853:). Odds as a ratio, odds as a number, and probability (also a number) are related by simple formulas, and similarly odds in favor and odds against, and probability of success and probability of failure have simple relations. Odds range from 0 to infinity, while probabilities range from 0 to 1, and hence are often represented as a percentage between 0% and 100%: reversing the ratio switches odds for with odds against, and similarly probability of success with probability of failure.
656:
2464:, fractional odds quote the net total that will be paid out to the bettor, should they win, relative to the stake. Odds of 4/1 would imply that the bettor stands to make a £400 profit on a £100 stake. If the odds are 1/4, the bettor will make £25 on a £100 stake. In either case, having won, the bettor always receives the original stake back; so if the odds are 4/1 the bettor receives a total of £500 (£400 plus the original £100). Odds of 1/1 are known as
2687:
of his profit is positive even if everybody bets on the same horse. The art of bookmaking is in setting the odds low enough so as to have a positive expected value of profit while keeping the odds high enough to attract customers, and at the same time attracting enough bets for each outcome to reduce
711:
day of the week is during a weekend are two to five (2:5), as days of the week form a sample space of seven outcomes, and the event occurs for two of the outcomes (Saturday and Sunday), and not for the other five. Conversely, given odds as a ratio of integers, this can be represented by a probability
2548:
the original stake, to the stake itself. Therefore, the decimal odds of an outcome are equivalent to the decimal value of the fractional odds plus one. Thus even odds 1/1 are quoted in decimal odds as 2.00. The 4/1 fractional odds discussed above are quoted as 5.00, while the 1/4 odds are quoted as
2432:
between two evenly matched horses, it is reasonable for two people to wager level stakes. However, in more variable situations, such as a multi-runner horse race or a football match between two unequally matched teams, betting "at odds" provides the possibility to take the respective likelihoods of
2366:
In the first example at top, saying the odds of a Sunday are "one to six" or, less commonly, "one-sixth" means the probability of picking a Sunday randomly is one-sixth the probability of not picking a Sunday. While the mathematical probability of an event has a value in the range from zero to one,
2673:
In a 3-horse race, for example, the true probabilities of each of the horses winning based on their relative abilities may be 50%, 40% and 10%. The total of these three percentages is 100%, thus representing a fair 'book'. The true odds against winning for each of the three horses are 1–1, 3–2 and
2553:
betting, because the odds to be paid out are simply the product of the odds for each outcome wagered on. When looking at decimal odds in betting terms, the underdog has the higher of the two decimals, while the favorite has the lower of the two. To calculate decimal odds, you can use the equation
844:
Odds can be expressed as a ratio of two numbers, in which case it is not unique—scaling both terms by the same factor does not change the proportions: 1:1 odds and 100:100 odds are the same (even odds). Odds can also be expressed as a number, by dividing the terms in the ratio—in this case it is
2669:
is less than that represented by the true chance of the event occurring. This profit is known as the 'overround' on the 'book' (the 'book' refers to the old-fashioned ledger in which wagers were recorded, and is the derivation of the term 'bookmaker') and relates to the sum of the 'odds' in the
2682:
of 30 (130−100). This value of 30 represents the amount of profit for the bookmaker if he gets bets in good proportions on each of the horses. For example, if he takes £60, £50, and £20 of stakes, respectively, for the three horses, he receives £130 in wagers but only pays £100 back (including
2677:
In order to generate a profit on the wagers accepted, the bookmaker may decide to increase the values to 60%, 50% and 20% for the three horses, respectively. This represents the odds against each, which are 4–6, 1–1 and 4–1, in order. These values now total 130%, meaning that the book has an
1079:
1794:
2710:
The odds or amounts the bookmaker will pay are determined by the total amount that has been bet on all of the possible events. They reflect the balance of wagers on either side of the event, and include the deduction of a bookmaker's brokerage fee ("vig" or
2691:
A study on soccer betting found that the probability for the home team to win was generally about 3.4% less than the value calculated from the odds (for example, 46.6% for even odds). It was about 3.7% less for wins by the visitors, and 5.7% less for draws.
2602:
When moneyline odds are negative, the figure indicates how much money must be wagered to for a net winning of $ 100 (this is done for an outcome that is considered more probable to happen than not). For example, net winnings of 1/4 would be quoted as
1464:
2695:
To understand roulette probabilities and calculate them, you need to know the formula. You take the numbers your bet is on and divide them by the total number of numbers in roulette (depending on your version of the game). Then you multiply by 100.
1239:
2487:, thus if the bookmaker's payout was to be £1.25 for every £1 stake, this would be equivalent to £5 for every £4 staked, and the odds would therefore be expressed as 5/4. However, not all fractional odds are traditionally read using the
2512:
odds. Fractional and Hong Kong odds are actually exchangeable. The only difference is that the UK odds are presented as a fractional notation (e.g. 6/5) whilst the Hong Kong odds are decimal (e.g. 1.2). Both exhibit the net return.
2356:. That value may be regarded as the relative probability the event will happen, expressed as a fraction (if it is less than 1), or a multiple (if it is equal to or greater than one) of the likelihood that the event will not happen.
2718:
Also, depending on how the betting is affected by jurisdiction, taxes may be involved for the bookmaker and/or the winning player. This may be taken into account when offering the odds and/or may reduce the amount won by a player.
2598:
When moneyline odds are positive, the figure indicates the net winnings for a $ 100 wager (this is done for an outcome that is considered less probable to happen than not). For example, net winnings of 4/1 would be quoted as
2615:. In most cases, the favorite will have negative moneyline odds (less payoff for a safer bet) and the underdog will have positive moneyline odds (more payoff for a risky bet). However, if the teams are evenly matched,
1096:(one), as they are the only possible outcomes. In case of a finite number of equally probable outcomes, this can be interpreted as the number of outcomes where the event occurs divided by the total number of events:
2565:
because they are the easiest to work with for trading, as they reflect the inverse of the probability of an outcome. For example, a quoted odds of 5.00 equals to a probability of 1 / 5.00, that is 0.20 or 20%.
2169:
These transforms have certain special geometric properties: the conversions between odds for and odds against (resp. probability of success with probability of failure) and between odds and probability are all
89:
the possible net loss. However in many situations, you pay the possible loss ("stake" or "wager") up front and, if you win, you are paid the net win plus you also get your stake returned. So wagering 2 at
2664:
will pay out on a winning bet, together with the required stake. In formulating the odds to display the bookmaker will have included a profit margin which effectively means that the payout to a successful
1615:
1285:
1107:
925:
828:) are often used interchangeably to vaguely indicate some measure of odds or probability, though the intended meaning can be deduced by noting whether the preposition between the two numbers is
2182:). Swapping odds for and odds against swaps 0 and infinity, fixing 1, while swapping probability of success with probability of failure swaps 0 and 1, fixing .5; these are both order 2, hence
2210:
of the probability. Most simply, odds are frequently multiplied or divided, and log converts multiplication to addition and division to subtractions. This is particularly important in the
920:
1610:
2505:. They are typically represented with a "/" but can also be represented with a "-", e.g. 4/1 or 4–1. Odds with a denominator of 1 are often presented in listings as the numerator only.
643:
demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes. Implied by this definition is the fact that the probability of an event is given by the
2491:. For example, given that there is a pattern of odds of 5/4, 7/4, 9/4 and so on, odds which are mathematically 3/2 are more easily compared if expressed in the equivalent form 6/4.
712:
space of a finite number of equally probable outcomes. These definitions are equivalent, since dividing both terms in the ratio by the number of outcomes yields the probabilities:
1602:
1280:
2404:
2354:
779:
2561:
For example, if you bet €100 on
Liverpool to beat Manchester City at 2.00 odds the payout, including your stake, would be €200 (€100 × 2.00). Decimal odds are favoured by
1533:
1102:
2660:
In gambling, the odds on display do not represent the true chances (as imagined by the bookmaker) that the event will or will not occur, but are the amount that the
1497:
2646:
is an index of all the prices in a probabilistic market operating at 100% competitiveness and displayed without any profit margin factored for market participants.
1887:
1859:
908:
881:
1272:
1823:). This is a minor difference if the probability is small (close to zero, or "long odds"), but is a major difference if the probability is large (close to one).
1929:
1908:
2930:
2981:
2433:
the possible outcomes into account. The use of odds in gambling facilitates betting on events where the probabilities of different outcomes vary.
2521:
The
European odds also represent the potential winnings (net returns), but in addition they factor in the stake (e.g. 6/5 or 1.2 plus 1 = 2.2).
2175:
856:
Given odds (in favor) as the ratio W:L (number of outcomes that are wins:number of outcomes that are losses), the odds in favor (as a number)
153:
and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied by 100%.
808:—the number of (equally probable) outcomes in favour relative to the number for and against combined. For example, "odds of a weekend are 2
2763:
781:
Conversely, the odds against is the opposite ratio. For example, the odds against a random day of the week being during a weekend are 5:2.
3088:
Lisandro
Kaunitz; et al. (October 2017). "Beating the bookies with their own numbers – and how the sports betting market is rigged".
2186:. Converting odds to probability fixes 0, sends infinity to 1, and sends 1 to .5 (even odds are 50% probable), and conversely; this is a
675:
is the ratio of the probability that the event will happen to the probability that the event will not happen. Mathematically, this is a
1799:
Thus if expressed as a fraction with a numerator of 1, probability and odds differ by exactly 1 in the denominator: a probability of 1
2955:
3029:
3003:
2240:
Odds are particularly useful in problems of sequential decision making, as for instance in problems of how to stop (online) on a
2855:
2440:, and an individual, rather than between individuals. Different traditions have grown up in how to express odds to customers.
2748:
2367:"the odds" in favor of that same event lie between zero and infinity. The odds against the event with probability given as
2627:
Wholesale odds are the "real odds" or 100% probability of an event occurring. This 100% book is displayed without any
2406:. The odds against Sunday are 6:1 or 6/1 = 6. It is 6 times as probable that a random day is not a Sunday.
2202:
and statistics, odds and similar ratios may be more natural or more convenient than probabilities. In some cases the
1074:{\displaystyle {\begin{aligned}o_{f}&=W/L=1/o_{a}\\o_{a}&=L/W=1/o_{f}\\o_{f}\cdot o_{a}&=1\end{aligned}}}
2290:
There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble?
1789:{\displaystyle {\begin{aligned}p&=o_{f}/(o_{f}+1)=1/(o_{a}+1)\\q&=o_{a}/(o_{a}+1)=1/(o_{f}+1)\end{aligned}}}
800:—the ratio of numbers of (equally probable) outcomes in favor and against (or vice versa); "chances of so many ,
17:
691:
where the event occurs to the number of outcomes where the event does not occur; these can be represented as
1459:{\displaystyle {\begin{aligned}o_{f}&=p/q=p/(1-p)=(1-q)/q\\o_{a}&=q/p=(1-p)/p=q/(1-q)\end{aligned}}}
2259:
is a ratio of odds, that is, a ratio of ratios of probabilities. Odds-ratios are often used in analysis of
3057:"Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds"
2797:
1538:
3136:
2982:"Understanding Betting Odds – Moneyline, Fractional Odds, Decimal Odds, Hong Kong Odds, IN Odds, MA Odds"
2179:
1274:(probability of success to probability of failure), and the odds as numbers can be computed by dividing:
2704:
668:
2594:
Moneyline odds are favoured by
American bookmakers. The figure quoted is either positive or negative.
2374:
2324:
2294:
Answer: The odds in favour of a blue marble are 2:13. One can equivalently say that the odds are 13:2
715:
2679:
2655:
2611:. A "moneyline" wager refers to odds on the straight-up outcome of a game with no consideration to a
2488:
149:. When probability is expressed as a number between 0 and 1, the relationships between probability
2226:
2619:
teams can have a negative line at the same time (e.g. −110 −110 or −105 −115), due to house take.
2171:
684:
2436:
In the modern era, most fixed-odd betting takes place between a betting organisation, such as a
1234:{\displaystyle {\begin{aligned}p&=W/(W+L)=1-q\\q&=L/(W+L)=1-p\\p+q&=1\end{aligned}}}
2707:
are often used by professional and semi-professional sports bettors to help achieve this goal.
911:
846:
2882:
1502:
1092:
can be computed by dividing, and the probability of success and probability of failure sum to
663:
In statistics, odds are an expression of relative probabilities, generally quoted as the odds
472:
and these can be scaled to equivalent odds. Similarly, fair betting odds can be expressed as
2264:
688:
1472:
3007:
2959:
2908:
2743:
1865:
1837:
886:
859:
8:
3131:
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2187:
1251:
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622:
60:
provide a measure of the probability of a particular outcome. Odds are commonly used in
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2419:
2415:
2302:
2215:
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2183:
1914:
1893:
604:
53:
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2703:
involves predicting the relationship of the true probabilities to the payout odds.
2222:
640:
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estimated risks, is found in the sixteenth century, well before the development of
46:
31:
2317:
in favor of a binary event, and the probability against the event is therefore 1-
850:
708:
676:
68:. For example for an event that is 40% probable, one could say that the odds are
2839:
Gelman, Andrew; Carlin, John B.; Stern, Hal S.; Rubin, Donald B. (2003). "1.5".
2799:
Some laws and problems in classical probability and how
Cardano anticipated them
2733:
2684:
2612:
2589:
2453:
2260:
2245:
111:
39:
2298:. There are 2 out of 15 chances in favour of blue, 13 out of 15 against blue.
2221:
Similar ratios are used elsewhere in statistics; of central importance is the
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2738:
2461:
2263:. While they have useful mathematical properties, they can produce counter-
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146:
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The language of odds, such as the use of phrases like "ten to one" for
65:
38:. For playing chess with odds, i.e. with a handicap on one player, see
655:
2931:"Betting School: Understanding Fractional & Decimal Betting Odds"
2661:
2636:
2628:
2541:
2529:
2476:
2449:
2437:
2425:
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results: an event with an 80% probability of occurring is four times
600:
784:
Odds and probability can be expressed in prose via the prepositions
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and similarly if "to" is replaced with "in" or "for". For example,
3094:
2712:
2700:
2203:
637:
82:
61:
27:
Ratio of the probability of an event happening versus not happening
2787:. Baltimore: The Johns Hopkins University Press. pp. 280–281.
1604:
from which the probability of success or failure can be computed:
45:"Odds against" redirects here. For the 1966 documentary film, see
2785:
The
Science of Conjecture: Evidence and Probability Before Pascal
2666:
2484:
2457:
647:
of favourable outcomes to the total number of possible outcomes.
387:(between 0 and 1; not a percentage) can be written as a fraction
30:
This article is about the gambling and statistical term. For the
2537:
2525:
1084:
Analogously, given odds as a ratio, the probability of success
85:, odds are often given as the ratio of the possible net profit
2252:
2207:
644:
2853:
2321:, "the odds" of the event are the quotient of the two, or
280:" means that the bet is a fair bet if the probability is
250:" means that the bet is a fair bet if the probability is
3030:"Understanding Sports betting odds and how to read them"
2749:
Formal mathematical specification of logistic regression
2649:
2271:
to happen than an event with a 20% probability, but the
707:(for Success and Failure). For example, the odds that a
2838:
679:, as it has exactly two outcomes. In case of a finite
2544:, decimal odds quote the ratio of the payout amount,
2377:
2327:
2214:, in which the log-odds of the target variable are a
1917:
1896:
1868:
1840:
1815:
100 (1/100 = 0.01) is the same as a probability of 1
1613:
1541:
1505:
1475:
1283:
1254:
1105:
923:
889:
862:
718:
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are 16 times higher on the less probable event (4–1
128:
When
Moneyline odds are quoted as a negative number
2279:, or 4) than on the more probable one (1–4, or 4–1
2174:(fractional linear transformations). They are thus
325:" means that the bet is fair if the probability is
304:" means that the bet is fair if the probability is
2883:"Odds of Finding Earth-Size Exoplanets Are 1-in-4"
2398:
2348:
1923:
1902:
1881:
1853:
1788:
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1527:
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1073:
902:
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773:
2858:. Multi-State Lottery Association. Archived from
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3087:
3081:
2880:
2815:
2764:Statistical association football predictions
910:can be computed by simply dividing, and are
617:That if we wrought out life 'twas ten to one
615:Knew that we ventured on such dangerous seas
2791:
2508:A variation of fractional odds is known as
1826:These are worked out for some simple odds:
2996:
1803:100 (1/100 = 1%) is the same as odds of 1
3093:
3072:
2906:
2549:1.25. This is considered to be ideal for
839:
659:Calculation of probability (risk) vs odds
2847:
2607:Moneyline odds are often referred to as
654:
344:The numbers for odds can be scaled. If
190:in favor" means that the probability is
2900:
2776:
2683:stakes), whichever horse wins. And the
1469:Conversely, given the odds as a number
220:against" means that the probability is
14:
3124:
3054:
3048:
2809:
2635:, often referred to as a bookmaker's "
2556:Payout = Initial Wager × Decimal Value
812:5", while "chances of a weekend are 2
2950:
2948:
2909:"Wolfram Alpha (Poker Probabilities)"
2832:
2782:
2650:Gambling odds vis-à-vis probabilities
1499:this can be represented as the ratio
687:, this is the ratio of the number of
145:Odds have a simple relationship with
2958:. World Bet Exchange. Archived from
2874:
1597:{\displaystyle 1:(1/o_{f})=1:o_{a},}
796:so many on (or against) " refers to
650:
2974:
2923:
24:
2945:
2494:Fractional odds are also known as
2443:
383:When the value of the probability
25:
3153:
2881:Lisa Grossman (28 October 2010).
2854:Multi-State Lottery Association.
2622:
2583:
2409:
2399:{\displaystyle {\frac {1-p}{p}}}
2349:{\displaystyle {\frac {p}{1-p}}}
774:{\displaystyle 2:5=(2/7):(5/7).}
397:then the odds can be said to be
165:" means that the probability is
114:are quoted as a positive number
3102:
3022:
2856:"Welcome to Powerball - Prizes"
2569:Decimal odds are also known as
2516:
2193:
1819:101 (1/101 = 0.00990099... = 0.
883:and odds against (as a number)
1779:
1760:
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1177:
1140:
1128:
765:
751:
745:
731:
13:
1:
3061:Journal of Prediction Markets
2769:
2483:of fractional odds are often
816:7". In casual use, the words
631:, Act I, Scene 1, lines 181–2
135:, it means that a wager pays
121:, it means that a wager pays
667:. The odds (in favor) of an
348:is any positive number then
7:
2722:
2705:Sports information services
2218:of the observed variables.
10:
3158:
2843:(2nd ed.). CRC Press.
2818:"Wolfram MathWorld (Odds)"
2653:
2587:
2413:
594:
44:
29:
2656:Mathematics of bookmaking
2489:lowest common denominator
2176:specified by three points
2073:
1807:99 (1/99 = 0.0101... = 0.
699:(for Wins and Losses) or
685:equally probable outcomes
3055:Cortis, Dominic (2015).
2783:James, Franklin (2001).
2524:Favoured in continental
2227:likelihoodist statistics
1528:{\displaystyle o_{f}:1,}
2933:. Goal. 10 January 2011
2244:which is solved by the
2206:are used, which is the
1248:the odds as a ratio is
912:multiplicative inverses
849:can represent the same
2841:Bayesian Data Analysis
2820:. Wolfram Research Inc
2400:
2350:
2172:Möbius transformations
1925:
1904:
1883:
1855:
1790:
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1529:
1493:
1492:{\displaystyle o_{f},}
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1268:
1235:
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904:
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840:Mathematical relations
775:
660:
636:The sixteenth-century
634:
2956:"Betting Odds Format"
2501:or, in that country,
2460:, and also common in
2401:
2351:
2309:, where the variable
2255:of probabilities; an
1926:
1905:
1884:
1882:{\displaystyle o_{a}}
1856:
1854:{\displaystyle o_{f}}
1791:
1599:
1530:
1494:
1461:
1269:
1236:
1076:
905:
903:{\displaystyle o_{a}}
878:
876:{\displaystyle o_{f}}
776:
658:
613:
3074:10.5750/jpm.v9i1.987
2744:Gambling mathematics
2375:
2325:
2180:sharply 3-transitive
1915:
1894:
1866:
1838:
1611:
1539:
1503:
1473:
1281:
1252:
1244:Given a probability
1103:
921:
887:
860:
804:so many " refers to
716:
373:is the same as both
3112:. 21 November 2023.
2816:Wolfram MathWorld.
2699:Making a profit in
2688:his risk exposure.
2674:9–1, respectively.
2642:A "wholesale odds"
2242:last specific event
2231:Bayesian statistics
2229:, which is used in
2188:parabolic transform
2184:circular transforms
1811:), while odds of 1
1267:{\displaystyle p:q}
623:William Shakespeare
3137:Statistical ratios
2862:on 19 October 2015
2759:Parimutuel betting
2420:Parimutuel betting
2416:Fixed-odds betting
2396:
2346:
2303:probability theory
2216:linear combination
2200:probability theory
1921:
1900:
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900:
873:
845:unique (different
771:
661:
605:probability theory
375:"1.5 to 1 against"
102:, which is called
73:"2 to 3 in favor",
54:probability theory
3036:. 25 January 2022
3004:"Fractional Odds"
2579:continental odds.
2563:betting exchanges
2394:
2344:
2167:
2166:
1924:{\displaystyle q}
1903:{\displaystyle p}
792:"odds of so many
651:Statistical usage
628:Henry IV, Part II
379:"6 to 4 against".
77:"3 to 2 against".
16:(Redirected from
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3006:. Archived from
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2503:traditional odds
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1930:
1928:
1927:
1922:
1909:
1907:
1906:
1901:
1888:
1886:
1885:
1880:
1878:
1877:
1860:
1858:
1857:
1852:
1850:
1849:
1829:
1828:
1822:
1810:
1795:
1793:
1792:
1787:
1785:
1772:
1771:
1759:
1739:
1738:
1726:
1721:
1720:
1688:
1687:
1675:
1655:
1654:
1642:
1637:
1636:
1603:
1601:
1600:
1595:
1590:
1589:
1568:
1567:
1558:
1534:
1532:
1531:
1526:
1515:
1514:
1498:
1496:
1495:
1490:
1485:
1484:
1465:
1463:
1462:
1457:
1455:
1436:
1422:
1396:
1381:
1380:
1364:
1326:
1312:
1297:
1296:
1273:
1271:
1270:
1265:
1240:
1238:
1237:
1232:
1230:
1176:
1127:
1091:
1087:
1080:
1078:
1077:
1072:
1070:
1056:
1055:
1043:
1042:
1029:
1028:
1019:
1005:
990:
989:
976:
975:
966:
952:
937:
936:
909:
907:
906:
901:
899:
898:
882:
880:
879:
874:
872:
871:
780:
778:
777:
772:
761:
741:
632:
591:
589:
571:
569:
553:
551:
547:
542:
540:
536:
525:
523:
510:
508:
496:
494:
486:
484:
471:
469:
465:
453:
451:
441:
436:
434:
430:
425:
423:
411:
409:
396:
386:
380:
376:
372:
371:"3 to 2 against"
368:
366:
362:
357:
356:
352:
347:
339:
324:
314:
303:
293:
279:
275:
268:
249:
245:
238:
219:
215:
208:
189:
185:
178:
164:
160:
152:
142:
140:
134:
127:
125:
120:
109:
101:
97:
78:
74:
71:
47:The Odds Against
32:alternative rock
21:
3157:
3156:
3152:
3151:
3150:
3148:
3147:
3146:
3122:
3121:
3118:
3117:
3108:
3107:
3103:
3086:
3082:
3053:
3049:
3039:
3037:
3028:
3027:
3023:
3013:
3011:
3010:on 2 April 2014
3002:
3001:
2997:
2987:
2985:
2980:
2979:
2975:
2965:
2963:
2954:
2953:
2946:
2936:
2934:
2929:
2928:
2924:
2914:
2912:
2911:. Wolfram Alpha
2907:Wolfram Alpha.
2905:
2901:
2891:
2889:
2879:
2875:
2865:
2863:
2852:
2848:
2837:
2833:
2823:
2821:
2814:
2810:
2796:
2792:
2781:
2777:
2772:
2725:
2670:following way:
2658:
2652:
2625:
2592:
2586:
2519:
2446:
2444:Fractional odds
2422:
2412:
2380:
2378:
2376:
2373:
2372:
2333:
2328:
2326:
2323:
2322:
2261:clinical trials
2251:The odds are a
2196:
2160:
2153:
2130:
2115:
2108:
2085:
2032:
2025:
2007:
2000:
1916:
1913:
1912:
1895:
1892:
1891:
1873:
1869:
1867:
1864:
1863:
1845:
1841:
1839:
1836:
1835:
1820:
1808:
1783:
1782:
1767:
1763:
1755:
1734:
1730:
1722:
1716:
1712:
1705:
1699:
1698:
1683:
1679:
1671:
1650:
1646:
1638:
1632:
1628:
1621:
1614:
1612:
1609:
1608:
1585:
1581:
1563:
1559:
1554:
1540:
1537:
1536:
1510:
1506:
1504:
1501:
1500:
1480:
1476:
1474:
1471:
1470:
1453:
1452:
1432:
1418:
1392:
1382:
1376:
1372:
1369:
1368:
1360:
1322:
1308:
1298:
1292:
1288:
1284:
1282:
1279:
1278:
1253:
1250:
1249:
1228:
1227:
1217:
1205:
1204:
1172:
1162:
1156:
1155:
1123:
1113:
1106:
1104:
1101:
1100:
1089:
1085:
1068:
1067:
1057:
1051:
1047:
1038:
1034:
1031:
1030:
1024:
1020:
1015:
1001:
991:
985:
981:
978:
977:
971:
967:
962:
948:
938:
932:
928:
924:
922:
919:
918:
894:
890:
888:
885:
884:
867:
863:
861:
858:
857:
851:rational number
842:
757:
737:
717:
714:
713:
709:randomly chosen
677:Bernoulli trial
653:
633:
621:
616:
597:
575:
573:
556:
554:
549:
545:
543:
538:
528:
526:
513:
511:
499:
497:
489:
487:
475:
473:
467:
457:
455:
443:
439:
437:
432:
428:
426:
414:
412:
410:to 1 in favor",
400:
398:
388:
384:
378:
374:
370:
364:
360:
359:
358:is the same as
354:
350:
349:
345:
326:
319:
305:
298:
281:
277:
273:
251:
247:
243:
221:
217:
213:
191:
187:
183:
166:
162:
158:
150:
138:
136:
129:
123:
122:
115:
103:
99:
91:
76:
72:
69:
50:
43:
28:
23:
22:
18:Fractional odds
15:
12:
11:
5:
3155:
3145:
3144:
3139:
3134:
3116:
3115:
3101:
3080:
3047:
3021:
2995:
2973:
2944:
2922:
2899:
2873:
2846:
2831:
2808:
2801:Gorrochum, P.
2790:
2774:
2773:
2771:
2768:
2767:
2766:
2761:
2756:
2751:
2746:
2741:
2736:
2734:Odds algorithm
2731:
2724:
2721:
2685:expected value
2654:Main article:
2651:
2648:
2624:
2623:Wholesale odds
2621:
2605:
2604:
2600:
2590:Moneyline odds
2588:Main article:
2585:
2584:Moneyline odds
2582:
2518:
2515:
2454:United Kingdom
2445:
2442:
2411:
2410:Gambling usage
2408:
2393:
2389:
2386:
2383:
2364:
2363:
2361:
2342:
2339:
2336:
2332:
2292:
2291:
2288:
2246:odds algorithm
2212:logistic model
2195:
2192:
2165:
2164:
2157:
2150:
2147:
2144:
2140:
2139:
2136:
2133:
2127:
2124:
2120:
2119:
2112:
2105:
2102:
2099:
2095:
2094:
2091:
2088:
2082:
2079:
2075:
2074:
2071:
2070:
2067:
2064:
2061:
2058:
2054:
2053:
2050:
2047:
2044:
2041:
2037:
2036:
2029:
2022:
2019:
2016:
2012:
2011:
2004:
1997:
1994:
1991:
1987:
1986:
1983:
1980:
1977:
1972:
1968:
1967:
1964:
1961:
1956:
1953:
1949:
1948:
1945:
1942:
1939:
1936:
1932:
1931:
1920:
1910:
1899:
1889:
1876:
1872:
1861:
1848:
1844:
1833:
1797:
1796:
1781:
1778:
1775:
1770:
1766:
1762:
1758:
1754:
1751:
1748:
1745:
1742:
1737:
1733:
1729:
1725:
1719:
1715:
1711:
1708:
1706:
1704:
1701:
1700:
1697:
1694:
1691:
1686:
1682:
1678:
1674:
1670:
1667:
1664:
1661:
1658:
1653:
1649:
1645:
1641:
1635:
1631:
1627:
1624:
1622:
1620:
1617:
1616:
1593:
1588:
1584:
1580:
1577:
1574:
1571:
1566:
1562:
1557:
1553:
1550:
1547:
1544:
1535:or conversely
1524:
1521:
1518:
1513:
1509:
1488:
1483:
1479:
1467:
1466:
1451:
1448:
1445:
1442:
1439:
1435:
1431:
1428:
1425:
1421:
1417:
1414:
1411:
1408:
1405:
1402:
1399:
1395:
1391:
1388:
1385:
1383:
1379:
1375:
1371:
1370:
1367:
1363:
1359:
1356:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1325:
1321:
1318:
1315:
1311:
1307:
1304:
1301:
1299:
1295:
1291:
1287:
1286:
1263:
1260:
1257:
1242:
1241:
1226:
1223:
1220:
1218:
1216:
1213:
1210:
1207:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1182:
1179:
1175:
1171:
1168:
1165:
1163:
1161:
1158:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1126:
1122:
1119:
1116:
1114:
1112:
1109:
1108:
1082:
1081:
1066:
1063:
1060:
1058:
1054:
1050:
1046:
1041:
1037:
1033:
1032:
1027:
1023:
1018:
1014:
1011:
1008:
1004:
1000:
997:
994:
992:
988:
984:
980:
979:
974:
970:
965:
961:
958:
955:
951:
947:
944:
941:
939:
935:
931:
927:
926:
897:
893:
870:
866:
841:
838:
770:
767:
764:
760:
756:
753:
750:
747:
744:
740:
736:
733:
730:
727:
724:
721:
652:
649:
619:
596:
593:
424:to 1 against",
342:
341:
316:
295:
270:
240:
210:
180:
112:Moneyline odds
40:Chess handicap
26:
9:
6:
4:
3:
2:
3154:
3143:
3140:
3138:
3135:
3133:
3130:
3129:
3127:
3120:
3111:
3105:
3096:
3091:
3084:
3075:
3070:
3066:
3062:
3058:
3051:
3035:
3031:
3025:
3009:
3005:
2999:
2984:. Soccerwidow
2983:
2977:
2962:on 2 May 2014
2961:
2957:
2951:
2949:
2932:
2926:
2910:
2903:
2888:
2884:
2877:
2861:
2857:
2850:
2842:
2835:
2819:
2812:
2806:
2805:magazine 2012
2804:
2800:
2794:
2786:
2779:
2775:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2745:
2742:
2740:
2737:
2735:
2732:
2730:
2727:
2726:
2720:
2716:
2714:
2708:
2706:
2702:
2697:
2693:
2689:
2686:
2681:
2675:
2671:
2668:
2663:
2657:
2647:
2645:
2640:
2638:
2634:
2633:profit margin
2630:
2620:
2618:
2614:
2610:
2609:American odds
2601:
2597:
2596:
2595:
2591:
2581:
2580:
2576:
2572:
2571:European odds
2567:
2564:
2560:
2557:
2552:
2547:
2543:
2539:
2535:
2531:
2527:
2522:
2514:
2511:
2506:
2504:
2500:
2497:
2496:British odds,
2492:
2490:
2486:
2482:
2478:
2473:
2471:
2467:
2463:
2459:
2455:
2451:
2441:
2439:
2434:
2431:
2427:
2421:
2417:
2407:
2391:
2387:
2384:
2381:
2370:
2362:
2359:
2358:
2357:
2340:
2337:
2334:
2330:
2320:
2316:
2312:
2308:
2304:
2299:
2297:
2289:
2286:
2285:
2284:
2282:
2278:
2274:
2270:
2269:more probable
2266:
2262:
2258:
2254:
2249:
2247:
2243:
2238:
2236:
2232:
2228:
2224:
2219:
2217:
2213:
2209:
2205:
2201:
2191:
2189:
2185:
2181:
2177:
2173:
2158:
2151:
2148:
2145:
2142:
2141:
2137:
2134:
2128:
2125:
2122:
2121:
2113:
2106:
2103:
2100:
2097:
2096:
2092:
2089:
2083:
2080:
2077:
2076:
2072:
2068:
2065:
2062:
2059:
2056:
2055:
2051:
2048:
2045:
2042:
2039:
2038:
2030:
2023:
2020:
2017:
2014:
2013:
2005:
1998:
1995:
1992:
1989:
1988:
1984:
1981:
1978:
1976:
1973:
1970:
1969:
1965:
1962:
1960:
1957:
1954:
1951:
1950:
1946:
1943:
1940:
1937:
1934:
1933:
1918:
1911:
1897:
1890:
1874:
1870:
1862:
1846:
1842:
1834:
1831:
1830:
1827:
1824:
1818:
1814:
1806:
1802:
1776:
1773:
1768:
1764:
1756:
1752:
1749:
1743:
1740:
1735:
1731:
1723:
1717:
1713:
1709:
1707:
1702:
1692:
1689:
1684:
1680:
1672:
1668:
1665:
1659:
1656:
1651:
1647:
1639:
1633:
1629:
1625:
1623:
1618:
1607:
1606:
1605:
1591:
1586:
1582:
1578:
1575:
1572:
1564:
1560:
1555:
1551:
1545:
1542:
1522:
1519:
1516:
1511:
1507:
1486:
1481:
1477:
1446:
1443:
1440:
1433:
1429:
1426:
1423:
1419:
1412:
1409:
1406:
1400:
1397:
1393:
1389:
1386:
1384:
1377:
1373:
1365:
1361:
1354:
1351:
1348:
1342:
1336:
1333:
1330:
1323:
1319:
1316:
1313:
1309:
1305:
1302:
1300:
1293:
1289:
1277:
1276:
1275:
1261:
1258:
1255:
1247:
1224:
1221:
1219:
1214:
1211:
1208:
1201:
1198:
1195:
1192:
1186:
1183:
1180:
1173:
1169:
1166:
1164:
1159:
1152:
1149:
1146:
1143:
1137:
1134:
1131:
1124:
1120:
1117:
1115:
1110:
1099:
1098:
1097:
1095:
1064:
1061:
1059:
1052:
1048:
1044:
1039:
1035:
1025:
1021:
1016:
1012:
1009:
1006:
1002:
998:
995:
993:
986:
982:
972:
968:
963:
959:
956:
953:
949:
945:
942:
940:
933:
929:
917:
916:
915:
913:
895:
891:
868:
864:
854:
852:
848:
837:
835:
831:
827:
823:
819:
815:
811:
807:
803:
799:
795:
791:
787:
782:
768:
762:
758:
754:
748:
742:
738:
734:
728:
725:
722:
719:
710:
706:
702:
698:
694:
690:
686:
682:
678:
674:
670:
666:
657:
648:
646:
642:
639:
630:
629:
624:
618:
612:
610:
606:
602:
592:
587:
583:
579:
568:
564:
560:
535:
531:
521:
517:
507:
503:
493:
483:
479:
464:
460:
450:
446:
422:
418:
407:
403:
395:
391:
381:
337:
333:
329:
323:
317:
312:
308:
302:
296:
292:
288:
284:
271:
266:
262:
258:
254:
241:
236:
232:
228:
224:
211:
206:
202:
198:
194:
181:
177:
173:
169:
156:
155:
154:
148:
143:
133:
119:
113:
107:
95:
88:
84:
79:
67:
63:
59:
55:
48:
41:
37:
33:
19:
3119:
3104:
3083:
3064:
3060:
3050:
3040:25 September
3038:. Retrieved
3034:The Athletic
3033:
3024:
3012:. Retrieved
3008:the original
2998:
2986:. Retrieved
2976:
2964:. Retrieved
2960:the original
2935:. Retrieved
2925:
2913:. Retrieved
2902:
2890:. Retrieved
2886:
2876:
2864:. Retrieved
2860:the original
2849:
2840:
2834:
2822:. Retrieved
2811:
2802:
2798:
2793:
2784:
2778:
2739:Galton board
2717:
2709:
2698:
2694:
2690:
2676:
2672:
2659:
2641:
2639:" built in.
2626:
2616:
2613:point spread
2608:
2606:
2593:
2578:
2575:digital odds
2574:
2570:
2568:
2558:
2555:
2545:
2523:
2520:
2517:Decimal odds
2509:
2507:
2502:
2498:
2495:
2493:
2474:
2469:
2465:
2462:horse racing
2448:Favoured by
2447:
2435:
2423:
2368:
2365:
2318:
2310:
2300:
2295:
2293:
2283:, or 0.25).
2280:
2276:
2272:
2268:
2250:
2241:
2239:
2235:Bayes factor
2220:
2197:
2194:Applications
2168:
1974:
1958:
1832:odds (ratio)
1825:
1816:
1812:
1804:
1800:
1798:
1468:
1245:
1243:
1083:
855:
843:
833:
829:
825:
821:
817:
813:
809:
805:
801:
797:
793:
789:
785:
783:
704:
700:
696:
692:
681:sample space
664:
662:
635:
626:
614:
598:
585:
581:
577:
566:
562:
558:
533:
529:
519:
515:
505:
501:
491:
481:
477:
462:
458:
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444:
420:
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401:
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335:
331:
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286:
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264:
260:
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234:
230:
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144:
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86:
80:
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51:
2988:10 December
2534:New Zealand
2481:denominator
2315:probability
1088:or failure
806:probability
673:proposition
609:Shakespeare
601:intuitively
147:probability
98:, pays out
36:Odds (band)
3132:Randomness
3126:Categories
3095:1710.02824
2770:References
2729:Odds ratio
2470:even money
2450:bookmakers
2430:match race
2414:See also:
2360:Example #2
2307:statistics
2287:Example #1
2257:odds ratio
452:in favor",
66:statistics
34:band, see
2680:overround
2662:bookmaker
2637:overround
2629:bookmaker
2546:including
2542:Singapore
2530:Australia
2510:Hong Kong
2477:numerator
2438:bookmaker
2426:coin toss
2385:−
2338:−
2265:intuitive
1444:−
1410:−
1352:−
1334:−
1199:−
1150:−
1045:⋅
847:fractions
470:against",
309:= 100 / (
100:3 + 2 = 5
70:"2 in 5",
3142:Wagering
3067:: 1–14.
3014:27 March
2966:27 March
2937:27 March
2723:See also
2713:vigorish
2701:gambling
2499:UK odds,
2485:integers
2204:log-odds
689:outcomes
665:in favor
638:polymath
620:—
83:gambling
62:gambling
2458:Ireland
2452:in the
2313:is the
2296:against
2277:against
2233:as the
822:chances
641:Cardano
611:wrote:
595:History
495:for 1",
137:100 to
126:to 100.
3110:"Odds"
2915:16 May
2892:16 May
2866:16 May
2824:16 May
2803:Chance
2667:bettor
2551:parlay
2540:, and
2538:Canada
2526:Europe
826:chance
500:100(1−
485:to 1",
338:+ 100)
318:"pays
313:+ 100)
297:"pays
272:"pays
242:"pays
3090:arXiv
3063:. 1.
2887:Wired
2644:index
2603:−400.
2599:+400.
2466:evens
2428:or a
2424:On a
2253:ratio
2208:logit
2143:100:1
1966:100%
1094:unity
671:or a
669:event
645:ratio
110:When
81:When
3042:2022
3016:2014
2990:2014
2968:2014
2939:2014
2917:2012
2894:2012
2868:2012
2826:2012
2617:both
2479:and
2475:The
2456:and
2418:and
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2305:and
2273:odds
2161:9900
2154:0099
2149:0.01
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2093:10%
2069:80%
2060:0.25
2052:20%
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1982:100%
1947:50%
1821:0099
824:(or
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818:odds
798:odds
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548:for
518:/(1−
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377:and
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2018:0.5
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1952:0:1
1944:50%
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