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135:) or a regular two-way coin flip between the two remaining players can decide. The three-way flip is 75% likely to work each time it is tried (if all coins are heads or all are tails, each of which occur 1/8 of the time due to the chances being 0.5 by 0.5 by 0.5, the flip is repeated until the results differ), and does not require that "heads" or "tails" be called. A well-known example of such a three-way coin flip (choose two out of three) is dramatized in
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78:
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Moreover, their theoretical analysis of the physics of coin tosses predicts a slight bias for a caught coin to be caught the same way up as it was thrown, with a probability of around 0.51, though a subsequent attempt to verify this experimentally gave ambiguous results. Stage magicians and gamblers,
549:
and a coin with one side painted black, the other white, so that when the speed of the strobe flash equaled the rotation rate of the coin, it would appear to always show the same side. This proved difficult to use, and rotation rate was more accurately computed by attaching floss to a coin, such that
330:
is often significant, as the decision whether to bat or bowl first can influence the outcome of the game. The coin toss in cricket is more important than in other games because in many situations it can lead a team winning or losing the game. Factors such as pitch conditions, weather and the time of
730:
to help in making difficult decisions is to toss a coin not actually to determine the decision, but to clarify the decision-maker's feelings. He explained: "I did not say you should follow blindly what the coin tells you. What I want you to do is to note what the coin indicates. Then look into your
582:
is often very poor and can give rise to some seemingly surprising observations. For example, if the successive tosses of a coin are recorded as a string of "H" and "T", then for any trial of tosses, it is twice as likely that the triplet TTH will occur before THT than after it. It is three times as
557:
Since the images on the two sides of actual coins are made of raised metal, the toss is likely to slightly favor one face or the other if the coin is allowed to roll on one edge upon landing. Coin spinning is much more likely to be biased than flipping, and conjurers trim the edges of coins so that
419:
In addition to its practical applications in sports, coin tossing is symbolic of the democratic principle of equal opportunity. When two parties face an impasse, the act of flipping a coin signifies a commitment to impartiality and a willingness to accept the outcome, no matter how arbitrary it may
271:
match, the team winning the coin toss chooses which goal to attack in the first half; the opposing team kicks off for the first half. For the second half, the teams switch ends, and the team that won the coin toss kicks off. Coin tosses are also used to decide which team has the pick of going first
1223:
Meredith, R. W.; JaneÄŤka, J. E.; Gatesy, J.; Ryder, O. A.; Fisher, C. A.; Teeling, E. C.; Goodbla, A.; Eizirik, E.; SimĂŁo, T. L. L.; Stadler, T.; Rabosky, D. L.; Honeycutt, R. L.; Flynn, J. J.; Ingram, C. M.; Steiner, C.; Williams, T. L.; Robinson, T. J.; Burk-Herrick, A.; Westerman, M.; Ayoub, N.
130:
Three-way coin flips are also possible, by a different process – this can be done either to choose one or two out of three. To choose two out of three, three coins are flipped, and if two coins come up the same and one different, the different one loses (is out), leaving two players. To choose one
117:
It is possible for a coin to land on its side, usually by landing up against an object (such as a shoe) or by getting stuck in the ground. However, even on a flat surface it is possible for a coin to land on its edge. A computational model suggests that the chance of a coin landing on its edge and
717:
uses a coin toss. If a player matches all 6 of their numbers, the coin toss will decide whether they win a cash jackpot (minimum of NZ$ 25,000) or a bigger jackpot with luxury prizes (minimum of NZ$ 2 million cash, plus value of luxury prizes.) The coin toss is also used in determining the Second
541:
and his collaborators. They have demonstrated that a mechanical coin flipper which imparts the same initial conditions for every toss has a highly predictable outcome – the phase space is fairly regular. Further, in actual flipping, people exhibit slight bias – "coin
528:
with Yancey's name, and he was declared the winner. Additionally, the outcome of the draw determined control of the entire House, as
Republicans won 50 of the other 99 seats and Democrats 49. A Yancey win extended the Republican advantage to 51–49, whereas a Simmonds win would have resulted in a
113:
During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge an unpredictable number of times. Either beforehand or when the coin is in the air, an interested party declares "heads" or "tails", indicating which side of the coin that party is choosing. The other party is
697:
Bob, by providing his own random word, guarantees that Alice is not able to precompute an image pair of "tail/random string" or "head/random string", for two different random words. Bob is also unable to reverse Alice's hash to see what her chosen outcome was before flipping the coin, and to lie
247:
style "opening scramble," in which one player from each team tried to recover a loose football; the team whose player recovered the ball got first choice. Because of the high rate of injury in these events, it has not achieved mainstream popularity in any football league (a modified version was
346:
The
National Football League also has a coin toss for tie-breaking among teams for playoff berths and seeding, but the rules make the need for coin toss, which is random rather than competitive, very unlikely. A similar procedure breaks ties for the purposes of seeding in the
114:
assigned the opposite side. Depending on custom, the coin may be caught; caught and inverted; or allowed to land on the ground. When the coin comes to rest, the toss is complete and the party who called correctly or was assigned the upper side is declared the winner.
523:
and
Democratic challenger Shelly Simmonds, with exactly 11,608 votes each. Under state law, the election was to be decided by drawing a name from a bowl, although a coin toss would also have been an acceptable option. The chair of the Board of Elections drew the
482:" is one of the methods to break ties to determine a winner in an election; the coin flip is considered an acceptable variant. Each candidate will be given five chances to flip a coin; the candidate with the most "heads" wins. The 2013 mayoral election in
494:
In the United
Kingdom, if a local or national election has resulted in a tie where candidates receive exactly the same number of votes, then the winner can be decided either by drawing straws/lots, coin flip, or drawing a high card in pack of cards.
731:
own reactions. Ask yourself: Am I pleased? Am I disappointed? That will help you to recognize how you really feel about the matter, deep down inside. With that as a basis, you'll then be ready to make up your mind and come to the right decision."
338:
a coin toss is used in professional matches to determine which player serves first. The player who wins the toss decides whether to serve first or return, while the loser of the toss decides which end of the court each player plays on first.
121:
The coin may be any type as long as it has two distinct sides. Larger coins tend to be more popular than smaller ones. Some high-profile coin tosses, such as the
Cricket World Cup and the Super Bowl, use custom-made ceremonial medallions.
342:
In duels a coin toss was sometimes used to determine which combatant had the sun at his back. In some other sports, the result of the toss is less crucial and merely a way to fairly choose between two more or less equal options.
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There is no reliable way to use a true coin flip to settle a dispute between two parties if they cannot both see the coin—for example, over the phone. The flipping party could easily lie about the outcome of the toss. In
469:
tender in 2003 for painting lines on 1,605 km of city streets: the bids were $ 161,110.00 ($ 100.3800623 per km), $ 146,584.65 ($ 91.33 per km, exactly), and two equal bids of $ 111,242.55 ($ 69.31 per km, exactly).
420:
seem. This shared acceptance of chance as the ultimate arbiter can foster cooperation and conflict resolution in various aspects of life beyond sports, including business negotiations and interpersonal conflicts.
155:
football teams use a three-way coin flip. A legacy of that particular 1988 coin flip was to reduce the use of coin flips to break ties in Texas sports, instead using point systems to reduce the frequency of ties.
515:. Also, a number of states provide for "drawing lots" in the event an election ends in a tie, and this is usually resolved by a coin toss or picking names from a hat. A 2017 election to the 94th District of the
187:
to decide arbitrary factors such as which side of the field a team will play from, or which side will attack or defend initially; these decisions may tend to favor one side, or may be neutral. Factors such as
1377:
can use any random method such as tossing a coin, but the recommended way is to ask each candidate to write their name on a blank slip of paper and place it in a container.
603:. In the study of statistics, coin-flipping plays the role of being an introductory example of the complexities of statistics. A commonly treated textbook topic is that of
1168:
570:
Graphs of best responses for Penney's games of sequence lengths 3 and 4 – each sequence is dominated by the sequence pointing to it with the given probability (
550:
it would wind around the coin – after a flip, one could count rotations by unwinding the floss, and then compute rotation rate as flips over air time.
219:
Coin flipping is used to decide which end of the field the teams will play to and/or which team gets first use of the ball, or similar questions in football matches,
179:
analysis it provides even odds to both sides involved, requiring little effort and preventing the dispute from escalating into a struggle. It is used widely in
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day are considered by the team captain who wins the toss. Now there are websites such as flip a coin online which domestic sports team use to toss the coin.
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50–50 tie. As there is no provision for breaking ties in the House as a whole, this would have forced a power sharing agreement between the two parties.
140:
351:; these coin tosses are more common, since the tie-breaking procedure for the draft is much less elaborate than the one used for playoff seeding.
525:
955:
1444:
1224:
A.; Springer, M. S.; Murphy, W. J. (2011). "Impacts of the
Cretaceous Terrestrial Revolution and KPg Extinction on Mammal Diversification".
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with practice, are able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.
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was decided on a coin flip, with a winner being proclaimed after the second round when both candidates remained tied in the first round.
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once conducted a series of coin flips as a contingency on the last month of its regular season to determine home teams for any potential
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usually oversees such proceedings. A competitive method may be used instead of a toss in some situations, for example in basketball the
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379:" extra minute of competition. Although in most international matches this is now done electronically by the scoring apparatus.
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There are two methods to decide the outcome in the event of a draw - either a coin is flipped or the parties draw straws.
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Coin tossing is a simple and unbiased way of settling a dispute or deciding between two or more arbitrary options. In a
1279:
252:, in which each player pursued his own ball), and coin tossing remains the method of choice in American football. (The
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which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins.
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direction, the position of the sun, and other conditions may affect the decision. In team sports it is often the
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In some jurisdictions, a coin is flipped to decide between two candidates who poll equal number of votes in an
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tossing is fair to two decimals but not to three. That is, typical flips show biases such as 0.495 or 0.503."
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Scientists sometimes use coin flipping to determine the order in which they appear on the list of authors of
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effectively about its outcome, because he does not know Alice's random word at that point in the process.
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games that might need to be added to the regular season. Most of these cases did not occur. From the
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511:(i.e., the election cycle in which the term each of the new state's senators will expire) in the
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307:, where it is used to decide which team gets the choice of bowling or batting first. Shown are
231:, and other sports requiring such decisions. In the U.S. a specially minted coin is flipped in
20:
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In studying coin flipping, to observe the rotation speed of coin flips, Diaconis first used a
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The mathematical abstraction of the statistics of coin flipping is described by means of the
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390:
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296:, which finished 0–0 after extra time. Italy won, and went on to become European champions.
260:, removed the coin toss altogether and allowed that decision to be made as part of a team's
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243:, a short-lived American football league, attempted to avoid coin tosses by implementing a
8:
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Bob performs the physical coin flip, and announces the result, heads or tails, to Alice.
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The outcome of coin flipping has been studied by the mathematician and former magician
280:, coin tosses were occasionally needed to decide the outcome of drawn matches where a
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when it lands, in order to randomly choose between two alternatives. It is a form of
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1646:
1627:
Vulovic, Vladimir Z.; Prange, Richard E. (1986). "Randomness of a true coin toss".
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1584:
1507:"Best response strings for strings of length 3. | Download Scientific Diagram"
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Both parties can now determine whether Alice's call of "tails" matched Bob's coin.
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was not possible. The most famous instance of this was the semifinal game of the
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likely that "THH will precede HHT" than that "THH will follow HHT"; see also
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Practice of throwing a coin in the air to choose between two alternatives
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out of three, the previous is either reversed (the odd coin out is the
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507:, when a new state is added to the Union, a coin toss determines the
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66:
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1102:"Flip A Coin Online - Coin Flipper to get heads or tails for toss!"
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205:
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Newport News House race tied after judges count outstanding ballot
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of a string that includes the two chosen words and the call (e.g.
397:, wanted to name the new town after their respective hometowns of
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372:
323:
304:
197:
1493:"40,000 coin tosses yield ambiguous evidence for dynamical bias"
1674:
1495:. Department of Statistics, University of California, Berkeley.
1450:. Department of Statistics, Stanford University. Archived from
1303:"Coin toss breaks tie in mayoral race in Oriental Mindoro town"
1101:
1048:"SAISD athletic director looks back on 1988's famous coin-flip"
819:
465:
equal prices for a project. For example, a coin toss decided a
393:, who each owned the claim to the land that would later become
335:
82:
1078:
956:"Want to bid for piece of World Cup history? Find out how..."
740:
180:
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includes a poem, "A Psychological Tip", on a similar theme:
365:, the method to determine home-field advantage was changed.
189:
184:
94:
58:
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Alice privately decides to call "tails" on the coin flip.
118:
staying there is about 1 in 6000 for an
American nickel.
1411:
Virginia
Republican David Yancey Wins Tiebreaker Drawing
634:
Alice and Bob each privately choose a random word, e.g.
1478:"Lifelong debunker takes on arbiter of neutral choices"
1596:
Keller, Joseph B. (1986). "The probability of heads".
371:
rules use a coin toss to determine the winner of some
1606:(3). Mathematical Association of America: 191–197.
1565:Ford, Joseph (1983). "How random is a coin toss?".
558:when spun they usually land on a particular face.
215:Juventus F.C. - Sheffield Wednesday F.C. coin toss
101:on the other. In England, this was referred to as
19:Several terms redirect here. For other uses, see
1390:"Frequently Asked Questions about a New Congress"
908:Murray, Daniel B.; Teare, Scott W. (1993-10-01).
433:In December 2006, Australian television networks
303:Tossing a coin is common in many sports, such as
1687:
1017:Friday Night Lights: A Town, a Team, and a Dream
1169:"Ownership approves two major rules amendments"
753:The best way to solve the dilemma, you'll find,
749:Whenever you're called on to make up your mind,
519:resulted in a tie between Republican incumbent
1282:. The Sydney Morning Herald. December 22, 2006
910:"Probability of a tossed coin landing on edge"
677:, including both of their words and a call of
561:
1626:
1272:
1118:
1001:
984:"A Brief History of the Super Bowl Coin Toss"
759:While you're passively standing there moping;
757:No—not so that chance shall decide the affair
673:Alice reveals that the string she hashed was
276:. Before the early-1970s introduction of the
159:
1266:"First authorship determined by coin toss.
1213:
907:
761:But the moment the penny is up in the air,
449:with the toss of a coin. Network Ten won.
375:matches that remain tied at the end of a "
1382:
1269:Last authorship determined by coin toss."
1007:
851:
847:
845:
89:Coin flipping was known to the Romans as
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1435:
1433:
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1351:
1321:
1161:
852:Allenunne, Richard (December 31, 2009).
565:
298:
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196:who makes the call, while the umpire or
163:
85:on the obverse and a ship on the reverse
76:
37:
1039:
872:
630:, the following algorithm can be used:
441:, which shared the broadcasting of the
1688:
1595:
1540:
1300:
1186:
842:
763:You suddenly know what you're hoping.
751:And you're hampered by not having any,
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93:("ship or head"), as some coins had a
1557:
1428:
981:
610:
1564:
1543:"Decision making defines the leader"
1280:"Ten wins AFL grand final coin toss"
235:games; the coin is then sent to the
208:plays a similar role in ice hockey.
1045:
369:Fédération Internationale d'Escrime
13:
1490:
1445:"The Problem of Thinking Too Much"
1192:
445:, decided who would broadcast the
14:
1722:
1667:
1476:Landhuis, Esther (June 7, 2004).
982:Allen, Scott (February 5, 2012).
489:
1673:
1195:"Francis Pettygrove (1812–1887)"
685:3fe97d8e6456a1dce4508d00251345e3
665:3fe97d8e6456a1dce4508d00251345e3
648:Bob sends Alice his chosen word
498:
97:on one side and the head of the
1534:
1520:
1499:
1484:
1469:
1416:
1404:
1329:"Hague savours local victories"
1294:
854:"Coin tossing through the ages"
795:Checking whether a coin is fair
599:; a single flip of a coin is a
1541:Mackay, Harvey (28 May 2009).
1301:Virola, Madonna (2013-05-16).
1094:
1066:
1046:Lee, Mike (November 7, 2008).
975:
948:
901:
884:Dictionary of Phrase and Fable
755:Is simply by spinning a penny.
683:Bob confirms for himself that
590:
473:
168:The coin toss at the start of
81:A Roman coin with the head of
57:is the practice of throwing a
1:
1599:American Mathematical Monthly
1365:. BBC News. February 17, 2001
830:
663:), and sends that hash (e.g.
484:San Teodoro, Oriental Mindoro
1074:"European Championship 1968"
1013:"Chapter 13: Heads or Tails"
835:
701:
428:
125:
7:
1201:. Portland State University
768:
562:Counterintuitive properties
517:Virginia House of Delegates
423:
10:
1727:
1009:Bissinger, H. G. Bissinger
726:A technique attributed to
614:
605:checking if a coin is fair
532:
286:1968 European Championship
108:
72:
18:
1308:Philippine Daily Inquirer
1053:San Angelo Standard-Times
689:bubblejet knockback tails
675:bubblejet knockback tails
661:bubblejet knockback tails
452:
237:Pro Football Hall of Fame
225:Australian rules football
160:Use in dispute resolution
934:10.1103/PhysRevE.48.2547
250:X-League Indoor Football
233:National Football League
61:in the air and checking
1651:10.1103/PhysRevA.33.576
1246:10.1126/science.1211028
1199:The Oregon Encyclopedia
718:Chance winner's prize.
580:conditional probability
574:) or odds (normal text)
204:is employed, while the
1392:. United States Senate
766:
578:Human intuition about
575:
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216:
172:
86:
43:
21:Flipping a Coin (song)
1706:Sampling (statistics)
1173:Major League Baseball
746:
615:Further information:
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509:class of the senators
405:; Pettygrove won the
399:Boston, Massachusetts
391:Francis W. Pettygrove
355:Major League Baseball
302:
214:
167:
80:
63:which side is showing
41:
1711:Gambling mathematics
1682:at Wikimedia Commons
1530:. Wolfram MathWorld.
1443:(11 December 2002).
269:association football
262:home field advantage
256:, which launched in
1643:1986PhRvA..33..576V
1581:1983PhT....36d..40F
1238:2011Sci...334..521M
1157:. January 23, 1876.
1106:flipacoinonline.com
926:1993PhRvE..48.2547M
815:Rock paper scissors
722:Clarifying feelings
461:, or two companies
316:tossing for innings
137:Friday Night Lights
25:Obverse and reverse
1558:General references
1480:. Stanford Report.
1457:on 19 October 2013
1175:. January 15, 2009
1154:The New York Times
1134:Scribner's Monthly
657:cryptographic hash
624:telecommunications
611:Telecommunications
576:
320:
217:
173:
87:
44:
31:, and
1678:Media related to
1630:Physical Review A
1589:10.1063/1.2915570
1232:(6055): 521–524.
1171:(Press release).
1019:. Da Capo Press.
914:Physical Review E
810:Gambler's fallacy
775:Bernoulli process
655:Alice computes a
617:Commitment scheme
597:Bernoulli process
274:penalty shoot-out
221:American football
153:Texas high school
151:), wherein three
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1549:on 24 July 2011.
1545:. Archived from
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963:. March 22, 2015
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359:one-game playoff
278:penalty shootout
170:Super Bowl XLIII
83:Pompey the Great
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474:Philippines
447:Grand Final
387:Asa Lovejoy
363:2009 season
313:Gubby Allen
309:Don Bradman
254:revived XFL
248:adopted by
1690:Categories
1374:He or she
1369:2012-12-08
1341:2012-12-08
1314:2013-03-16
1179:2012-12-08
1111:2024-06-19
1059:2012-12-08
1032:2012-12-08
960:Rediff.com
894:2012-12-08
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229:volleyball
183:and other
1205:March 29,
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967:March 30,
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790:Fair coin
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702:Lotteries
667:) to Bob.
650:knockback
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429:Australia
407:coin flip
349:NFL Draft
202:jump ball
149:TV series
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1262:38120449
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1220:Example:
1011:(1990).
825:Two-Face
769:See also
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800:Flipism
711:lottery
572:italics
533:Physics
503:In the
382:In the
373:fencing
324:cricket
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223:games,
198:referee
194:captain
109:Process
99:emperor
73:History
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820:Two-up
741:Grooks
453:Canada
336:tennis
282:replay
267:In an
181:sports
133:winner
27:,
23:,
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1616:JSTOR
1455:(PDF)
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1258:S2CID
1149:(PDF)
1129:(PDF)
1079:RSSSF
713:game
679:tails
435:Seven
290:Italy
185:games
53:, or
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