Three-way coin flips are also possible, by a different process — this can be done either to choose two out of three, or to choose one 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 out of three, either reverse this the odd coin out is the winner , or add a regular two-way coin flip between the remaining players as a second step.
A famous example of such a three-way coin flip choose two out of three is dramatized in Friday Night Lights originally a book , subsequently film and TV series , where three high school football teams with identical records use a three-way coin flip — at a truck stop — to determine which two will advance to the playoffs.
Coin tossing is a simple and unbiased way of settling a dispute or deciding between two or more arbitrary options. In a game theoretic 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 sports and other games 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 wind direction, the position of the sun, and other conditions may affect the decision. In team sports it is often the captain who makes the call, while the umpire or referee usually oversees such proceedings.
A competitive method may be used instead of a toss in some situations, for example in basketball the jump ball is employed, while the face-off plays a similar role in ice hockey.
The XFL , a short-lived American football league, attempted to avoid coin tosses by implementing a face-off 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 adopted by X-League Indoor Football , in which each player pursued his own ball , and coin tossing remains the method of choice in American football.
In an association football 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 or second in a penalty shoot-out.
Before the earlys introduction of the penalty shootout , coin tosses were occasionally needed to decide the outcome of tied matches.
The most famous instance of this was the semifinal game of the European Championship in Italy between Italy and the Soviet Union , which finished after extra time.
Italy won, and went on to become European champions. In cricket the toss is often significant, as the decision whether to bat or bowl first can influence the outcome of the game.
Similarly, in tennis 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.
In duels a coin toss was sometimes used to determine which combatant had the sun at his back. 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 NFL Draft ; 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.
Major League Baseball 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 one-game playoff games that might need to be added to the regular season.
Most of these cases did not occur. From the season , the method to determine home-field advantage was changed. Although in most international matches this is now done electronically by the scoring apparatus.
Pettygrove , who each owned the claim to the land that would later become Portland, Oregon , wanted to name the new town after their respective hometowns of Boston, Massachusetts and Portland, Maine ; Pettygrove won the coin flip.
Scientists sometimes use coin flipping to determine the order in which they appear on the list of authors of scholarly papers.
In December , Australian television networks Seven and Ten , which shared the broadcasting of the AFL Season , decided who would broadcast the Grand Final with the toss of a coin.
In some jurisdictions, a coin is flipped to decide between two candidates who poll equal number of votes in an election , or two companies tendering equal prices for a project.
Each candidate will be given five chances to flip a coin; the candidate with the most number of "heads" wins. The mayoral election in San Teodoro, Oriental Mindoro was decided on a coin flip, with a winner being proclaimed after the second round when both candidates remained tied in the first round.
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.
A Yancey win extended the Republican advantage to , whereas a Simmonds win would have resulted in a 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.
The outcome of coin flipping has been studied by Persi Diaconis and his collaborators. Further, in actual flipping, people exhibit slight bias — "coin tossing is fair to two decimals but not to three.
That is, typical flips show biases such as. In studying coin flipping, to observe the rotation speed of coin flips, Diaconis first used a strobe light 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 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.
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.
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 when spun they usually land on a particular face.
Human intuition about conditional probability 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.
The mathematical abstraction of the statistics of coin flipping is described by means of the Bernoulli process ; a single flip of a coin is a Bernoulli trial.
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 checking if a coin is fair.
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.
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