Coin flipping

Coin flipping, coin tossing, or heads or tails involves launching a coin in the air and then checking which side is showing once it has landed, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes. Used in such a fashion, the coin serves as a binary lot.

History and nomenclature

Coin flipping was known to the Romans as navia aut caput ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other. In England, this was referred to as cross and pile, "pile" denoted the reverse side, a usage dating back to Medieval times. In France the term is inverted: pile ou face. Dutch has kop of munt (head or coin), Spanish cara o cruz (face or cross), German Kopf oder Zahl (head or number), Portuguese cara ou coroa (face or crown), Polish rzut monetą (coin toss), or (less commonly) orzeł czy reszka (eagle or remainder, i.e.change), and in Czech simply hod mincí (toss of a coin).

Process 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 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. 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, and sometimes even on a flat surface. A computational model suggests that the chance of a coin landing on its edge and staying there is about 1 in 6,000 for an American nickel. The thickness of a fair coin, taking into account the coin landing on its third side as a third option, has been the subject of research both experimentally and in statistical mechanics. The ratio of the thickness of the coin to its diameter is thought to be between 0.577 and 0.866. 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 those in the Cricket World Cup and the Super Bowl, use custom-made ceremonial medallions.

Three-way Three-way coin flips are also possible, by a different process –too, which 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 out of three, the previous is either reversed (the odd coin out is the winner) 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 Friday Night Lights (originally a book, subsequently film and TV series), wherein three Texas high school 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, replacing them with [[Tiebreaker#In tournaments and playoffs |point systems]] to reduce the frequency of ties.

Larger numbers

"Heads and Tails" or "Heads or Tails" is an informal game of chance using repeated coin tosses, suitable for a roomful of seated people, typically a social or children's event. Initially all players stand. Before each coin toss, all still standing put their hands on either their head to indicate "heads" or their hips or buttocks to indicate "tails"; once the toss result is announced, those who guessed incorrectly sit down. The process repeats until the last player standing wins; often the last few players remaining are called to the announcer's table for the climax. A variant with faster elimination is played with two coins and players placing each hand separately.

Use in dispute resolution

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.

… excerpt ends here. Continue reading the full article.