922: 1815: 1704: 1658: 1623: 1545: 1518: 1491: 1396: 1335: 1186: 1166: 1146: 1119: 1073: 1003: 936: 869: 796: 645: 474: 453: 11158: 11156: 10024: 10001: 5044:, is introduced. We note, however, that the scores 612:

For each loss, add your opponent's rating minus 400,

345:

For top players, the most important rating is their

272:

The table is actually built with standard deviation

213:(FIDE) in 1970. Elo described his work in detail in 12546:(Second ed.). New York: Arco Publishing, Inc. 11594:Silver, Nate; Fischer-Baum, Reuben (May 21, 2015). 10317:A subsequent version of this paper appeared in the 10215:"The USCF Rating System - A Scientific Achievement" 10018: 9995: 7433:{\displaystyle S_{\mathsf {A}}+S_{\mathsf {B}}+D=1} 3196:for players who have always been rated under 2400. 3068:for players who have always been rated under 2400. 2757: 2317:{\displaystyle \;Q_{\mathsf {A}}/Q_{\mathsf {B}}\;} 1140:is based on a player's tournament percentage score 365:

Since July 2012, the list has been updated monthly.

12442: 12133:"Fabric inspection based on the Elo rating method" 11593: 11131:"Rating inflation – its causes and possible cures" 10335:FIDE Rating Regulations effective from 1 July 2017 9936:The Elo rating system was featured prominently in 9699:fencers worldwide in different categories such as 9297:Comparison of top chess players throughout history 9238: 9113: 9084: 8909: 8883: 8857: 8807: 8778: 8719: 8654: 8588: 8490: 8200: 8107: 7991: 7959: 7935: 7891: 7867: 7823: 7799: 7755: 7693: 7644: 7529: 7497: 7432: 7373: 7032: 7000: 6864: 6745: 6701: 6677: 6651: 6627: 6592: 6566: 6528: 6329: 5971: 5929: 5671: 5645: 5616: 5500: 5372: 5284: 5188: 5159: 5130: 5106: 5071: 5036: 4992: 4906: 4874: 4815: 4791: 4756: 4732: 4697: 4677: 4657: 4611: 4522: 4314: 4236: 4161: 4066: 4042: 3951: 3854: 3663: 3542: 3513: 3436: 3302: 3220: 3185: 3149: 3092: 3057: 3022: 2958: 2923: 2888: 2806: 2656: 2576: 2478: 2447: 2416: 2380: 2352: 2316: 2264: 2207: 2141: 2074: 1985: 1902: 1791: 1675: 1640: 1558: 1531: 1504: 1474: 1370: 1199: 1172: 1152: 1132: 1105: 1050: 983: 927:If you beat two players with Elo ratings of 1000, 916: 849: 776: 615:And divide this sum by the number of played games. 609:For each win, add your opponent's rating plus 400, 487: 459: 429:Comparison of top chess players throughout history 11331:Larry Kaufman, Chess Board Options (2021), p. 179 11153: 11124: 11122: 10927:Szczecinski, Leszek; Djebbi, Aymen (2020-09-01). 10926: 9902:, which uses a variant of the Elo rating system. 9512:used the Elo system for its ranked games such as 14656: 10676:"Pairwise Comparison and Ranking in Tournaments" 8292: 8262: 5689: 5390: 5302: 5217: 3563: 3320: 1302: 787:This can be expressed by the following formula: 10980:Journal of the American Statistical Association 10036: 9718: 1253:(USCF) uses its own classification of players: 11564:"Revision of the FIFA/Coca-Cola World Ranking" 11119: 10640: 10421:), then regained it, then Carlsen took No. 1 ( 10374: 10372: 1802:Similarly, the expected score for player 415:4 players had an active rating of over 2800. ( 353:From 1971 to 1980, one list a year was issued. 297:(PCA), and online chess servers including the 12884: 12607: 12218:"FAQ: What are the rating and the divisions?" 11804:"AirMech developer explains why they use Elo" 10929:"Understanding draws in Elo rating algorithm" 10742:"The Sonas rating formula — better than Elo?" 10673: 10329: 10327: 9580:is an example of the method applied to men's 9418: 423:The highest ever FIDE rating was 2882, which 349:rating. FIDE has issued the following lists: 12544:The Rating of Chessplayers, Past and Present 11781:. Wow-europe.com. 2011-12-14. Archived from 11724:"Matchmaking | LoL – League of Legends" 11187: 11033:, Don Heisman, Chesscafe.com, August 4, 2002 10799: 10768: 10766: 10079: 10077: 9916:The Elo rating system has also been used in 9130:Game activity versus protecting one's rating 8313: 8295: 8283: 8265: 7868:{\displaystyle {\hat {S}}_{\mathsf {A}}=0.5} 7498:{\displaystyle g(-r;\kappa )=1-g(r;\kappa )} 5712: 5692: 5413: 5393: 5325: 5305: 5240: 5220: 4322:, the adaptation is then written as follows 3586: 3566: 3343: 3323: 1469: 1412: 287: 215:The Rating of Chessplayers, Past and Present 200: 11275: 11273: 11271: 11188:Regan, Kenneth; Haworth, Guy (2011-08-04). 10369: 9475:North American Scrabble Players Association 9194:. Unsourced material may be challenged and 5982:Using the ordinal model defined above, the 64:The Elo system was invented as an improved 12891: 12877: 12614: 12600: 12415:Selingo, Jeffrey J. (September 23, 2015). 12087: 11779:"World of Warcraft Europe -> The Arena" 11398:"What are the World Football Elo Ratings?" 11128: 10933:Journal of Quantitative Analysis in Sports 10900: 10324: 9931: 9615:and is frequently used in segments on the 7936:{\displaystyle {\hat {S}}_{\mathsf {A}}=0} 7800:{\displaystyle {\hat {S}}_{\mathsf {A}}=1} 5203:Since the loss, the draw, and the win are 3217: 3207: 3182: 3172: 3146: 3136: 3089: 3079: 3054: 3044: 3019: 3009: 2955: 2945: 2920: 2910: 2885: 2875: 2803: 2793: 2747:actually have a true difference of around 2653: 2637: 2377: 2367: 2349: 2339: 2313: 2283: 2222: 2156: 2135: 2092: 1371:{\displaystyle K={\frac {800}{N_{e}+m}}\,} 61:, a Hungarian-American physics professor. 12726: 12621: 12448: 12164: 11749:"Welcome to Season 8 of competitive play" 11483:"Elo rankings for international baseball" 11205: 10906: 10763: 10691: 10658: 10463: 10314:"A Comprehensive Guide to Chess Ratings". 10074: 9918:U.S. revealed preference college rankings 9214:Learn how and when to remove this message 7952: 7884: 7816: 5005:Formal derivation for win/draw/loss games 4823:wins, and the expected score is given by 4665:is the new adaptation step which absorbs 2778:The second major concern is the correct " 2773: 2734: 2605:(0.51 + 0.69 + 0.79 + 0.54 + 0.35) = 2.88 2475: 2462: 2444: 2431: 2324:times the expected score for player 1672: 1659: 1637: 1624: 1367: 72:, but is also used as a rating system in 12787:Harris Interactive College Football Poll 12567: 11945:"Wayback Machine record of Clanbase.com" 11268: 10973: 10674:Buhlmann, Hans; Huber, Peter J. (1963). 10296:Glickman, Mark E., and Jones, Albyn C., 10238: 9584:. In 2006, Elo ratings were adapted for 9555:after which the BCS was replaced by the 9543:used the Elo method as a portion of its 9473:, where a different system is used. The 9290:'s decreases by the same amount to 1771. 9242: 1691:) for the expected score of player 1539:is the number of rated games drawn, and 1233:, has been maintained since May 2011 by 29: 12414: 12224:from the original on September 25, 2011 10521:from The United States Chess Federation 10272: 9869:The Elo rating system has been used in 9413: 9373: 6746:{\displaystyle \log \sigma (r;\kappa )} 4885:Analogously, the update for the rating 3270:If we assume that the game results are 1592: 37:, the inventor of the Elo rating system 14: 14657: 11810:from the original on February 17, 2015 11726:. Na.leagueoflegends.com. 2010-07-06. 11638: 11426: 10879:. ICC Help. 2002-10-18. Archived from 10269:Elo 1986, Preface to the First Edition 10139: 9648:From the first ranking list after the 9338: 8767: 8764: 8761: 8740: 8702: 8699: 8696: 8675: 8643: 8613: 8577: 8562: 8532: 8517: 8469: 8466: 8463: 8424: 8421: 8418: 8388: 8385: 8382: 8344: 8341: 8338: 8300: 8270: 8246: 8192: 8189: 8186: 8168: 8153: 8138: 8135: 8132: 8087: 8084: 8081: 8060: 8030: 8015: 7983: 7921: 7853: 7785: 7738: 7723: 7624: 7621: 7618: 7597: 7567: 7552: 7521: 7412: 7397: 7344: 7341: 7338: 7308: 7243: 7240: 7237: 7207: 7177: 7174: 7171: 7132: 7075: 7024: 6694: 6644: 6613: 6585: 6552: 6496: 6493: 6490: 6444: 6417: 6414: 6411: 6368: 6302: 6273: 6270: 6267: 6218: 6215: 6212: 6147: 6118: 6115: 6112: 6066: 6037: 6034: 6031: 5900: 5897: 5894: 5846: 5843: 5840: 5810: 5807: 5804: 5773: 5770: 5767: 5736: 5733: 5730: 5697: 5478: 5475: 5472: 5442: 5439: 5436: 5398: 5352: 5349: 5346: 5310: 5264: 5261: 5258: 5225: 5180: 5151: 5123: 5092: 5057: 5022: 4981: 4966: 4945: 4930: 4898: 4863: 4860: 4857: 4836: 4808: 4777: 4749: 4718: 4600: 4585: 4564: 4549: 4495: 4472: 4469: 4466: 4442: 4417: 4394: 4391: 4388: 4361: 4338: 4294: 4273: 4270: 4267: 4219: 4198: 4195: 4192: 4031: 3991: 3976: 3940: 3900: 3885: 3869:the log loss is minimized as follows: 3827: 3804: 3801: 3798: 3752: 3729: 3726: 3723: 3649: 3646: 3643: 3616: 3613: 3610: 3571: 3502: 3487: 3469: 3466: 3463: 3367: 3364: 3361: 3328: 3295: 2782:-factor" used. The chess statistician 2675:is slightly penalized. If player 2626:; in the event of a draw, the players 2610:Therefore, the player's new rating is 2559: 2544: 2520: 2502: 2469: 2438: 2408: 2307: 2290: 2244: 2229: 2183: 2163: 2119: 2099: 2057: 2042: 2029: 2012: 1974: 1959: 1946: 1929: 1872: 1857: 1822: 1761: 1746: 1711: 1666: 1631: 1245:United States Chess Federation ratings 12872: 12782:FWAA-NFF Grantland Rice Super 16 Poll 12595: 12382: 12276:from the original on October 13, 2011 12250:from the original on October 13, 2011 12192:"Algorithm Competition Rating System" 12130: 11916:"Frequently Asked Questions: ratings" 11649: 11523:from the original on 27 February 2021 11395: 11377:from the original on January 15, 2015 11247: 11141:from the original on 23 November 2013 11107:from the original on October 18, 2016 10922: 10920: 10918: 10680:The Annals of Mathematical Statistics 10641:Trawinski, B.J.; David, H.A. (1963). 10605: 10042: 6712:As before, we need the derivative of 1268:2000–2199: Expert or Candidate Master 434: 11972:. Wiki.guildwars.com. Archived from 11875:from the original on 27 January 2022 11480: 10562: 10392:from the original on 7 February 2020 9192:adding citations to reliable sources 9159: 9155: 3263:Formal derivation for win/loss games 2657:{\displaystyle \;{\tfrac {1}{2}}K\;} 1229:until August 2011. Another website, 341:List of FIDE chess world number ones 12538: 12194:. December 23, 2009. Archived from 12045:"Golden Tee Fan Player Rating Page" 11497:from the original on 2 January 2016 11074:. September 6, 2011. Archived from 10212: 10171: 10083: 9310:) with a rating this high. In 1992 9124: 5037:{\displaystyle S_{\mathsf {A}}=0.5} 2479:{\displaystyle \,S_{\mathsf {A}}\,} 2448:{\displaystyle \,E_{\mathsf {A}}\,} 1676:{\displaystyle \,R_{\mathsf {B}}\,} 1641:{\displaystyle \,R_{\mathsf {A}}\,} 24: 12703:Pomeroy College Basketball Ratings 12561: 12357:The Quarterly Journal of Economics 12344: 12325:"The Best Smartphone Camera 2022!" 12288: 11759:from the original on 12 March 2018 11700:"About the Ratings - Hema Ratings" 11650:Paine, Neil (September 10, 2015). 11639:Silver, Nate (September 4, 2014). 11596:"How We Calculate NBA Elo Ratings" 11279:A conversation with Mark Glickman 10915: 10248:. United States Chess Federation. 9816:and a highly modified Elo system. 9609:Intercollegiate Tennis Association 9528: 6340:which may be compactly written as 4533:which may be compactly written as 3125:Used for players with ratings ... 2998:Used for players with ratings ... 2864:Used for players with ratings ... 1512:is the number of rated games won, 209:. Elo's system was adopted by the 25: 14681: 12580: 11654:. FiveThirtyEight. Archived from 11643:. FiveThirtyEight. Archived from 11569:. FIFA. June 2018. Archived from 11408:from the original on 15 June 2019 11072:"Introducing Planeswalker Points" 10739: 10647:Annals of Mathematical Statistics 9942:during the algorithm scene where 8858:{\displaystyle g(r;0)=\sigma (r)} 8655:{\displaystyle E_{\mathsf {A}}=E} 7999:is derived in the same manner as 7694:{\displaystyle K=2\eta \log 10/s} 6628:{\displaystyle S_{\mathsf {B}}=1} 6567:{\displaystyle S_{\mathsf {A}}=1} 5107:{\displaystyle S_{\mathsf {A}}=0} 5072:{\displaystyle S_{\mathsf {A}}=1} 4792:{\displaystyle S_{\mathsf {A}}=0} 4733:{\displaystyle S_{\mathsf {A}}=1} 810:total of opponents' ratings 137:and an active participant in the 14632: 14303:List of strong chess tournaments 12688:English Chess Federation grading 12383:Irwin, Neil (4 September 2014). 12102:10.1111/j.1365-294X.2010.04665.x 11432:"Lies, Damned Lies: We are Elo?" 10410:Anand lost No. 1 to Morozevich ( 10299:"Rating the chess rating system" 10014: 9991: 9697:Historical European martial arts 9521:Star Wars Customizable Card Game 9515:Star Trek Customizable Card Game 9443:First Internet Backgammon Server 9406:For some ratings estimates, see 9255:with 1800 in a tournament using 9164: 7384:where we used the relationships 4658:{\displaystyle K=\eta \log 10/s} 2984:FIDE uses the following ranges: 2758:Most accurate distribution model 2590:An example may help to clarify: 1913:This could also be expressed by 1381: 57:. It is named after its creator 13281:Gökyay Association Chess Museum 12505: 12481: 12457: 12436: 12408: 12376: 12317: 12262: 12236: 12210: 12184: 12124: 12081: 12062: 12051:from the original on 2014-01-01 12037: 12026:from the original on 2017-10-30 12012: 12001:from the original on 2013-12-24 11987: 11962: 11937: 11926:from the original on 2019-04-02 11908: 11887: 11861: 11850:from the original on 2018-08-27 11832: 11822: 11796: 11771: 11741: 11730:from the original on 2012-02-26 11716: 11692: 11681:from the original on 2016-10-02 11663: 11632: 11610: 11587: 11556: 11535: 11509: 11481:Cole, Bryan (August 15, 2014). 11474: 11463:from the original on 2012-03-07 11449: 11420: 11389: 11363: 11334: 11325: 11296: 11241: 11230:from the original on 2021-04-20 11181: 11170:from the original on 2013-03-28 11050:from the original on 2011-11-19 11036: 11014: 10967: 10894: 10861: 10836:"Changes to Rating Regulations" 10817:from the original on 2014-07-15 10788:from the original on 2014-07-01 10752:from the original on 2005-03-05 10732: 10723: 10709: 10700: 10667: 10634: 10599: 10556: 10547: 10524: 10505: 10487: 10476:from the original on 2017-09-28 10457: 10404: 10360: 10349:from the original on 2019-11-27 10305: 10290: 10281: 10263: 10252:from the original on 2008-09-26 10172:Elo, Arpad E. (March 5, 1960). 10154:from the original on 2020-06-30 9665:National Basketball Association 9383:Deep Blue versus Garry Kasparov 9239:Ratings inflation and deflation 8789:Of course, as noted above, for 7992:{\displaystyle R_{\mathsf {B}}} 7530:{\displaystyle R_{\mathsf {A}}} 7033:{\displaystyle R_{\mathsf {A}}} 5189:{\displaystyle R_{\mathsf {B}}} 5160:{\displaystyle R_{\mathsf {A}}} 4907:{\displaystyle R_{\mathsf {B}}} 3379: 3310:winning the game is modeled as 2842:The USCF (which makes use of a 2417:{\displaystyle R_{\mathsf {A}}} 1683:, the exact formula (using the 1210: 328: 11457:"Postseason Odds, ELO version" 11342:"Backgammon Ratings Explained" 11046:. ChessBase.com. 8 June 2005. 10542:United States Chess Federation 10206: 10197: 10165: 10142:"Remembering Richard, Part II" 10133: 10122: 10105: 10035:in English. The original name 9983: 9864: 9652:, FIFA has used Elo for their 9358:after 30 played games, and to 9251:starts with a 1400 rating and 9146:to abandon the Elo system for 9079: 9073: 8942: 8930: 8852: 8846: 8837: 8825: 8773: 8752: 8714: 8687: 8649: 8635: 8625: 8583: 8554: 8544: 8523: 8481: 8454: 8436: 8406: 8400: 8373: 8356: 8329: 8252: 8238: 8228: 8102: 8099: 8072: 8052: 8042: 8021: 7913: 7845: 7777: 7715: 7639: 7636: 7609: 7589: 7579: 7558: 7492: 7480: 7465: 7450: 7356: 7329: 7255: 7228: 7222: 7198: 7192: 7189: 7162: 7150: 7147: 7123: 6901: 6889: 6859: 6856: 6844: 6832: 6805: 6793: 6740: 6728: 6508: 6478: 6466: 6435: 6429: 6402: 6390: 6359: 6285: 6255: 6230: 6203: 6130: 6100: 6049: 6022: 5748: 5721: 5536: 5524: 5490: 5460: 5454: 5427: 5364: 5334: 5276: 5249: 4987: 4957: 4936: 4869: 4848: 4606: 4576: 4555: 4478: 4457: 4400: 4376: 4344: 4156: 4147: 4120: 4114: 3982: 3891: 3810: 3786: 3735: 3714: 3655: 3631: 3622: 3601: 3508: 3478: 3389: 3383: 3373: 3352: 3278:, where the games results are 2565: 2535: 1878: 1848: 1767: 1737: 1251:United States Chess Federation 1033: 1027: 966: 960: 899: 893: 838: 822: 761: 755: 746: 740: 295:Professional Chess Association 139:United States Chess Federation 13: 1: 14670:Sports records and statistics 14401:Computer chess championships 12802:USA Today/Amway Coaches' Poll 12713:Rating Percentage Index (RPI) 11641:"Introducing NFL Elo Ratings" 11396:Lyons, Keith (10 June 2014). 11371:"Play! Pokémon Glossary: Elo" 10302:(1999), Chance, 12, 2, 21-28. 10084:Elo, Arpad E. (August 1967). 10062: 9826:PlayerUnknown’s Battlegrounds 9810:Nintendo Entertainment System 9396:first-move advantage in chess 9385:) and 2006 demonstrated that 7960:{\displaystyle {\textsf {A}}} 7892:{\displaystyle {\textsf {A}}} 7824:{\displaystyle {\textsf {A}}} 6702:{\displaystyle {\mathsf {A}}} 6652:{\displaystyle {\mathsf {B}}} 6593:{\displaystyle {\mathsf {A}}} 5646:{\displaystyle \kappa \geq 0} 5131:{\displaystyle {\mathsf {A}}} 4816:{\displaystyle {\mathsf {B}}} 4757:{\displaystyle {\mathsf {A}}} 3303:{\displaystyle {\mathsf {A}}} 1303:The K-factor used by the USCF 1257:2400 and above: Senior Master 1084:average of opponents' ratings 74:association football (soccer) 12302:. 2016-01-14. Archived from 12157:10.1016/j.patcog.2015.09.022 10846:. 2011-07-21. Archived from 10445:Chessbase, September 13 2008 10434:Chessbase, September 11 2008 9719:Video games and online games 9379:Human–computer chess matches 7: 14183:Bishop and knight checkmate 12668:Advanced Football Analytics 12661:Methods and computer models 12131:Tsang; et al. (2016). 11995:"Clanbase farewell message" 11517:"Is Rafa the GOAT of Clay?" 11129:Jeff Sonas (27 July 2009). 10974:Davidson, Roger R. (1970). 10544:, Mark Glickman, April 2017 10423:Chessbase, September 5 2008 10213:Elo, Arpad E. (June 1961). 10147:. Illinois Chess Bulletin. 9958: 9635:FIFA Women's World Rankings 3867:stochastic gradient descent 3282:, the players' ratings are 2786:believes that the original 2601:(0 + 0.5 + 1 + 1 + 0) = 2.5 2455:points but actually scored 1260:2200–2399: National Master 619:Example: 2 wins (opponents 217:, first published in 1978. 10: 14686: 14346:Other world championships 12532: 12270:"Regarding rating: Part 2" 11755:. Blizzard Entertainment. 11652:"NFL Elo Ratings Are Back" 11459:. Baseballprospectus.com. 10385:(Report). April 24, 2017. 10380:The US Chess Rating system 10311:Glickman, Mark E. (1995), 10067: 9741:, the basis of the unique 9578:World Football Elo Ratings 9419:Other board and card games 2727: 2705:Free Internet Chess Server 1113:where "rating difference" 441:Performance rating (chess) 438: 338: 332: 303:Free Internet Chess Server 125: 14627: 14537: 14440: 14293: 14193:Opposite-coloured bishops 14173: 14119: 13982: 13824: 13764: 13755: 13666: 13534: 13395: 13296: 13132: 13036: 12906: 12898: 12810: 12769: 12660: 12629: 12020:"Scrimbase Gaming Ladder" 11190:"Intrinsic Chess Ratings" 11021:A Parent's Guide to Chess 10412:Chessbase, August 24 2008 10140:Redman, Tim (July 2002). 9913:models launched in 2022. 9755:also previously used the 9541:American college football 9481:also uses the Elo system. 9114:{\displaystyle \kappa =2} 9095:which means that, using 8910:{\displaystyle \kappa =2} 8884:{\displaystyle \kappa =0} 8808:{\displaystyle \kappa =0} 5672:{\displaystyle \kappa =0} 1581: 407:International Grandmaster 400:International Grandmaster 393:International Grandmaster 288:Different ratings systems 201:Implementing Elo's scheme 68:over the previously used 14320:World Chess Championship 13286:World Chess Hall of Fame 12678:Bowl Championship Series 10565:The Mathematical Gazette 10443:), and finally Topalov ( 10174:"The USCF Rating System" 9976: 9681:An Elo-based ranking of 9669:National Football League 9571:College Football Playoff 9557:College Football Playoff 9545:Bowl Championship Series 4074:is the adaptation step. 3552:law of total probability 3221:{\displaystyle \;K=10\;} 3186:{\displaystyle \;K=15\;} 3150:{\displaystyle \;K=30\;} 3093:{\displaystyle \;K=10\;} 3058:{\displaystyle \;K=20\;} 3023:{\displaystyle \;K=40\;} 2959:{\displaystyle \;K=16\;} 2924:{\displaystyle \;K=24\;} 2889:{\displaystyle \;K=32\;} 2807:{\displaystyle \;K=10\;} 2424:) was expected to score 2381:{\displaystyle \;K=32\;} 2353:{\displaystyle \;K=16\;} 276:as an approximation for 14614:Simultaneous exhibition 14524:Chess newspaper columns 14213:Rook and bishop vs rook 14203:Queen and pawn vs queen 12708:Pythagorean expectation 12573:Official Chess Handbook 11675:Hockey Stats Revolution 11207:10.1609/aaai.v25i1.7951 11101:"Getting to the Points" 10738:A key Sonas article is 10693:10.1214/aoms/1177704161 10660:10.1214/aoms/1177704243 10400:– via glicko.net. 9970:Rating percentage index 9932:References in the media 1602:of approximately 0.75. 1227:the Live Rating website 627:), 2 losses (opponents 14069:Richter–Veresov Attack 14057:Queen's Indian Defence 11658:on September 11, 2015. 11647:on September 12, 2015. 10945:10.1515/jqas-2019-0102 10840:FIDE Online (fide.com) 10813:(Report). 2013-07-01. 10811:FIDE Online (fide.com) 10778:FIDE Online (fide.com) 10339:FIDE Online (fide.com) 10319:American Chess Journal 10037: 9683:National Hockey League 9431:European Go Federation 9408:Chess engine § Ratings 9291: 9266:). The probability of 9115: 9086: 8911: 8885: 8859: 8809: 8780: 8721: 8656: 8590: 8492: 8202: 8109: 7993: 7961: 7937: 7893: 7869: 7825: 7801: 7757: 7695: 7646: 7531: 7499: 7434: 7375: 7034: 7002: 6866: 6747: 6703: 6679: 6653: 6629: 6594: 6568: 6530: 6331: 5973: 5972:{\displaystyle s'=s/2} 5931: 5673: 5647: 5618: 5502: 5374: 5286: 5190: 5161: 5132: 5108: 5073: 5038: 4994: 4908: 4876: 4817: 4793: 4758: 4734: 4699: 4679: 4659: 4613: 4524: 4316: 4238: 4163: 4068: 4044: 3953: 3856: 3678:is then calculated as 3665: 3544: 3515: 3438: 3304: 3222: 3187: 3151: 3094: 3059: 3024: 2960: 2934:between 2100 and 2400 2925: 2890: 2808: 2774:Most accurate K-factor 2735:Suggested modification 2685: 2658: 2578: 2480: 2449: 2418: 2382: 2354: 2318: 2266: 2209: 2143: 2076: 1987: 1904: 1793: 1677: 1642: 1560: 1533: 1506: 1476: 1372: 1201: 1174: 1154: 1134: 1107: 1052: 985: 918: 851: 778: 489: 461: 270: 211:World Chess Federation 207:Harkness rating system 100:, and, more recently, 38: 14330:Candidates Tournament 14218:Rook and pawn vs rook 14188:King and pawn vs king 14139:List of chess gambits 14042:King's Indian Defence 13720:Isolated Queen's Pawn 13244:List of chess players 13186:Top player comparison 12985:Internet chess server 12623:Sports rating systems 12352:Avery, Christopher N. 12244:"Rating Distribution" 11103:. September 9, 2011. 11078:on September 30, 2011 9797:Age of Empires III DE 9586:Major League Baseball 9246: 9116: 9087: 8912: 8886: 8860: 8810: 8781: 8722: 8657: 8591: 8493: 8203: 8110: 7994: 7962: 7938: 7894: 7870: 7826: 7802: 7758: 7696: 7647: 7532: 7500: 7435: 7376: 7035: 7003: 6867: 6748: 6704: 6680: 6654: 6630: 6595: 6569: 6531: 6332: 5986:is now calculated as 5974: 5932: 5674: 5648: 5619: 5503: 5375: 5287: 5191: 5162: 5133: 5109: 5074: 5039: 4995: 4909: 4877: 4818: 4794: 4759: 4735: 4700: 4680: 4678:{\displaystyle \eta } 4660: 4614: 4525: 4317: 4239: 4164: 4069: 4067:{\displaystyle \eta } 4045: 3954: 3857: 3666: 3545: 3543:{\displaystyle s=400} 3516: 3439: 3305: 3284:independent variables 3239:The gradation of the 3223: 3188: 3152: 3095: 3060: 3025: 2961: 2926: 2891: 2844:logistic distribution 2809: 2768:logistic distribution 2659: 2592: 2579: 2481: 2450: 2419: 2383: 2355: 2319: 2267: 2210: 2144: 2077: 1988: 1905: 1794: 1678: 1643: 1561: 1559:{\displaystyle N_{R}} 1534: 1532:{\displaystyle N_{D}} 1507: 1505:{\displaystyle N_{W}} 1477: 1373: 1202: 1200:{\displaystyle d_{p}} 1175: 1155: 1135: 1133:{\displaystyle d_{p}} 1108: 1053: 986: 919: 852: 779: 490: 488:{\displaystyle d_{p}} 462: 258:= 160 / 282.84 = .566 233: 102:large language models 33: 14665:Chess rating systems 14047:Nimzo-Indian Defence 13943:Scandinavian Defense 13904:Semi-Italian Opening 13809:King's Indian Attack 13698:first-move advantage 13351:Threefold repetition 13276:Bobby Fischer Center 13161:Charlemagne chessmen 13155:Göttingen manuscript 13119: 12960:Correspondence chess 12647:Strength of schedule 12198:on September 2, 2011 12047:. 26 December 2007. 11871:. 14 November 2019. 11487:Beyond the Box Score 10119:equal to 100 or 200. 9814:personal best scores 9791:Age of Empires II DE 9547:rating systems from 9506:Magic: The Gathering 9496:Wizards of the Coast 9491:Magic: The Gathering 9414:Use outside of chess 9374:Ratings of computers 9188:improve this section 9149:Magic: the Gathering 9144:Wizards of the Coast 9099: 8924: 8895: 8869: 8819: 8793: 8731: 8666: 8604: 8508: 8218: 8123: 8006: 7974: 7947: 7903: 7879: 7835: 7811: 7767: 7705: 7659: 7543: 7512: 7444: 7388: 7047: 7015: 6883: 6760: 6716: 6689: 6663: 6639: 6604: 6580: 6543: 6347: 5993: 5944: 5686: 5657: 5631: 5518: 5387: 5299: 5214: 5171: 5142: 5118: 5083: 5048: 5013: 4921: 4889: 4827: 4803: 4768: 4744: 4709: 4689: 4669: 4626: 4540: 4329: 4248: 4173: 4081: 4058: 3967: 3876: 3685: 3560: 3528: 3454: 3317: 3290: 3204: 3169: 3133: 3076: 3041: 3006: 2942: 2907: 2872: 2790: 2634: 2594:Suppose player 2493: 2459: 2428: 2399: 2391:Suppose player 2388:for weaker players. 2364: 2336: 2280: 2219: 2153: 2089: 2003: 1920: 1813: 1702: 1656: 1621: 1593:Mathematical details 1587:Pairwise comparisons 1543: 1516: 1489: 1394: 1333: 1184: 1164: 1144: 1117: 1071: 1001: 934: 867: 794: 643: 472: 451: 389:International Master 169:normally distributed 14275:Two knights endgame 14027:Bogo-Indian Defence 13914:Two Knights Defense 13854:Nimzowitsch Defence 13544:Artificial castling 13181:Soviet chess school 13056:Dubrovnik chess set 12422:The Washington Post 12149:2016PatRe..51..378T 12137:Pattern Recognition 11314:on December 5, 2013 11308:Norges Sjakkforbund 11164:"Viswanathan Anand" 10553:Elo 1986, ch. 1.12. 10494:US Chess Federation 10287:Elo 1986, ch. 8.73. 9926:Bradley–Terry model 9747:sports organization 9654:FIFA World Rankings 9650:2018 FIFA World Cup 9594:Baseball Prospectus 9339:Combating deflation 6678:{\displaystyle D=1} 3280:dependent variables 3276:logistic regression 2848:normal distribution 2764:normal distribution 2701:Internet Chess Club 2510: 2395:(again with rating 335:FIDE world rankings 299:Internet Chess Club 222:normal distribution 184:standard deviations 66:chess-rating system 14505:endgame literature 14052:Old Indian Defense 13962:Accelerated Dragon 13834:Alekhine's Defence 13566:Checkmate patterns 13435:symbols in Unicode 13430:annotation symbols 13193:Geography of chess 13061:Staunton chess set 12797:NAIA Coaches' Poll 12693:Litkenhous Ratings 12673:ARGH Power Ratings 12521:2012-09-04 at the 12514:The Social Network 12394:The New York Times 12370:10.1093/qje/qjs043 12074:2013-03-08 at the 11626:2015-05-23 at the 11293:October 2006 issue 11285:2011-08-07 at the 11248:Bergersen, Per A. 11166:. Chessgames.com. 11026:2008-05-28 at the 10729:Elo 1986, ch. 8.73 10536:2019-11-04 at the 10517:2013-03-08 at the 10499:2012-06-18 at the 10450:2008-09-15 at the 10439:2008-09-13 at the 10432:), then Ivanchuk ( 10428:2012-11-09 at the 10417:2008-09-10 at the 10111:Using the formula 9939:The Social Network 9785:Mechwarrior Online 9292: 9111: 9082: 8907: 8881: 8855: 8805: 8776: 8717: 8652: 8586: 8488: 8486: 8198: 8105: 7989: 7957: 7933: 7889: 7865: 7821: 7797: 7753: 7691: 7642: 7527: 7495: 7430: 7371: 7369: 7030: 6998: 6862: 6753:which is given by 6743: 6699: 6675: 6649: 6625: 6590: 6564: 6526: 6327: 6322: 5969: 5927: 5669: 5643: 5614: 5498: 5370: 5282: 5186: 5157: 5128: 5104: 5069: 5034: 4990: 4904: 4872: 4813: 4789: 4754: 4730: 4695: 4675: 4655: 4609: 4520: 4515: 4312: 4234: 4159: 4064: 4040: 3949: 3852: 3847: 3661: 3540: 3511: 3434: 3300: 3218: 3183: 3147: 3090: 3055: 3020: 2956: 2921: 2886: 2804: 2723:Go rating with Elo 2654: 2648: 2614:, assuming that a 2574: 2496: 2476: 2445: 2414: 2378: 2350: 2314: 2262: 2205: 2139: 2072: 1983: 1900: 1789: 1673: 1638: 1556: 1529: 1502: 1472: 1368: 1283:1000–1199: Class E 1280:1200–1399: Class D 1277:1400–1599: Class C 1274:1600–1799: Class B 1271:1800–1999: Class A 1197: 1170: 1150: 1130: 1103: 1076:performance rating 1048: 1006:performance rating 981: 939:performance rating 914: 872:performance rating 847: 799:performance rating 774: 772: 485: 457: 435:Performance rating 260:. The table gives 39: 14652: 14651: 14529:Chess periodicals 14458:Chess in the arts 14390:Chess composition 14228:Philidor position 14169: 14168: 14111:Trompowsky Attack 14094:Semi-Slav Defence 13984:Queen's Pawn Game 13864:Four Knights Game 13839:Caro–Kann Defence 13804:Zukertort Opening 13591:Discovered attack 13311:Cheating in chess 13148:Versus de scachis 12866: 12865: 12770:Polls and opinion 12765: 12764: 12569:Harkness, Kenneth 12553:978-0-668-04721-0 12090:Molecular Ecology 11753:PlayOverwatch.com 11346:results.ukbgf.com 10842:(Press release). 9878:fabric inspection 9752:World of Warcraft 9729:League of Legends 9351:, which drops to 9312:Viswanathan Anand 9224: 9223: 9216: 9156:Selective pairing 9065: 9026: 8638: 8557: 8439: 8311: 8307: 8281: 8277: 8241: 8055: 7954: 7916: 7886: 7848: 7818: 7780: 7718: 7592: 7295: 7116: 7082: 7066: 7059: 6993: 6830: 6782: 6775: 6768: 6461: 6385: 6314: 6309: 6299: 6294: 6244: 6192: 6159: 6154: 6144: 6139: 6078: 6073: 6063: 6058: 5922: 5863: 5709: 5704: 5612: 5493: 5410: 5405: 5322: 5317: 5237: 5232: 5205:ordinal variables 4698:{\displaystyle s} 4507: 4502: 4492: 4487: 4429: 4424: 4414: 4409: 4301: 4285: 4258: 4226: 4210: 4183: 4142: 4103: 4096: 4089: 4038: 4022: 4010: 3947: 3931: 3919: 3839: 3834: 3824: 3819: 3764: 3759: 3749: 3744: 3583: 3578: 3429: 3340: 3335: 3235: 3234: 3107: 3106: 2973: 2972: 2647: 2570: 2258: 2201: 2068: 2064: 1981: 1896: 1892: 1785: 1781: 1572:1464 − 200 = 1264 1365: 1173:{\displaystyle p} 1153:{\displaystyle p} 1085: 1077: 1040: 1007: 973: 940: 906: 873: 845: 844: 836: 828: 811: 800: 768: 703: 602: 601: 460:{\displaystyle p} 246:For example, let 78:American football 43:Elo rating system 16:(Redirected from 14677: 14639:Chess portal 14637: 14636: 14580:Leela Chess Zero 14511:Oxford Companion 14463:early literature 14453:Chess aesthetics 14198:Pawnless endgame 14149:Bongcloud Attack 14127:List of openings 14099:Chigorin Defense 14037:Grünfeld Defence 13948:Sicilian Defence 13894:Ponziani Opening 13889:Philidor Defence 13884:Petrov's Defence 13826:King's Pawn Game 13799:Larsen's Opening 13762: 13761: 13123: 12893: 12886: 12879: 12870: 12869: 12724: 12723: 12683:Dickinson System 12616: 12609: 12602: 12593: 12592: 12576: 12557: 12526: 12509: 12503: 12502: 12500: 12499: 12485: 12479: 12478: 12476: 12475: 12461: 12455: 12454: 12452: 12440: 12434: 12433: 12431: 12429: 12412: 12406: 12405: 12403: 12401: 12380: 12374: 12373: 12348: 12342: 12341: 12339: 12338: 12321: 12315: 12314: 12312: 12311: 12292: 12286: 12285: 12283: 12281: 12266: 12260: 12259: 12257: 12255: 12240: 12234: 12233: 12231: 12229: 12214: 12208: 12207: 12205: 12203: 12188: 12182: 12181: 12179: 12178: 12169:. Archived from 12168: 12128: 12122: 12121: 12085: 12079: 12066: 12060: 12059: 12057: 12056: 12041: 12035: 12034: 12032: 12031: 12016: 12010: 12009: 12007: 12006: 11991: 11985: 11984: 11982: 11981: 11966: 11960: 11959: 11957: 11956: 11947:. Archived from 11941: 11935: 11934: 11932: 11931: 11912: 11906: 11905: 11903: 11901: 11891: 11885: 11884: 11882: 11880: 11865: 11859: 11858: 11856: 11855: 11836: 11830: 11826: 11820: 11819: 11817: 11815: 11800: 11794: 11793: 11791: 11790: 11775: 11769: 11768: 11766: 11764: 11745: 11739: 11738: 11736: 11735: 11720: 11714: 11713: 11711: 11710: 11696: 11690: 11689: 11687: 11686: 11667: 11661: 11659: 11648: 11636: 11630: 11618:FiveThirtyEight, 11614: 11608: 11607: 11602:. Archived from 11591: 11585: 11584: 11582: 11581: 11575: 11568: 11560: 11554: 11553: 11551: 11549: 11539: 11533: 11532: 11530: 11528: 11513: 11507: 11506: 11504: 11502: 11478: 11472: 11471: 11469: 11468: 11453: 11447: 11446: 11444: 11443: 11434:. Archived from 11424: 11418: 11417: 11415: 11413: 11402:The Conversation 11393: 11387: 11386: 11384: 11382: 11367: 11361: 11360: 11358: 11357: 11348:. Archived from 11338: 11332: 11329: 11323: 11322: 11320: 11319: 11310:. Archived from 11300: 11294: 11277: 11266: 11265: 11263: 11261: 11245: 11239: 11238: 11236: 11235: 11209: 11185: 11179: 11178: 11176: 11175: 11160: 11151: 11150: 11148: 11146: 11126: 11117: 11116: 11114: 11112: 11097: 11088: 11087: 11085: 11083: 11068: 11059: 11058: 11056: 11055: 11040: 11034: 11018: 11012: 11011: 10986:(329): 317–328. 10971: 10965: 10964: 10924: 10913: 10912: 10910: 10898: 10892: 10891: 10889: 10888: 10865: 10859: 10858: 10856: 10855: 10832: 10826: 10825: 10823: 10822: 10803: 10797: 10796: 10794: 10793: 10770: 10761: 10760: 10758: 10757: 10736: 10730: 10727: 10721: 10720: 10719:. 30 March 2011. 10713: 10707: 10704: 10698: 10697: 10695: 10671: 10665: 10664: 10662: 10638: 10632: 10631: 10614:(1/2): 139–149. 10603: 10597: 10596: 10571:(330): 292–296. 10560: 10554: 10551: 10545: 10528: 10522: 10509: 10503: 10491: 10485: 10484: 10482: 10481: 10470:ratings.fide.com 10461: 10455: 10408: 10402: 10401: 10399: 10397: 10391: 10384: 10376: 10367: 10364: 10358: 10357: 10355: 10354: 10331: 10322: 10321:, 3, pp. 59–102. 10316: 10309: 10303: 10301: 10294: 10288: 10285: 10279: 10276: 10270: 10267: 10261: 10260: 10258: 10257: 10246:"About the USCF" 10242: 10236: 10235: 10219: 10210: 10204: 10201: 10195: 10194: 10178: 10169: 10163: 10162: 10160: 10159: 10153: 10146: 10137: 10131: 10126: 10120: 10118: 10114: 10109: 10103: 10102: 10090: 10081: 10056: 10054: 10053: 10052: 10046: 10044:[ˈeːløː] 10040: 10034: 10033: 10030: 10029: 10026: 10023: 10020: 10011: 10010: 10007: 10006: 10003: 10000: 9997: 9987: 9907:Marques Brownlee 9743:Overwatch League 9711:and Sword & 9643:women's football 9613:World TeamTennis 9364: 9357: 9350: 9289: 9285: 9281: 9277: 9273: 9269: 9265: 9261: 9254: 9250: 9219: 9212: 9208: 9205: 9199: 9168: 9160: 9125:Practical issues 9120: 9118: 9117: 9112: 9091: 9089: 9088: 9083: 9066: 9064: 9063: 9062: 9058: 9032: 9027: 9025: 9024: 9023: 9019: 8997: 8996: 8992: 8975: 8968: 8967: 8963: 8949: 8916: 8914: 8913: 8908: 8890: 8888: 8887: 8882: 8864: 8862: 8861: 8856: 8814: 8812: 8811: 8806: 8785: 8783: 8782: 8777: 8772: 8771: 8770: 8745: 8744: 8743: 8726: 8724: 8723: 8718: 8707: 8706: 8705: 8680: 8679: 8678: 8661: 8659: 8658: 8653: 8648: 8647: 8646: 8640: 8639: 8631: 8618: 8617: 8616: 8595: 8593: 8592: 8587: 8582: 8581: 8580: 8567: 8566: 8565: 8559: 8558: 8550: 8537: 8536: 8535: 8522: 8521: 8520: 8497: 8495: 8494: 8489: 8487: 8474: 8473: 8472: 8444: 8440: 8429: 8428: 8427: 8393: 8392: 8391: 8369: 8349: 8348: 8347: 8319: 8312: 8309: 8305: 8304: 8303: 8282: 8279: 8275: 8274: 8273: 8251: 8250: 8249: 8243: 8242: 8234: 8207: 8205: 8204: 8199: 8197: 8196: 8195: 8173: 8172: 8171: 8158: 8157: 8156: 8143: 8142: 8141: 8114: 8112: 8111: 8106: 8092: 8091: 8090: 8065: 8064: 8063: 8057: 8056: 8048: 8035: 8034: 8033: 8020: 8019: 8018: 7998: 7996: 7995: 7990: 7988: 7987: 7986: 7966: 7964: 7963: 7958: 7956: 7955: 7942: 7940: 7939: 7934: 7926: 7925: 7924: 7918: 7917: 7909: 7898: 7896: 7895: 7890: 7888: 7887: 7874: 7872: 7871: 7866: 7858: 7857: 7856: 7850: 7849: 7841: 7830: 7828: 7827: 7822: 7820: 7819: 7806: 7804: 7803: 7798: 7790: 7789: 7788: 7782: 7781: 7773: 7762: 7760: 7759: 7754: 7743: 7742: 7741: 7728: 7727: 7726: 7720: 7719: 7711: 7700: 7698: 7697: 7692: 7687: 7651: 7649: 7648: 7643: 7629: 7628: 7627: 7602: 7601: 7600: 7594: 7593: 7585: 7572: 7571: 7570: 7557: 7556: 7555: 7536: 7534: 7533: 7528: 7526: 7525: 7524: 7504: 7502: 7501: 7496: 7439: 7437: 7436: 7431: 7417: 7416: 7415: 7402: 7401: 7400: 7380: 7378: 7377: 7372: 7370: 7363: 7359: 7349: 7348: 7347: 7313: 7312: 7311: 7296: 7291: 7277: 7266: 7262: 7258: 7248: 7247: 7246: 7212: 7211: 7210: 7182: 7181: 7180: 7137: 7136: 7135: 7117: 7112: 7098: 7083: 7081: 7080: 7079: 7078: 7068: 7067: 7064: 7060: 7057: 7055: 7039: 7037: 7036: 7031: 7029: 7028: 7027: 7007: 7005: 7004: 6999: 6994: 6992: 6991: 6990: 6986: 6964: 6963: 6959: 6942: 6938: 6927: 6926: 6922: 6908: 6871: 6869: 6868: 6863: 6831: 6826: 6812: 6783: 6781: 6777: 6776: 6773: 6769: 6766: 6764: 6752: 6750: 6749: 6744: 6708: 6706: 6705: 6700: 6698: 6697: 6684: 6682: 6681: 6676: 6658: 6656: 6655: 6650: 6648: 6647: 6634: 6632: 6631: 6626: 6618: 6617: 6616: 6599: 6597: 6596: 6591: 6589: 6588: 6573: 6571: 6570: 6565: 6557: 6556: 6555: 6535: 6533: 6532: 6527: 6501: 6500: 6499: 6462: 6454: 6449: 6448: 6447: 6422: 6421: 6420: 6386: 6378: 6373: 6372: 6371: 6336: 6334: 6333: 6328: 6326: 6325: 6316: 6315: 6312: 6307: 6306: 6305: 6297: 6296: 6295: 6292: 6278: 6277: 6276: 6245: 6237: 6223: 6222: 6221: 6193: 6185: 6161: 6160: 6157: 6152: 6151: 6150: 6142: 6141: 6140: 6137: 6123: 6122: 6121: 6080: 6079: 6076: 6071: 6070: 6069: 6061: 6060: 6059: 6056: 6042: 6041: 6040: 5978: 5976: 5975: 5970: 5965: 5954: 5936: 5934: 5933: 5928: 5923: 5921: 5920: 5919: 5918: 5910: 5905: 5904: 5903: 5869: 5864: 5862: 5861: 5860: 5856: 5851: 5850: 5849: 5825: 5824: 5820: 5815: 5814: 5813: 5788: 5787: 5783: 5778: 5777: 5776: 5755: 5741: 5740: 5739: 5711: 5710: 5707: 5702: 5701: 5700: 5678: 5676: 5675: 5670: 5652: 5650: 5649: 5644: 5623: 5621: 5620: 5615: 5613: 5611: 5610: 5609: 5605: 5583: 5582: 5578: 5561: 5560: 5556: 5543: 5507: 5505: 5504: 5499: 5494: 5483: 5482: 5481: 5447: 5446: 5445: 5423: 5412: 5411: 5408: 5403: 5402: 5401: 5379: 5377: 5376: 5371: 5357: 5356: 5355: 5324: 5323: 5320: 5315: 5314: 5313: 5291: 5289: 5288: 5283: 5269: 5268: 5267: 5239: 5238: 5235: 5230: 5229: 5228: 5195: 5193: 5192: 5187: 5185: 5184: 5183: 5166: 5164: 5163: 5158: 5156: 5155: 5154: 5137: 5135: 5134: 5129: 5127: 5126: 5113: 5111: 5110: 5105: 5097: 5096: 5095: 5078: 5076: 5075: 5070: 5062: 5061: 5060: 5043: 5041: 5040: 5035: 5027: 5026: 5025: 4999: 4997: 4996: 4991: 4986: 4985: 4984: 4971: 4970: 4969: 4950: 4949: 4948: 4935: 4934: 4933: 4913: 4911: 4910: 4905: 4903: 4902: 4901: 4881: 4879: 4878: 4873: 4868: 4867: 4866: 4841: 4840: 4839: 4822: 4820: 4819: 4814: 4812: 4811: 4798: 4796: 4795: 4790: 4782: 4781: 4780: 4763: 4761: 4760: 4755: 4753: 4752: 4739: 4737: 4736: 4731: 4723: 4722: 4721: 4704: 4702: 4701: 4696: 4684: 4682: 4681: 4676: 4664: 4662: 4661: 4656: 4651: 4618: 4616: 4615: 4610: 4605: 4604: 4603: 4590: 4589: 4588: 4569: 4568: 4567: 4554: 4553: 4552: 4529: 4527: 4526: 4521: 4519: 4518: 4509: 4508: 4505: 4500: 4499: 4498: 4490: 4489: 4488: 4485: 4477: 4476: 4475: 4447: 4446: 4445: 4431: 4430: 4427: 4422: 4421: 4420: 4412: 4411: 4410: 4407: 4399: 4398: 4397: 4366: 4365: 4364: 4343: 4342: 4341: 4321: 4319: 4318: 4313: 4302: 4300: 4299: 4298: 4297: 4287: 4286: 4283: 4279: 4278: 4277: 4276: 4260: 4259: 4256: 4252: 4243: 4241: 4240: 4235: 4227: 4225: 4224: 4223: 4222: 4212: 4211: 4208: 4204: 4203: 4202: 4201: 4185: 4184: 4181: 4177: 4168: 4166: 4165: 4160: 4143: 4138: 4127: 4104: 4102: 4098: 4097: 4094: 4090: 4087: 4085: 4073: 4071: 4070: 4065: 4049: 4047: 4046: 4041: 4039: 4037: 4036: 4035: 4034: 4024: 4023: 4020: 4016: 4012: 4011: 4008: 4004: 3996: 3995: 3994: 3981: 3980: 3979: 3958: 3956: 3955: 3950: 3948: 3946: 3945: 3944: 3943: 3933: 3932: 3929: 3925: 3921: 3920: 3917: 3913: 3905: 3904: 3903: 3890: 3889: 3888: 3861: 3859: 3858: 3853: 3851: 3850: 3841: 3840: 3837: 3832: 3831: 3830: 3822: 3821: 3820: 3817: 3809: 3808: 3807: 3766: 3765: 3762: 3757: 3756: 3755: 3747: 3746: 3745: 3742: 3734: 3733: 3732: 3670: 3668: 3667: 3662: 3654: 3653: 3652: 3621: 3620: 3619: 3585: 3584: 3581: 3576: 3575: 3574: 3549: 3547: 3546: 3541: 3520: 3518: 3517: 3512: 3507: 3506: 3505: 3492: 3491: 3490: 3474: 3473: 3472: 3443: 3441: 3440: 3435: 3430: 3428: 3427: 3426: 3422: 3396: 3372: 3371: 3370: 3342: 3341: 3338: 3333: 3332: 3331: 3309: 3307: 3306: 3301: 3299: 3298: 3253: 3246: 3242: 3227: 3225: 3224: 3219: 3192: 3190: 3189: 3184: 3156: 3154: 3153: 3148: 3121: 3116: 3115: 3099: 3097: 3096: 3091: 3064: 3062: 3061: 3056: 3029: 3027: 3026: 3021: 2994: 2989: 2988: 2980: 2965: 2963: 2962: 2957: 2930: 2928: 2927: 2922: 2895: 2893: 2892: 2887: 2860: 2855: 2854: 2846:as opposed to a 2838: 2828: 2824: 2817: 2813: 2811: 2810: 2805: 2781: 2753: 2746: 2682: 2678: 2674: 2670: 2663: 2661: 2660: 2655: 2649: 2640: 2625: 2621: 2617: 2613: 2606: 2602: 2597: 2583: 2581: 2580: 2575: 2568: 2564: 2563: 2562: 2549: 2548: 2547: 2525: 2524: 2523: 2506: 2505: 2485: 2483: 2482: 2477: 2474: 2473: 2472: 2454: 2452: 2451: 2446: 2443: 2442: 2441: 2423: 2421: 2420: 2415: 2413: 2412: 2411: 2394: 2387: 2385: 2384: 2379: 2360:for masters and 2359: 2357: 2356: 2351: 2327: 2323: 2321: 2320: 2315: 2312: 2311: 2310: 2300: 2295: 2294: 2293: 2275: 2271: 2269: 2268: 2263: 2256: 2249: 2248: 2247: 2234: 2233: 2232: 2214: 2212: 2211: 2206: 2199: 2198: 2197: 2193: 2188: 2187: 2186: 2168: 2167: 2166: 2148: 2146: 2145: 2140: 2134: 2133: 2129: 2124: 2123: 2122: 2104: 2103: 2102: 2081: 2079: 2078: 2073: 2066: 2065: 2063: 2062: 2061: 2060: 2047: 2046: 2045: 2034: 2033: 2032: 2022: 2017: 2016: 2015: 1992: 1990: 1989: 1984: 1982: 1980: 1979: 1978: 1977: 1964: 1963: 1962: 1951: 1950: 1949: 1939: 1934: 1933: 1932: 1909: 1907: 1906: 1901: 1894: 1893: 1891: 1890: 1889: 1885: 1877: 1876: 1875: 1862: 1861: 1860: 1832: 1827: 1826: 1825: 1805: 1798: 1796: 1795: 1790: 1783: 1782: 1780: 1779: 1778: 1774: 1766: 1765: 1764: 1751: 1750: 1749: 1721: 1716: 1715: 1714: 1694: 1682: 1680: 1679: 1674: 1671: 1670: 1669: 1651: 1648:and player 1647: 1645: 1644: 1639: 1636: 1635: 1634: 1617:has a rating of 1616: 1573: 1565: 1563: 1562: 1557: 1555: 1554: 1538: 1536: 1535: 1530: 1528: 1527: 1511: 1509: 1508: 1503: 1501: 1500: 1481: 1479: 1478: 1473: 1462: 1461: 1449: 1448: 1433: 1432: 1377: 1375: 1374: 1369: 1366: 1364: 1357: 1356: 1343: 1325: 1321: 1298:100–199: Class J 1295:200–399: Class I 1292:400–599: Class H 1289:600–799: Class G 1286:800–999: Class F 1206: 1204: 1203: 1198: 1196: 1195: 1179: 1177: 1176: 1171: 1159: 1157: 1156: 1151: 1139: 1137: 1136: 1131: 1129: 1128: 1112: 1110: 1109: 1104: 1099: 1098: 1086: 1083: 1078: 1075: 1057: 1055: 1054: 1049: 1041: 1036: 1013: 1008: 1005: 990: 988: 987: 982: 974: 969: 946: 941: 938: 923: 921: 920: 915: 907: 902: 879: 874: 871: 856: 854: 853: 848: 846: 842: 841: 837: 834: 829: 826: 812: 809: 806: 801: 798: 783: 781: 780: 775: 773: 769: 764: 711: 708: 704: 699: 652: 649: 634: 630: 626: 622: 494: 492: 491: 486: 484: 483: 466: 464: 463: 458: 445: 444: 375:Candidate Master 322:Tatev Abrahamyan 279: 275: 267: 263: 259: 252: 242: 143:Kenneth Harkness 21: 14685: 14684: 14680: 14679: 14678: 14676: 14675: 14674: 14655: 14654: 14653: 14648: 14631: 14623: 14533: 14519:Chess libraries 14436: 14340:FIDE Grand Prix 14335:Chess World Cup 14289: 14285:Wrong rook pawn 14223:Lucena position 14165: 14115: 14032:Catalan Opening 14007:English Defence 13992:Budapest Gambit 13978: 13936:Austrian Attack 13820: 13789:English Opening 13751: 13747:School of chess 13730:Minority attack 13662: 13631:Queen sacrifice 13530: 13391: 13387:White and Black 13382:Touch-move rule 13341:Perpetual check 13336:Fifty-move rule 13292: 13128: 13125: 13032: 12902: 12897: 12867: 12862: 12806: 12761: 12722: 12656: 12652:Win probability 12625: 12620: 12583: 12564: 12562:Further reading 12554: 12535: 12530: 12529: 12523:Wayback Machine 12516:, Sony Pictures 12512:Screenplay for 12510: 12506: 12497: 12495: 12487: 12486: 12482: 12473: 12471: 12463: 12462: 12458: 12441: 12437: 12427: 12425: 12413: 12409: 12399: 12397: 12381: 12377: 12349: 12345: 12336: 12334: 12323: 12322: 12318: 12309: 12307: 12294: 12293: 12289: 12279: 12277: 12268: 12267: 12263: 12253: 12251: 12242: 12241: 12237: 12227: 12225: 12216: 12215: 12211: 12201: 12199: 12190: 12189: 12185: 12176: 12174: 12129: 12125: 12096:(12): 2574–86. 12086: 12082: 12076:Wayback Machine 12067: 12063: 12054: 12052: 12043: 12042: 12038: 12029: 12027: 12018: 12017: 12013: 12004: 12002: 11993: 11992: 11988: 11979: 11977: 11968: 11967: 11963: 11954: 11952: 11943: 11942: 11938: 11929: 11927: 11914: 11913: 11909: 11899: 11897: 11893: 11892: 11888: 11878: 11876: 11867: 11866: 11862: 11853: 11851: 11838: 11837: 11833: 11827: 11823: 11813: 11811: 11802: 11801: 11797: 11788: 11786: 11777: 11776: 11772: 11762: 11760: 11747: 11746: 11742: 11733: 11731: 11722: 11721: 11717: 11708: 11706: 11698: 11697: 11693: 11684: 11682: 11669: 11668: 11664: 11637: 11633: 11628:Wayback Machine 11615: 11611: 11600:FiveThirtyEight 11592: 11588: 11579: 11577: 11573: 11566: 11562: 11561: 11557: 11547: 11545: 11541: 11540: 11536: 11526: 11524: 11515: 11514: 11510: 11500: 11498: 11479: 11475: 11466: 11464: 11455: 11454: 11450: 11441: 11439: 11425: 11421: 11411: 11409: 11394: 11390: 11380: 11378: 11369: 11368: 11364: 11355: 11353: 11340: 11339: 11335: 11330: 11326: 11317: 11315: 11302: 11301: 11297: 11289:, Published in 11287:Wayback Machine 11278: 11269: 11259: 11257: 11256:on 8 March 2013 11246: 11242: 11233: 11231: 11186: 11182: 11173: 11171: 11162: 11161: 11154: 11144: 11142: 11127: 11120: 11110: 11108: 11099: 11098: 11091: 11081: 11079: 11070: 11069: 11062: 11053: 11051: 11042: 11041: 11037: 11028:Wayback Machine 11019: 11015: 10992:10.2307/2283595 10972: 10968: 10925: 10916: 10899: 10895: 10886: 10884: 10867: 10866: 10862: 10853: 10851: 10834: 10833: 10829: 10820: 10818: 10805: 10804: 10800: 10791: 10789: 10772: 10771: 10764: 10755: 10753: 10737: 10733: 10728: 10724: 10715: 10714: 10710: 10705: 10701: 10672: 10668: 10639: 10635: 10620:10.2307/2332816 10604: 10600: 10577:10.2307/3608567 10561: 10557: 10552: 10548: 10538:Wayback Machine 10529: 10525: 10519:Wayback Machine 10510: 10506: 10501:Wayback Machine 10492: 10488: 10479: 10477: 10464:Administrator. 10462: 10458: 10452:Wayback Machine 10441:Wayback Machine 10430:Wayback Machine 10419:Wayback Machine 10409: 10405: 10395: 10393: 10389: 10382: 10378: 10377: 10370: 10366:Elo 1986, p159. 10365: 10361: 10352: 10350: 10333: 10332: 10325: 10312: 10310: 10306: 10297: 10295: 10291: 10286: 10282: 10277: 10273: 10268: 10264: 10255: 10253: 10244: 10243: 10239: 10217: 10211: 10207: 10202: 10198: 10176: 10170: 10166: 10157: 10155: 10151: 10144: 10138: 10134: 10127: 10123: 10116: 10113:100% / (1 + 10) 10112: 10110: 10106: 10088: 10082: 10075: 10070: 10065: 10060: 10059: 10048: 10047: 10017: 10013: 9994: 9990: 9988: 9984: 9979: 9961: 9952:Eduardo Saverin 9950:. In the scene 9944:Mark Zuckerberg 9934: 9871:soft biometrics 9867: 9847:Golden Tee Live 9721: 9661:FiveThirtyEight 9531: 9529:Athletic sports 9421: 9416: 9387:chess computers 9376: 9359: 9352: 9345: 9341: 9322:Using a strong 9287: 9283: 9279: 9275: 9271: 9267: 9263: 9256: 9252: 9248: 9241: 9220: 9209: 9203: 9200: 9185: 9169: 9158: 9132: 9127: 9100: 9097: 9096: 9054: 9047: 9043: 9036: 9031: 9015: 9011: 9007: 8988: 8981: 8977: 8976: 8959: 8955: 8951: 8950: 8948: 8925: 8922: 8921: 8896: 8893: 8892: 8870: 8867: 8866: 8820: 8817: 8816: 8794: 8791: 8790: 8760: 8759: 8755: 8739: 8738: 8734: 8732: 8729: 8728: 8695: 8694: 8690: 8674: 8673: 8669: 8667: 8664: 8663: 8642: 8641: 8630: 8629: 8628: 8612: 8611: 8607: 8605: 8602: 8601: 8576: 8575: 8571: 8561: 8560: 8549: 8548: 8547: 8531: 8530: 8526: 8516: 8515: 8511: 8509: 8506: 8505: 8485: 8484: 8462: 8461: 8457: 8442: 8441: 8417: 8416: 8412: 8381: 8380: 8376: 8368: 8337: 8336: 8332: 8317: 8316: 8308: 8299: 8298: 8278: 8269: 8268: 8255: 8245: 8244: 8233: 8232: 8231: 8221: 8219: 8216: 8215: 8185: 8184: 8180: 8167: 8166: 8162: 8152: 8151: 8147: 8131: 8130: 8126: 8124: 8121: 8120: 8080: 8079: 8075: 8059: 8058: 8047: 8046: 8045: 8029: 8028: 8024: 8014: 8013: 8009: 8007: 8004: 8003: 7982: 7981: 7977: 7975: 7972: 7971: 7970:The update for 7951: 7950: 7948: 7945: 7944: 7920: 7919: 7908: 7907: 7906: 7904: 7901: 7900: 7883: 7882: 7880: 7877: 7876: 7852: 7851: 7840: 7839: 7838: 7836: 7833: 7832: 7815: 7814: 7812: 7809: 7808: 7784: 7783: 7772: 7771: 7770: 7768: 7765: 7764: 7737: 7736: 7732: 7722: 7721: 7710: 7709: 7708: 7706: 7703: 7702: 7683: 7660: 7657: 7656: 7617: 7616: 7612: 7596: 7595: 7584: 7583: 7582: 7566: 7565: 7561: 7551: 7550: 7546: 7544: 7541: 7540: 7520: 7519: 7515: 7513: 7510: 7509: 7445: 7442: 7441: 7411: 7410: 7406: 7396: 7395: 7391: 7389: 7386: 7385: 7368: 7367: 7337: 7336: 7332: 7307: 7306: 7302: 7301: 7297: 7278: 7276: 7264: 7263: 7236: 7235: 7231: 7206: 7205: 7201: 7170: 7169: 7165: 7131: 7130: 7126: 7122: 7118: 7099: 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5794: 5790: 5789: 5779: 5766: 5765: 5761: 5760: 5756: 5754: 5729: 5728: 5724: 5706: 5705: 5696: 5695: 5687: 5684: 5683: 5658: 5655: 5654: 5632: 5629: 5628: 5601: 5597: 5593: 5574: 5567: 5563: 5562: 5552: 5548: 5544: 5542: 5519: 5516: 5515: 5471: 5470: 5466: 5435: 5434: 5430: 5422: 5407: 5406: 5397: 5396: 5388: 5385: 5384: 5345: 5344: 5340: 5319: 5318: 5309: 5308: 5300: 5297: 5296: 5257: 5256: 5252: 5234: 5233: 5224: 5223: 5215: 5212: 5211: 5179: 5178: 5174: 5172: 5169: 5168: 5150: 5149: 5145: 5143: 5140: 5139: 5122: 5121: 5119: 5116: 5115: 5091: 5090: 5086: 5084: 5081: 5080: 5056: 5055: 5051: 5049: 5046: 5045: 5021: 5020: 5016: 5014: 5011: 5010: 5007: 4980: 4979: 4975: 4965: 4964: 4960: 4944: 4943: 4939: 4929: 4928: 4924: 4922: 4919: 4918: 4897: 4896: 4892: 4890: 4887: 4886: 4856: 4855: 4851: 4835: 4834: 4830: 4828: 4825: 4824: 4807: 4806: 4804: 4801: 4800: 4776: 4775: 4771: 4769: 4766: 4765: 4748: 4747: 4745: 4742: 4741: 4717: 4716: 4712: 4710: 4707: 4706: 4690: 4687: 4686: 4670: 4667: 4666: 4647: 4627: 4624: 4623: 4599: 4598: 4594: 4584: 4583: 4579: 4563: 4562: 4558: 4548: 4547: 4543: 4541: 4538: 4537: 4514: 4513: 4504: 4503: 4494: 4493: 4484: 4483: 4481: 4465: 4464: 4460: 4441: 4440: 4436: 4433: 4432: 4426: 4425: 4416: 4415: 4406: 4405: 4403: 4387: 4386: 4382: 4360: 4359: 4355: 4348: 4347: 4337: 4336: 4332: 4330: 4327: 4326: 4293: 4292: 4288: 4282: 4281: 4280: 4266: 4265: 4261: 4255: 4254: 4253: 4251: 4249: 4246: 4245: 4218: 4217: 4213: 4207: 4206: 4205: 4191: 4190: 4186: 4180: 4179: 4178: 4176: 4174: 4171: 4170: 4128: 4126: 4093: 4092: 4091: 4086: 4084: 4082: 4079: 4078: 4059: 4056: 4055: 4030: 4029: 4025: 4019: 4018: 4017: 4007: 4006: 4005: 4003: 3990: 3989: 3985: 3975: 3974: 3970: 3968: 3965: 3964: 3939: 3938: 3934: 3928: 3927: 3926: 3916: 3915: 3914: 3912: 3899: 3898: 3894: 3884: 3883: 3879: 3877: 3874: 3873: 3865:and, using the 3846: 3845: 3836: 3835: 3826: 3825: 3816: 3815: 3813: 3797: 3796: 3792: 3771: 3770: 3761: 3760: 3751: 3750: 3741: 3740: 3738: 3722: 3721: 3717: 3695: 3694: 3686: 3683: 3682: 3642: 3641: 3637: 3609: 3608: 3604: 3580: 3579: 3570: 3569: 3561: 3558: 3557: 3529: 3526: 3525: 3501: 3500: 3496: 3486: 3485: 3481: 3462: 3461: 3457: 3455: 3452: 3451: 3418: 3411: 3407: 3400: 3395: 3360: 3359: 3355: 3337: 3336: 3327: 3326: 3318: 3315: 3314: 3294: 3293: 3291: 3288: 3287: 3265: 3251: 3244: 3240: 3205: 3202: 3201: 3170: 3167: 3166: 3157: 3134: 3131: 3130: 3122:-factor 3119: 3077: 3074: 3073: 3042: 3039: 3038: 3007: 3004: 3003: 2995:-factor 2992: 2978: 2943: 2940: 2939: 2908: 2905: 2904: 2873: 2870: 2869: 2861:-factor 2858: 2833: 2826: 2822: 2821:Elo's original 2815: 2791: 2788: 2787: 2779: 2776: 2760: 2748: 2744: 2737: 2732: 2680: 2676: 2672: 2668: 2638: 2635: 2632: 2631: 2623: 2619: 2615: 2611: 2604: 2600: 2595: 2558: 2557: 2553: 2543: 2542: 2538: 2519: 2518: 2514: 2501: 2500: 2494: 2491: 2490: 2468: 2467: 2463: 2460: 2457: 2456: 2437: 2436: 2432: 2429: 2426: 2425: 2407: 2406: 2402: 2400: 2397: 2396: 2392: 2365: 2362: 2361: 2337: 2334: 2333: 2325: 2306: 2305: 2301: 2296: 2289: 2288: 2284: 2281: 2278: 2277: 2273: 2243: 2242: 2238: 2228: 2227: 2223: 2220: 2217: 2216: 2189: 2182: 2181: 2177: 2176: 2172: 2162: 2161: 2157: 2154: 2151: 2150: 2125: 2118: 2117: 2113: 2112: 2108: 2098: 2097: 2093: 2090: 2087: 2086: 2056: 2055: 2051: 2041: 2040: 2036: 2035: 2028: 2027: 2023: 2021: 2011: 2010: 2006: 2004: 2001: 2000: 1973: 1972: 1968: 1958: 1957: 1953: 1952: 1945: 1944: 1940: 1938: 1928: 1927: 1923: 1921: 1918: 1917: 1881: 1871: 1870: 1866: 1856: 1855: 1851: 1847: 1843: 1836: 1831: 1821: 1820: 1816: 1814: 1811: 1810: 1803: 1770: 1760: 1759: 1755: 1745: 1744: 1740: 1736: 1732: 1725: 1720: 1710: 1709: 1705: 1703: 1700: 1699: 1692: 1665: 1664: 1660: 1657: 1654: 1653: 1649: 1630: 1629: 1625: 1622: 1619: 1618: 1614: 1613:If player 1595: 1584: 1571: 1550: 1546: 1544: 1541: 1540: 1523: 1519: 1517: 1514: 1513: 1496: 1492: 1490: 1487: 1486: 1457: 1453: 1444: 1440: 1428: 1424: 1395: 1392: 1391: 1384: 1352: 1348: 1347: 1342: 1334: 1331: 1330: 1323: 1320: 1312: 1305: 1247: 1235:Artiom Tsepotan 1213: 1191: 1187: 1185: 1182: 1181: 1165: 1162: 1161: 1145: 1142: 1141: 1124: 1120: 1118: 1115: 1114: 1094: 1090: 1082: 1074: 1072: 1069: 1068: 1014: 1012: 1004: 1002: 999: 998: 947: 945: 937: 935: 932: 931: 880: 878: 870: 868: 865: 864: 833: 825: 808: 807: 805: 797: 795: 792: 791: 771: 770: 712: 710: 706: 705: 653: 651: 646: 644: 641: 640: 636: 632: 628: 624: 620: 479: 475: 473: 470: 469: 452: 449: 448: 443: 437: 343: 337: 331: 290: 277: 273: 265: 261: 254: 247: 237: 203: 172:random variable 128: 70:Harkness system 28: 23: 22: 15: 12: 11: 5: 14683: 14673: 14672: 14667: 14650: 14649: 14647: 14646: 14641: 14628: 14625: 14624: 14622: 14621: 14616: 14611: 14606: 14605: 14604: 14599: 14589: 14588: 14587: 14582: 14577: 14572: 14562: 14560:Chess composer 14557: 14552: 14547: 14541: 14539: 14535: 14534: 14532: 14531: 14526: 14521: 14516: 14515: 14514: 14507: 14502: 14492: 14491: 14490: 14485: 14480: 14475: 14470: 14465: 14455: 14450: 14444: 14442: 14438: 14437: 14435: 14434: 14433: 14432: 14427: 14422: 14417: 14415:North American 14412: 14407: 14399: 14398: 14397: 14392: 14387: 14382: 14377: 14372: 14367: 14362: 14357: 14352: 14344: 14343: 14342: 14337: 14332: 14327: 14317: 14316: 14315: 14308:Chess Olympiad 14305: 14299: 14297: 14291: 14290: 14288: 14287: 14282: 14277: 14272: 14267: 14262: 14261: 14260: 14255: 14250: 14245: 14240: 14232: 14231: 14230: 14225: 14215: 14210: 14205: 14200: 14195: 14190: 14185: 14179: 14177: 14171: 14170: 14167: 14166: 14164: 14163: 14162: 14161: 14159:Scholar's mate 14156: 14151: 14141: 14136: 14135: 14134: 14123: 14121: 14117: 14116: 14114: 14113: 14108: 14103: 14102: 14101: 14096: 14091: 14086: 14081: 14074:Queen's Gambit 14071: 14066: 14061: 14060: 14059: 14054: 14049: 14044: 14039: 14034: 14029: 14024: 14019: 14017:Benoni Defence 14012:Indian Defence 14009: 14004: 13999: 13994: 13988: 13986: 13980: 13979: 13977: 13976: 13975: 13974: 13969: 13964: 13955: 13945: 13940: 13939: 13938: 13928: 13926:Owen's Defence 13923: 13922: 13921: 13916: 13911: 13906: 13901: 13896: 13891: 13886: 13881: 13876: 13871: 13866: 13856: 13851: 13849:Modern Defence 13846: 13844:French Defence 13841: 13836: 13830: 13828: 13822: 13821: 13819: 13818: 13817: 13816: 13811: 13801: 13796: 13791: 13786: 13781: 13779:Bird's Opening 13776: 13770: 13768: 13759: 13753: 13752: 13750: 13749: 13744: 13739: 13734: 13733: 13732: 13727: 13722: 13717: 13710:Pawn structure 13707: 13702: 13701: 13700: 13690: 13689: 13688: 13678: 13672: 13670: 13664: 13663: 13661: 13660: 13655: 13650: 13645: 13640: 13635: 13634: 13633: 13623: 13618: 13613: 13608: 13603: 13598: 13593: 13588: 13583: 13578: 13573: 13568: 13563: 13558: 13557: 13556: 13554:Alekhine's gun 13546: 13540: 13538: 13532: 13531: 13529: 13528: 13523: 13518: 13513: 13508: 13507: 13506: 13501: 13496: 13491: 13486: 13476: 13471: 13470: 13469: 13467:Half-open file 13459: 13454: 13449: 13444: 13439: 13438: 13437: 13432: 13427: 13422: 13417: 13410:Chess notation 13407: 13401: 13399: 13393: 13392: 13390: 13389: 13384: 13379: 13378: 13377: 13367: 13365:Pawn promotion 13362: 13355: 13354: 13353: 13348: 13343: 13338: 13333: 13323: 13318: 13313: 13308: 13302: 13300: 13294: 13293: 13291: 13290: 13289: 13288: 13283: 13278: 13268: 13266:Women in chess 13263: 13262: 13261: 13256: 13251: 13241: 13236: 13235: 13234: 13229: 13228: 13227: 13222: 13212: 13207: 13206: 13205: 13190: 13189: 13188: 13183: 13178: 13176:Hypermodernism 13173: 13171:Romantic chess 13168: 13166:Lewis chessmen 13163: 13158: 13151: 13138: 13136: 13130: 13129: 13127: 13126: 13117: 13112: 13107: 13106: 13105: 13100: 13095: 13090: 13085: 13080: 13075: 13065: 13064: 13063: 13058: 13053: 13042: 13040: 13034: 13033: 13031: 13030: 13025: 13024: 13023: 13013: 13012: 13011: 13006: 13004:world rankings 12996: 12995: 12994: 12993: 12992: 12982: 12972: 12967: 12962: 12957: 12956: 12955: 12950: 12945: 12940: 12933:Computer chess 12930: 12929: 12928: 12918: 12912: 12910: 12904: 12903: 12896: 12895: 12888: 12881: 12873: 12864: 12863: 12861: 12860: 12855: 12850: 12845: 12840: 12835: 12833:Kenneth Massey 12830: 12825: 12823:John Hollinger 12820: 12814: 12812: 12808: 12807: 12805: 12804: 12799: 12794: 12789: 12784: 12779: 12773: 12771: 12767: 12766: 12763: 12762: 12760: 12759: 12754: 12749: 12744: 12739: 12733: 12731: 12721: 12720: 12715: 12710: 12705: 12700: 12695: 12690: 12685: 12680: 12675: 12670: 12664: 12662: 12658: 12657: 12655: 12654: 12649: 12644: 12639: 12637:Home advantage 12633: 12631: 12627: 12626: 12619: 12618: 12611: 12604: 12596: 12590: 12589: 12582: 12581:External links 12579: 12578: 12577: 12563: 12560: 12559: 12558: 12552: 12534: 12531: 12528: 12527: 12504: 12480: 12456: 12435: 12407: 12375: 12364:(1): 425–467. 12343: 12316: 12287: 12261: 12235: 12209: 12183: 12123: 12080: 12061: 12036: 12011: 11986: 11970:"Guild ladder" 11961: 11936: 11907: 11886: 11860: 11831: 11821: 11795: 11770: 11740: 11715: 11691: 11662: 11631: 11609: 11606:on 2015-05-23. 11586: 11555: 11534: 11519:. 8 May 2018. 11508: 11473: 11448: 11430:(2006-06-28). 11419: 11388: 11362: 11333: 11324: 11304:"Elo-systemet" 11295: 11267: 11250:"ELO-SYSTEMET" 11240: 11200:(1): 834–839. 11180: 11152: 11118: 11089: 11060: 11035: 11013: 10966: 10939:(3): 211–220. 10914: 10893: 10860: 10827: 10798: 10784:. 2014-07-01. 10762: 10731: 10722: 10708: 10699: 10686:(2): 501–510. 10666: 10633: 10598: 10555: 10546: 10523: 10504: 10486: 10456: 10403: 10368: 10359: 10323: 10304: 10289: 10280: 10271: 10262: 10237: 10205: 10203:Elo 1986, p. 4 10196: 10164: 10132: 10121: 10104: 10072: 10071: 10069: 10066: 10064: 10061: 10058: 10057: 10041:is pronounced 9981: 9980: 9978: 9975: 9974: 9973: 9967: 9960: 9957: 9933: 9930: 9866: 9863: 9808:played on the 9802:Classic Tetris 9766:Puzzle Pirates 9720: 9717: 9617:Tennis Channel 9530: 9527: 9526: 9525: 9510:Decipher, Inc. 9482: 9471:United Kingdom 9462: 9441:: The popular 9434: 9420: 9417: 9415: 9412: 9381:between 1997 ( 9375: 9372: 9340: 9337: 9308:Anatoly Karpov 9240: 9237: 9222: 9221: 9172: 9170: 9163: 9157: 9154: 9131: 9128: 9126: 9123: 9110: 9107: 9104: 9093: 9092: 9081: 9078: 9075: 9072: 9069: 9061: 9057: 9053: 9050: 9046: 9042: 9039: 9035: 9030: 9022: 9018: 9014: 9010: 9006: 9003: 9000: 8995: 8991: 8987: 8984: 8980: 8974: 8971: 8966: 8962: 8958: 8954: 8947: 8944: 8941: 8938: 8935: 8932: 8929: 8906: 8903: 8900: 8880: 8877: 8874: 8854: 8851: 8848: 8845: 8842: 8839: 8836: 8833: 8830: 8827: 8824: 8804: 8801: 8798: 8775: 8769: 8766: 8763: 8758: 8754: 8751: 8748: 8742: 8737: 8716: 8713: 8710: 8704: 8701: 8698: 8693: 8689: 8686: 8683: 8677: 8672: 8651: 8645: 8637: 8634: 8627: 8624: 8621: 8615: 8610: 8598: 8597: 8585: 8579: 8574: 8570: 8564: 8556: 8553: 8546: 8543: 8540: 8534: 8529: 8525: 8519: 8514: 8499: 8498: 8483: 8480: 8477: 8471: 8468: 8465: 8460: 8456: 8453: 8450: 8447: 8445: 8443: 8438: 8435: 8432: 8426: 8423: 8420: 8415: 8411: 8408: 8405: 8402: 8399: 8396: 8390: 8387: 8384: 8379: 8375: 8372: 8367: 8364: 8361: 8358: 8355: 8352: 8346: 8343: 8340: 8335: 8331: 8328: 8325: 8322: 8320: 8318: 8315: 8302: 8297: 8294: 8291: 8288: 8285: 8272: 8267: 8264: 8261: 8258: 8256: 8254: 8248: 8240: 8237: 8230: 8227: 8224: 8223: 8194: 8191: 8188: 8183: 8179: 8176: 8170: 8165: 8161: 8155: 8150: 8146: 8140: 8137: 8134: 8129: 8117: 8116: 8104: 8101: 8098: 8095: 8089: 8086: 8083: 8078: 8074: 8071: 8068: 8062: 8054: 8051: 8044: 8041: 8038: 8032: 8027: 8023: 8017: 8012: 7985: 7980: 7932: 7929: 7923: 7915: 7912: 7864: 7861: 7855: 7847: 7844: 7796: 7793: 7787: 7779: 7776: 7752: 7749: 7746: 7740: 7735: 7731: 7725: 7717: 7714: 7690: 7686: 7682: 7679: 7676: 7673: 7670: 7667: 7664: 7653: 7652: 7641: 7638: 7635: 7632: 7626: 7623: 7620: 7615: 7611: 7608: 7605: 7599: 7591: 7588: 7581: 7578: 7575: 7569: 7564: 7560: 7554: 7549: 7523: 7518: 7494: 7491: 7488: 7485: 7482: 7479: 7476: 7473: 7470: 7467: 7464: 7461: 7458: 7455: 7452: 7449: 7429: 7426: 7423: 7420: 7414: 7409: 7405: 7399: 7394: 7382: 7381: 7366: 7362: 7358: 7355: 7352: 7346: 7343: 7340: 7335: 7331: 7328: 7325: 7322: 7319: 7316: 7310: 7305: 7300: 7294: 7290: 7287: 7284: 7281: 7275: 7272: 7269: 7267: 7265: 7261: 7257: 7254: 7251: 7245: 7242: 7239: 7234: 7230: 7227: 7224: 7221: 7218: 7215: 7209: 7204: 7200: 7197: 7194: 7191: 7188: 7185: 7179: 7176: 7173: 7168: 7164: 7161: 7158: 7155: 7152: 7149: 7146: 7143: 7140: 7134: 7129: 7125: 7121: 7115: 7111: 7108: 7105: 7102: 7096: 7093: 7090: 7088: 7086: 7077: 7072: 7053: 7052: 7026: 7021: 7009: 7008: 6997: 6989: 6985: 6981: 6977: 6973: 6970: 6967: 6962: 6958: 6954: 6951: 6947: 6941: 6937: 6933: 6930: 6925: 6921: 6917: 6913: 6906: 6903: 6900: 6897: 6894: 6891: 6888: 6874: 6873: 6861: 6858: 6855: 6852: 6849: 6846: 6843: 6840: 6837: 6834: 6829: 6825: 6822: 6819: 6816: 6810: 6807: 6804: 6801: 6798: 6795: 6792: 6789: 6786: 6780: 6742: 6739: 6736: 6733: 6730: 6727: 6724: 6721: 6696: 6674: 6671: 6668: 6646: 6624: 6621: 6615: 6610: 6587: 6563: 6560: 6554: 6549: 6537: 6536: 6525: 6522: 6519: 6516: 6513: 6510: 6507: 6504: 6498: 6495: 6492: 6487: 6483: 6480: 6477: 6474: 6471: 6468: 6465: 6460: 6457: 6452: 6446: 6441: 6437: 6434: 6431: 6428: 6425: 6419: 6416: 6413: 6408: 6404: 6401: 6398: 6395: 6392: 6389: 6384: 6381: 6376: 6370: 6365: 6361: 6358: 6355: 6352: 6338: 6337: 6324: 6319: 6304: 6289: 6287: 6284: 6281: 6275: 6272: 6269: 6264: 6260: 6257: 6254: 6251: 6248: 6243: 6240: 6235: 6232: 6229: 6226: 6220: 6217: 6214: 6209: 6205: 6202: 6199: 6196: 6191: 6188: 6183: 6180: 6177: 6174: 6171: 6168: 6167: 6164: 6149: 6134: 6132: 6129: 6126: 6120: 6117: 6114: 6109: 6105: 6102: 6099: 6096: 6093: 6090: 6087: 6086: 6083: 6068: 6053: 6051: 6048: 6045: 6039: 6036: 6033: 6028: 6024: 6021: 6018: 6015: 6012: 6009: 6008: 6006: 6001: 5998: 5968: 5964: 5960: 5957: 5953: 5950: 5938: 5937: 5926: 5917: 5914: 5909: 5902: 5899: 5896: 5891: 5887: 5883: 5879: 5876: 5872: 5867: 5859: 5855: 5848: 5845: 5842: 5837: 5832: 5828: 5823: 5819: 5812: 5809: 5806: 5801: 5797: 5793: 5786: 5782: 5775: 5772: 5769: 5764: 5759: 5753: 5750: 5747: 5744: 5738: 5735: 5732: 5727: 5723: 5720: 5717: 5714: 5699: 5694: 5691: 5668: 5665: 5662: 5642: 5639: 5636: 5625: 5624: 5608: 5604: 5600: 5596: 5592: 5589: 5586: 5581: 5577: 5573: 5570: 5566: 5559: 5555: 5551: 5547: 5541: 5538: 5535: 5532: 5529: 5526: 5523: 5509: 5508: 5497: 5492: 5489: 5486: 5480: 5477: 5474: 5469: 5465: 5462: 5459: 5456: 5453: 5450: 5444: 5441: 5438: 5433: 5429: 5426: 5421: 5418: 5415: 5400: 5395: 5392: 5381: 5380: 5369: 5366: 5363: 5360: 5354: 5351: 5348: 5343: 5339: 5336: 5333: 5330: 5327: 5312: 5307: 5304: 5293: 5292: 5281: 5278: 5275: 5272: 5266: 5263: 5260: 5255: 5251: 5248: 5245: 5242: 5227: 5222: 5219: 5182: 5177: 5153: 5148: 5125: 5103: 5100: 5094: 5089: 5068: 5065: 5059: 5054: 5033: 5030: 5024: 5019: 5006: 5003: 5002: 5001: 4989: 4983: 4978: 4974: 4968: 4963: 4959: 4956: 4953: 4947: 4942: 4938: 4932: 4927: 4900: 4895: 4871: 4865: 4862: 4859: 4854: 4850: 4847: 4844: 4838: 4833: 4810: 4788: 4785: 4779: 4774: 4751: 4729: 4726: 4720: 4715: 4694: 4674: 4654: 4650: 4646: 4643: 4640: 4637: 4634: 4631: 4620: 4619: 4608: 4602: 4597: 4593: 4587: 4582: 4578: 4575: 4572: 4566: 4561: 4557: 4551: 4546: 4531: 4530: 4517: 4512: 4497: 4482: 4480: 4474: 4471: 4468: 4463: 4459: 4456: 4453: 4450: 4444: 4439: 4435: 4434: 4419: 4404: 4402: 4396: 4393: 4390: 4385: 4381: 4378: 4375: 4372: 4369: 4363: 4358: 4354: 4353: 4351: 4346: 4340: 4335: 4311: 4308: 4305: 4296: 4291: 4275: 4272: 4269: 4264: 4233: 4230: 4221: 4216: 4200: 4197: 4194: 4189: 4158: 4155: 4152: 4149: 4146: 4141: 4137: 4134: 4131: 4125: 4122: 4119: 4116: 4113: 4110: 4107: 4101: 4063: 4052: 4051: 4033: 4028: 4015: 4002: 3999: 3993: 3988: 3984: 3978: 3973: 3961: 3960: 3942: 3937: 3924: 3911: 3908: 3902: 3897: 3893: 3887: 3882: 3863: 3862: 3849: 3844: 3829: 3814: 3812: 3806: 3803: 3800: 3795: 3791: 3788: 3785: 3782: 3779: 3776: 3773: 3772: 3769: 3754: 3739: 3737: 3731: 3728: 3725: 3720: 3716: 3713: 3710: 3707: 3704: 3701: 3700: 3698: 3693: 3690: 3672: 3671: 3660: 3657: 3651: 3648: 3645: 3640: 3636: 3633: 3630: 3627: 3624: 3618: 3615: 3612: 3607: 3603: 3600: 3597: 3594: 3591: 3588: 3573: 3568: 3565: 3539: 3536: 3533: 3522: 3521: 3510: 3504: 3499: 3495: 3489: 3484: 3480: 3477: 3471: 3468: 3465: 3460: 3445: 3444: 3433: 3425: 3421: 3417: 3414: 3410: 3406: 3403: 3399: 3394: 3391: 3388: 3385: 3382: 3378: 3375: 3369: 3366: 3363: 3358: 3354: 3351: 3348: 3345: 3330: 3325: 3322: 3297: 3264: 3261: 3237: 3236: 3233: 3232: 3229: 3216: 3213: 3210: 3198: 3197: 3194: 3181: 3178: 3175: 3163: 3162: 3159: 3145: 3142: 3139: 3127: 3126: 3123: 3109: 3108: 3105: 3104: 3101: 3088: 3085: 3082: 3070: 3069: 3066: 3053: 3050: 3047: 3035: 3034: 3031: 3018: 3015: 3012: 3000: 2999: 2996: 2975: 2974: 2971: 2970: 2967: 2954: 2951: 2948: 2936: 2935: 2932: 2919: 2916: 2913: 2901: 2900: 2897: 2884: 2881: 2878: 2866: 2865: 2862: 2802: 2799: 2796: 2775: 2772: 2759: 2756: 2736: 2733: 2703:(ICC) and the 2652: 2646: 2643: 2585: 2584: 2573: 2567: 2561: 2556: 2552: 2546: 2541: 2537: 2534: 2531: 2528: 2522: 2517: 2513: 2509: 2504: 2499: 2471: 2466: 2440: 2435: 2410: 2405: 2376: 2373: 2370: 2348: 2345: 2342: 2309: 2304: 2299: 2292: 2287: 2261: 2255: 2252: 2246: 2241: 2237: 2231: 2226: 2204: 2196: 2192: 2185: 2180: 2175: 2171: 2165: 2160: 2138: 2132: 2128: 2121: 2116: 2111: 2107: 2101: 2096: 2083: 2082: 2071: 2059: 2054: 2050: 2044: 2039: 2031: 2026: 2020: 2014: 2009: 1994: 1993: 1976: 1971: 1967: 1961: 1956: 1948: 1943: 1937: 1931: 1926: 1911: 1910: 1899: 1888: 1884: 1880: 1874: 1869: 1865: 1859: 1854: 1850: 1846: 1842: 1839: 1835: 1830: 1824: 1819: 1800: 1799: 1788: 1777: 1773: 1769: 1763: 1758: 1754: 1748: 1743: 1739: 1735: 1731: 1728: 1724: 1719: 1713: 1708: 1685:logistic curve 1668: 1663: 1633: 1628: 1607:expected score 1600:expected score 1594: 1591: 1583: 1580: 1553: 1549: 1526: 1522: 1499: 1495: 1483: 1482: 1471: 1468: 1465: 1460: 1456: 1452: 1447: 1443: 1439: 1436: 1431: 1427: 1423: 1420: 1417: 1414: 1411: 1408: 1405: 1402: 1399: 1383: 1380: 1379: 1378: 1363: 1360: 1355: 1351: 1346: 1341: 1338: 1316: 1304: 1301: 1300: 1299: 1296: 1293: 1290: 1287: 1284: 1281: 1278: 1275: 1272: 1269: 1266: 1265: 1264: 1258: 1246: 1243: 1212: 1209: 1194: 1190: 1169: 1149: 1127: 1123: 1102: 1097: 1093: 1089: 1081: 1059: 1058: 1047: 1044: 1039: 1035: 1032: 1029: 1026: 1023: 1020: 1017: 1011: 992: 991: 980: 977: 972: 968: 965: 962: 959: 956: 953: 950: 944: 925: 924: 913: 910: 905: 901: 898: 895: 892: 889: 886: 883: 877: 858: 857: 840: 832: 824: 821: 818: 815: 804: 785: 784: 767: 763: 760: 757: 754: 751: 748: 745: 742: 739: 736: 733: 730: 727: 724: 721: 718: 715: 709: 707: 702: 698: 695: 692: 689: 686: 683: 680: 677: 674: 671: 668: 665: 662: 659: 656: 650: 648: 617: 616: 613: 610: 600: 599: 596: 592: 591: 588: 584: 583: 580: 576: 575: 572: 568: 567: 564: 560: 559: 556: 552: 551: 548: 544: 543: 540: 536: 535: 532: 528: 527: 524: 520: 519: 516: 512: 511: 508: 504: 503: 500: 496: 495: 482: 478: 467: 456: 436: 433: 425:Magnus Carlsen 421: 420: 417:Magnus Carlsen 413: 410: 403: 396: 385: 378: 367: 366: 363: 360: 357: 354: 330: 327: 289: 286: 202: 199: 127: 124: 47:zero-sum games 26: 9: 6: 4: 3: 2: 14682: 14671: 14668: 14666: 14663: 14662: 14660: 14645: 14642: 14640: 14635: 14630: 14629: 14626: 14620: 14619:Solving chess 14617: 14615: 14612: 14610: 14609:Chess prodigy 14607: 14603: 14600: 14598: 14595: 14594: 14593: 14592:Chess problem 14590: 14586: 14583: 14581: 14578: 14576: 14573: 14571: 14568: 14567: 14566: 14563: 14561: 14558: 14556: 14553: 14551: 14548: 14546: 14543: 14542: 14540: 14536: 14530: 14527: 14525: 14522: 14520: 14517: 14513: 14512: 14508: 14506: 14503: 14501: 14500:opening books 14498: 14497: 14496: 14493: 14489: 14488:short stories 14486: 14484: 14481: 14479: 14476: 14474: 14471: 14469: 14466: 14464: 14461: 14460: 14459: 14456: 14454: 14451: 14449: 14446: 14445: 14443: 14441:Art and media 14439: 14431: 14428: 14426: 14423: 14421: 14418: 14416: 14413: 14411: 14408: 14406: 14403: 14402: 14400: 14396: 14393: 14391: 14388: 14386: 14383: 14381: 14378: 14376: 14373: 14371: 14368: 14366: 14363: 14361: 14358: 14356: 14353: 14351: 14348: 14347: 14345: 14341: 14338: 14336: 14333: 14331: 14328: 14326: 14323: 14322: 14321: 14318: 14314: 14311: 14310: 14309: 14306: 14304: 14301: 14300: 14298: 14296: 14292: 14286: 14283: 14281: 14278: 14276: 14273: 14271: 14268: 14266: 14263: 14259: 14256: 14254: 14253:triangulation 14251: 14249: 14248:Tarrasch rule 14246: 14244: 14241: 14239: 14236: 14235: 14233: 14229: 14226: 14224: 14221: 14220: 14219: 14216: 14214: 14211: 14209: 14208:Queen vs pawn 14206: 14204: 14201: 14199: 14196: 14194: 14191: 14189: 14186: 14184: 14181: 14180: 14178: 14176: 14172: 14160: 14157: 14155: 14152: 14150: 14147: 14146: 14145: 14142: 14140: 14137: 14133: 14130: 14129: 14128: 14125: 14124: 14122: 14118: 14112: 14109: 14107: 14104: 14100: 14097: 14095: 14092: 14090: 14087: 14085: 14082: 14080: 14077: 14076: 14075: 14072: 14070: 14067: 14065: 14064:London System 14062: 14058: 14055: 14053: 14050: 14048: 14045: 14043: 14040: 14038: 14035: 14033: 14030: 14028: 14025: 14023: 14022:Modern Benoni 14020: 14018: 14015: 14014: 14013: 14010: 14008: 14005: 14003: 14002:Dutch Defence 14000: 13998: 13995: 13993: 13990: 13989: 13987: 13985: 13981: 13973: 13970: 13968: 13965: 13963: 13959: 13956: 13954: 13951: 13950: 13949: 13946: 13944: 13941: 13937: 13934: 13933: 13932: 13929: 13927: 13924: 13920: 13917: 13915: 13912: 13910: 13907: 13905: 13902: 13900: 13897: 13895: 13892: 13890: 13887: 13885: 13882: 13880: 13879:King's Gambit 13877: 13875: 13872: 13870: 13867: 13865: 13862: 13861: 13860: 13857: 13855: 13852: 13850: 13847: 13845: 13842: 13840: 13837: 13835: 13832: 13831: 13829: 13827: 13823: 13815: 13812: 13810: 13807: 13806: 13805: 13802: 13800: 13797: 13795: 13794:Grob's Attack 13792: 13790: 13787: 13785: 13784:Dunst Opening 13782: 13780: 13777: 13775: 13774:Benko Opening 13772: 13771: 13769: 13767: 13766:Flank opening 13763: 13760: 13758: 13754: 13748: 13745: 13743: 13740: 13738: 13735: 13731: 13728: 13726: 13723: 13721: 13718: 13716: 13713: 13712: 13711: 13708: 13706: 13703: 13699: 13696: 13695: 13694: 13691: 13687: 13684: 13683: 13682: 13679: 13677: 13674: 13673: 13671: 13669: 13665: 13659: 13656: 13654: 13651: 13649: 13646: 13644: 13641: 13639: 13636: 13632: 13629: 13628: 13627: 13624: 13622: 13619: 13617: 13614: 13612: 13609: 13607: 13604: 13602: 13599: 13597: 13594: 13592: 13589: 13587: 13584: 13582: 13579: 13577: 13574: 13572: 13569: 13567: 13564: 13562: 13559: 13555: 13552: 13551: 13550: 13547: 13545: 13542: 13541: 13539: 13537: 13533: 13527: 13524: 13522: 13521:Transposition 13519: 13517: 13514: 13512: 13509: 13505: 13502: 13500: 13497: 13495: 13492: 13490: 13487: 13485: 13482: 13481: 13480: 13477: 13475: 13472: 13468: 13465: 13464: 13463: 13460: 13458: 13455: 13453: 13450: 13448: 13445: 13443: 13440: 13436: 13433: 13431: 13428: 13426: 13423: 13421: 13418: 13416: 13413: 13412: 13411: 13408: 13406: 13403: 13402: 13400: 13398: 13394: 13388: 13385: 13383: 13380: 13376: 13373: 13372: 13371: 13368: 13366: 13363: 13361: 13360: 13356: 13352: 13349: 13347: 13344: 13342: 13339: 13337: 13334: 13332: 13329: 13328: 13327: 13324: 13322: 13319: 13317: 13314: 13312: 13309: 13307: 13304: 13303: 13301: 13299: 13295: 13287: 13284: 13282: 13279: 13277: 13274: 13273: 13272: 13271:Chess museums 13269: 13267: 13264: 13260: 13257: 13255: 13252: 13250: 13247: 13246: 13245: 13242: 13240: 13239:Notable games 13237: 13233: 13230: 13226: 13223: 13221: 13218: 13217: 13216: 13213: 13211: 13208: 13204: 13201: 13200: 13199: 13196: 13195: 13194: 13191: 13187: 13184: 13182: 13179: 13177: 13174: 13172: 13169: 13167: 13164: 13162: 13159: 13157: 13156: 13152: 13150: 13149: 13145: 13144: 13143: 13140: 13139: 13137: 13135: 13131: 13124: 13118: 13116: 13113: 13111: 13108: 13104: 13101: 13099: 13096: 13094: 13091: 13089: 13086: 13084: 13081: 13079: 13076: 13074: 13071: 13070: 13069: 13066: 13062: 13059: 13057: 13054: 13052: 13049: 13048: 13047: 13044: 13043: 13041: 13039: 13035: 13029: 13028:World records 13026: 13022: 13019: 13018: 13017: 13014: 13010: 13007: 13005: 13002: 13001: 13000: 12999:Rating system 12997: 12991: 12988: 12987: 12986: 12983: 12981: 12978: 12977: 12976: 12973: 12971: 12968: 12966: 12963: 12961: 12958: 12954: 12951: 12949: 12946: 12944: 12941: 12939: 12936: 12935: 12934: 12931: 12927: 12924: 12923: 12922: 12919: 12917: 12914: 12913: 12911: 12909: 12905: 12901: 12894: 12889: 12887: 12882: 12880: 12875: 12874: 12871: 12859: 12856: 12854: 12851: 12849: 12846: 12844: 12841: 12839: 12836: 12834: 12831: 12829: 12826: 12824: 12821: 12819: 12818:Mark Glickman 12816: 12815: 12813: 12809: 12803: 12800: 12798: 12795: 12793: 12790: 12788: 12785: 12783: 12780: 12778: 12775: 12774: 12772: 12768: 12758: 12755: 12753: 12750: 12748: 12745: 12743: 12740: 12738: 12735: 12734: 12732: 12729: 12725: 12719: 12716: 12714: 12711: 12709: 12706: 12704: 12701: 12699: 12696: 12694: 12691: 12689: 12686: 12684: 12681: 12679: 12676: 12674: 12671: 12669: 12666: 12665: 12663: 12659: 12653: 12650: 12648: 12645: 12643: 12640: 12638: 12635: 12634: 12632: 12628: 12624: 12617: 12612: 12610: 12605: 12603: 12598: 12597: 12594: 12588: 12585: 12584: 12574: 12570: 12566: 12565: 12555: 12549: 12545: 12541: 12537: 12536: 12524: 12520: 12517: 12515: 12508: 12494: 12490: 12484: 12470: 12466: 12460: 12451: 12446: 12439: 12424: 12423: 12418: 12411: 12396: 12395: 12390: 12386: 12379: 12371: 12367: 12363: 12359: 12358: 12353: 12347: 12332: 12331: 12326: 12320: 12306:on 2017-08-19 12305: 12301: 12297: 12291: 12280:September 16, 12275: 12271: 12265: 12254:September 16, 12249: 12245: 12239: 12228:September 16, 12223: 12219: 12213: 12202:September 16, 12197: 12193: 12187: 12173:on 2020-11-05 12172: 12167: 12162: 12158: 12154: 12150: 12146: 12142: 12138: 12134: 12127: 12119: 12115: 12111: 12107: 12103: 12099: 12095: 12091: 12084: 12077: 12073: 12070: 12065: 12050: 12046: 12040: 12025: 12021: 12015: 12000: 11996: 11990: 11976:on 2012-03-01 11975: 11971: 11965: 11951:on 2017-11-05 11950: 11946: 11940: 11925: 11921: 11917: 11911: 11896: 11890: 11874: 11870: 11864: 11849: 11845: 11841: 11835: 11829: 11825: 11809: 11805: 11799: 11785:on 2010-09-23 11784: 11780: 11774: 11758: 11754: 11750: 11744: 11729: 11725: 11719: 11705: 11701: 11695: 11680: 11676: 11672: 11666: 11657: 11653: 11646: 11642: 11635: 11629: 11625: 11622: 11620:May 21, 2015. 11619: 11613: 11605: 11601: 11597: 11590: 11576:on 2018-06-12 11572: 11565: 11559: 11544: 11538: 11522: 11518: 11512: 11496: 11492: 11488: 11484: 11477: 11462: 11458: 11452: 11438:on 2006-08-22 11437: 11433: 11429: 11423: 11407: 11403: 11399: 11392: 11376: 11372: 11366: 11352:on 2019-11-14 11351: 11347: 11343: 11337: 11328: 11313: 11309: 11305: 11299: 11292: 11288: 11284: 11281: 11276: 11274: 11272: 11255: 11251: 11244: 11229: 11225: 11221: 11217: 11213: 11208: 11203: 11199: 11195: 11191: 11184: 11169: 11165: 11159: 11157: 11140: 11136: 11135:chessbase.com 11132: 11125: 11123: 11106: 11102: 11096: 11094: 11077: 11073: 11067: 11065: 11049: 11045: 11039: 11032: 11029: 11025: 11022: 11017: 11009: 11005: 11001: 10997: 10993: 10989: 10985: 10981: 10977: 10970: 10962: 10958: 10954: 10950: 10946: 10942: 10938: 10934: 10930: 10923: 10921: 10919: 10909: 10904: 10897: 10883:on 2012-03-13 10882: 10878: 10877:Chessclub.com 10874: 10872: 10864: 10850:on 2012-05-13 10849: 10845: 10841: 10837: 10831: 10816: 10812: 10808: 10802: 10787: 10783: 10779: 10775: 10769: 10767: 10751: 10747: 10746:chessbase.com 10743: 10740:Sonas, Jeff. 10735: 10726: 10718: 10712: 10703: 10694: 10689: 10685: 10681: 10677: 10670: 10661: 10656: 10652: 10648: 10644: 10637: 10629: 10625: 10621: 10617: 10613: 10609: 10602: 10594: 10590: 10586: 10582: 10578: 10574: 10570: 10566: 10559: 10550: 10543: 10539: 10535: 10532: 10527: 10520: 10516: 10513: 10508: 10502: 10498: 10495: 10490: 10475: 10471: 10467: 10460: 10453: 10449: 10446: 10442: 10438: 10435: 10431: 10427: 10424: 10420: 10416: 10413: 10407: 10388: 10381: 10375: 10373: 10363: 10348: 10344: 10340: 10336: 10330: 10328: 10320: 10315: 10308: 10300: 10293: 10284: 10275: 10266: 10251: 10247: 10241: 10233: 10229: 10225: 10224: 10216: 10209: 10200: 10192: 10188: 10184: 10183: 10175: 10168: 10150: 10143: 10136: 10130: 10125: 10108: 10101:(8): 242–247. 10100: 10096: 10095: 10087: 10080: 10078: 10073: 10055:in Hungarian. 10051: 10045: 10039: 10032: 10009: 9986: 9982: 9971: 9968: 9966: 9963: 9962: 9956: 9953: 9949: 9945: 9941: 9940: 9929: 9927: 9921: 9919: 9914: 9912: 9908: 9905:The YouTuber 9903: 9901: 9896: 9894: 9890: 9886: 9881: 9879: 9874: 9872: 9862: 9860: 9856: 9851: 9849: 9848: 9843: 9838: 9834: 9833: 9828: 9827: 9822: 9817: 9815: 9811: 9807: 9803: 9799: 9798: 9793: 9792: 9787: 9786: 9781: 9780: 9775: 9774: 9768: 9767: 9762: 9758: 9754: 9753: 9748: 9745:professional 9744: 9740: 9739: 9734: 9730: 9726: 9716: 9714: 9710: 9707:, historical 9706: 9702: 9698: 9693: 9691: 9686: 9684: 9679: 9677: 9672: 9670: 9666: 9662: 9657: 9655: 9651: 9646: 9644: 9640: 9636: 9631: 9629: 9624: 9622: 9618: 9614: 9610: 9605: 9603: 9599: 9595: 9591: 9587: 9583: 9579: 9574: 9572: 9568: 9567: 9562: 9558: 9554: 9550: 9546: 9542: 9538: 9536: 9523: 9522: 9517: 9516: 9511: 9508:. Similarly, 9507: 9502: 9497: 9493: 9492: 9487: 9483: 9480: 9476: 9472: 9468: 9467: 9463: 9460: 9456: 9452: 9448: 9444: 9440: 9439: 9435: 9432: 9428: 9427: 9423: 9422: 9411: 9409: 9404: 9402: 9397: 9392: 9388: 9384: 9380: 9371: 9367: 9362: 9355: 9348: 9336: 9332: 9328: 9325: 9320: 9316: 9313: 9309: 9304: 9300: 9298: 9259: 9245: 9236: 9232: 9228: 9218: 9215: 9207: 9197: 9193: 9189: 9183: 9182: 9178: 9173:This section 9171: 9167: 9162: 9161: 9153: 9151: 9150: 9145: 9140: 9138: 9122: 9108: 9105: 9102: 9076: 9070: 9067: 9059: 9055: 9051: 9048: 9044: 9040: 9037: 9033: 9028: 9020: 9016: 9012: 9008: 9004: 9001: 8998: 8993: 8989: 8985: 8982: 8978: 8972: 8969: 8964: 8960: 8956: 8952: 8945: 8939: 8936: 8933: 8927: 8920: 8919: 8918: 8904: 8901: 8898: 8878: 8875: 8872: 8849: 8843: 8840: 8834: 8831: 8828: 8822: 8802: 8799: 8796: 8787: 8756: 8749: 8746: 8735: 8711: 8708: 8691: 8684: 8681: 8670: 8632: 8622: 8619: 8608: 8572: 8568: 8551: 8541: 8538: 8527: 8512: 8504: 8503: 8502: 8478: 8475: 8458: 8451: 8448: 8446: 8433: 8430: 8413: 8409: 8403: 8397: 8394: 8377: 8370: 8365: 8362: 8359: 8353: 8350: 8333: 8326: 8323: 8321: 8289: 8286: 8259: 8257: 8235: 8225: 8214: 8213: 8212: 8211:We note that 8209: 8181: 8177: 8174: 8163: 8159: 8148: 8144: 8127: 8096: 8093: 8076: 8069: 8066: 8049: 8039: 8036: 8025: 8010: 8002: 8001: 8000: 7978: 7968: 7930: 7927: 7910: 7862: 7859: 7842: 7794: 7791: 7774: 7763:. Of course, 7750: 7747: 7744: 7733: 7729: 7712: 7688: 7684: 7680: 7677: 7674: 7671: 7668: 7665: 7662: 7633: 7630: 7613: 7606: 7603: 7586: 7576: 7573: 7562: 7547: 7539: 7538: 7537: 7516: 7506: 7489: 7486: 7483: 7477: 7474: 7471: 7468: 7462: 7459: 7456: 7453: 7447: 7427: 7424: 7421: 7418: 7407: 7403: 7392: 7364: 7360: 7353: 7350: 7333: 7326: 7323: 7320: 7317: 7314: 7303: 7298: 7292: 7288: 7285: 7282: 7279: 7273: 7270: 7268: 7259: 7252: 7249: 7232: 7225: 7219: 7216: 7213: 7202: 7195: 7186: 7183: 7166: 7159: 7156: 7153: 7144: 7141: 7138: 7127: 7119: 7113: 7109: 7106: 7103: 7100: 7094: 7091: 7089: 7084: 7070: 7043: 7042: 7041: 7019: 6995: 6987: 6983: 6979: 6975: 6971: 6968: 6965: 6960: 6956: 6952: 6949: 6945: 6939: 6935: 6931: 6928: 6923: 6919: 6915: 6911: 6904: 6898: 6895: 6892: 6886: 6879: 6878: 6877: 6853: 6850: 6847: 6841: 6838: 6835: 6827: 6823: 6820: 6817: 6814: 6808: 6802: 6799: 6796: 6790: 6787: 6784: 6778: 6756: 6755: 6754: 6737: 6734: 6731: 6725: 6722: 6719: 6710: 6672: 6669: 6666: 6622: 6619: 6608: 6576: 6561: 6558: 6547: 6523: 6520: 6517: 6514: 6511: 6505: 6502: 6485: 6481: 6475: 6472: 6469: 6463: 6458: 6455: 6450: 6439: 6432: 6426: 6423: 6406: 6399: 6396: 6393: 6387: 6382: 6379: 6374: 6363: 6356: 6353: 6350: 6343: 6342: 6341: 6317: 6282: 6279: 6262: 6258: 6252: 6249: 6246: 6241: 6238: 6233: 6227: 6224: 6207: 6200: 6197: 6194: 6189: 6186: 6181: 6178: 6175: 6172: 6169: 6162: 6127: 6124: 6107: 6103: 6097: 6094: 6091: 6088: 6081: 6046: 6043: 6026: 6019: 6016: 6013: 6010: 6004: 5999: 5996: 5989: 5988: 5987: 5985: 5980: 5966: 5962: 5958: 5955: 5951: 5948: 5924: 5915: 5912: 5907: 5889: 5885: 5881: 5877: 5874: 5870: 5865: 5857: 5853: 5835: 5830: 5826: 5821: 5817: 5799: 5795: 5791: 5784: 5780: 5762: 5757: 5751: 5745: 5742: 5725: 5718: 5715: 5682: 5681: 5680: 5666: 5663: 5660: 5640: 5637: 5634: 5606: 5602: 5598: 5594: 5590: 5587: 5584: 5579: 5575: 5571: 5568: 5564: 5557: 5553: 5549: 5545: 5539: 5533: 5530: 5527: 5521: 5514: 5513: 5512: 5495: 5487: 5484: 5467: 5463: 5457: 5451: 5448: 5431: 5424: 5419: 5416: 5383: 5382: 5367: 5361: 5358: 5341: 5337: 5331: 5328: 5295: 5294: 5279: 5273: 5270: 5253: 5246: 5243: 5210: 5209: 5208: 5206: 5201: 5197: 5175: 5146: 5101: 5098: 5087: 5066: 5063: 5052: 5031: 5028: 5017: 4976: 4972: 4961: 4954: 4951: 4940: 4925: 4917: 4916: 4915: 4893: 4883: 4852: 4845: 4842: 4831: 4786: 4783: 4772: 4727: 4724: 4713: 4692: 4672: 4652: 4648: 4644: 4641: 4638: 4635: 4632: 4629: 4595: 4591: 4580: 4573: 4570: 4559: 4544: 4536: 4535: 4534: 4510: 4461: 4454: 4451: 4448: 4437: 4383: 4379: 4373: 4370: 4367: 4356: 4349: 4333: 4325: 4324: 4323: 4309: 4306: 4303: 4289: 4262: 4231: 4228: 4214: 4187: 4153: 4150: 4144: 4139: 4135: 4132: 4129: 4123: 4117: 4111: 4108: 4105: 4099: 4075: 4061: 4026: 4013: 4000: 3997: 3986: 3971: 3963: 3962: 3935: 3922: 3909: 3906: 3895: 3880: 3872: 3871: 3870: 3868: 3842: 3793: 3789: 3783: 3780: 3777: 3774: 3767: 3718: 3711: 3708: 3705: 3702: 3696: 3691: 3688: 3681: 3680: 3679: 3677: 3658: 3638: 3634: 3628: 3625: 3605: 3598: 3595: 3592: 3589: 3556: 3555: 3554: 3553: 3537: 3534: 3531: 3497: 3493: 3482: 3475: 3458: 3450: 3449: 3448: 3431: 3423: 3419: 3415: 3412: 3408: 3404: 3401: 3397: 3392: 3386: 3380: 3376: 3356: 3349: 3346: 3313: 3312: 3311: 3285: 3281: 3277: 3273: 3268: 3260: 3257: 3248: 3230: 3214: 3211: 3208: 3200: 3199: 3195: 3179: 3176: 3173: 3165: 3164: 3160: 3143: 3140: 3137: 3129: 3128: 3124: 3118: 3117: 3114: 3113: 3112: 3102: 3086: 3083: 3080: 3072: 3071: 3067: 3051: 3048: 3045: 3037: 3036: 3032: 3016: 3013: 3010: 3002: 3001: 2997: 2991: 2990: 2987: 2986: 2985: 2982: 2968: 2952: 2949: 2946: 2938: 2937: 2933: 2917: 2914: 2911: 2903: 2902: 2898: 2882: 2879: 2876: 2868: 2867: 2863: 2857: 2856: 2853: 2852: 2851: 2849: 2845: 2840: 2836: 2830: 2819: 2800: 2797: 2794: 2785: 2771: 2769: 2765: 2755: 2751: 2742: 2731: 2730:Hubbert curve 2726: 2724: 2720: 2715: 2713: 2708: 2706: 2702: 2698: 2694: 2690: 2684: 2665: 2664:points each. 2650: 2644: 2641: 2629: 2628:split the pot 2608: 2591: 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5018:S 5000:. 4988:) 4982:B 4977:E 4967:B 4962:S 4958:( 4955:K 4952:+ 4946:B 4941:R 4931:B 4926:R 4899:B 4894:R 4870:) 4864:B 4861:, 4858:A 4853:r 4849:( 4843:= 4837:A 4832:E 4809:B 4787:0 4784:= 4778:A 4773:S 4750:A 4728:1 4725:= 4719:A 4714:S 4693:s 4653:s 4649:/ 4633:= 4630:K 4607:) 4601:A 4596:E 4586:A 4581:S 4577:( 4574:K 4571:+ 4565:A 4560:R 4550:A 4545:R 4511:, 4496:B 4479:) 4473:B 4470:, 4467:A 4462:r 4458:( 4452:K 4443:A 4438:R 4418:A 4401:) 4395:B 4392:, 4389:A 4384:r 4377:( 4371:K 4368:+ 4362:A 4357:R 4350:{ 4339:A 4334:R 4310:1 4304:= 4295:B 4290:R 4284:d 4274:B 4271:, 4268:A 4263:r 4257:d 4232:1 4229:= 4220:A 4215:R 4209:d 4199:B 4196:, 4193:A 4188:r 4182:d 4157:) 4154:r 4148:( 4140:s 4124:= 4121:) 4118:r 4115:( 4100:r 4095:d 4088:d 4050:. 4032:B 4027:R 4021:d 4009:d 3992:B 3987:R 3977:B 3972:R 3959:, 3941:A 3936:R 3930:d 3918:d 3901:A 3896:R 3886:A 3881:R 3843:, 3828:B 3811:) 3805:B 3802:, 3799:A 3794:r 3787:( 3768:, 3753:A 3736:) 3730:B 3727:, 3724:A 3719:r 3715:( 3697:{ 3692:= 3659:. 3656:) 3650:B 3647:, 3644:A 3639:r 3632:( 3626:= 3623:) 3617:B 3614:, 3611:A 3606:r 3602:( 3593:1 3590:= 3587:} 3572:B 3567:{ 3535:= 3532:s 3509:) 3503:B 3498:R 3488:A 3483:R 3479:( 3476:= 3470:B 3467:, 3464:A 3459:r 3432:, 3424:s 3420:/ 3416:r 3405:+ 3402:1 3398:1 3393:= 3390:) 3387:r 3384:( 3377:, 3374:) 3368:B 3365:, 3362:A 3357:r 3353:( 3347:= 3344:} 3329:A 3324:{ 3296:A 3252:K 3245:K 3241:K 3212:= 3209:K 3177:= 3174:K 3141:= 3138:K 3120:K 3084:= 3081:K 3049:= 3046:K 3014:= 3011:K 2993:K 2979:K 2950:= 2947:K 2915:= 2912:K 2880:= 2877:K 2859:K 2835:K 2827:K 2823:K 2816:K 2798:= 2795:K 2780:K 2750:X 2745:X 2683:. 2677:A 2673:A 2669:A 2651:K 2645:2 2642:1 2624:K 2620:K 2616:K 2596:A 2572:. 2566:) 2560:A 2555:E 2545:A 2540:S 2536:( 2530:K 2527:+ 2521:A 2516:R 2512:= 2503:A 2498:R 2470:A 2465:S 2439:A 2434:E 2409:A 2404:R 2393:A 2372:= 2369:K 2344:= 2341:K 2326:B 2308:B 2303:Q 2298:/ 2291:A 2286:Q 2274:A 2260:. 2254:1 2251:= 2245:B 2240:E 2236:+ 2230:A 2225:E 2203:. 2191:/ 2184:B 2179:R 2170:= 2164:B 2159:Q 2137:, 2127:/ 2120:A 2115:R 2106:= 2100:A 2095:Q 2070:, 2058:B 2053:Q 2049:+ 2043:A 2038:Q 2030:B 2025:Q 2019:= 2013:B 2008:E 1975:B 1970:Q 1966:+ 1960:A 1955:Q 1947:A 1942:Q 1936:= 1930:A 1925:E 1898:. 1883:/ 1879:) 1873:B 1868:R 1858:A 1853:R 1849:( 1841:+ 1838:1 1834:1 1829:= 1823:B 1818:E 1804:B 1787:. 1772:/ 1768:) 1762:A 1757:R 1747:B 1742:R 1738:( 1730:+ 1727:1 1723:1 1718:= 1712:A 1707:E 1693:A 1667:B 1662:R 1650:B 1632:A 1627:R 1615:A 1552:R 1548:N 1525:D 1521:N 1498:W 1494:N 1470:} 1464:, 1459:R 1455:N 1451:+ 1446:D 1442:N 1438:2 1435:+ 1430:W 1426:N 1422:4 1419:+ 1413:{ 1404:= 1401:F 1398:A 1362:m 1359:+ 1354:e 1350:N 1340:= 1337:K 1324:m 1318:e 1314:N 1193:p 1189:d 1168:p 1148:p 1126:p 1122:d 1101:, 1096:p 1092:d 1088:+ 1080:= 1043:= 1038:1 1034:) 1031:0 1028:( 1019:+ 1010:= 976:= 971:2 967:) 964:2 961:( 952:+ 943:= 909:= 904:1 900:) 897:1 894:( 885:+ 876:= 839:) 823:( 814:+ 803:= 766:4 762:) 759:2 756:( 747:) 744:2 741:( 735:+ 732:z 729:+ 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