Coin flipping or
coin tossing or
heads or tails is the practice of throwing a
coinA coin is a piece of hard material that is standardized in weight, is produced in large quantities in order to facilitate trade, and primarily can be used as a legal tender token for commerce in the designated country, region, or territory....
in the air to choose between two alternatives, sometimes to resolve a dispute between two parties. It is a form of
sortitionIn politics, sortition is the selection of decision makers by lottery. The decision-makers are chosen as a random sample from a larger pool of candidates....
which inherently has only two possible and equally likely outcomes.
History
The historical origin of coin flipping is the interpretation of a chance outcome as the expression of divine will.
A well-known example of such
divinationDivination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...
(although not involving a coin) is the episode in which the prophet
JonahJonah is the name given in the Hebrew Bible to a prophet of the northern kingdom of Israel in about the 8th century BC, the eponymous central character in the Book of Jonah, famous for being swallowed by a fish or a whale, depending on translation...
was chosen by lot to be cast out of the boat, only to be swallowed by a giant fish (
Book of JonahThe Book of Jonah is a book in the Hebrew Bible. It tells the story of a Hebrew prophet named Jonah ben Amittai who is sent by God to prophesy the destruction of Nineveh but tries to escape the divine mission...
, Chapter 1).
Coin flipping as a game was known to the Romans as "navia aut caput" (
ship or head), as some coins had a
shipSince the end of the age of sail a ship has been any large buoyant marine vessel. Ships are generally distinguished from boats based on size and cargo or passenger capacity. Ships are used on lakes, seas, and rivers for a variety of activities, such as the transport of people or goods, fishing,...
on one side and the head of the
emperorThe Roman emperor was the ruler of the Roman State during the imperial period . The Romans had no single term for the office although at any given time, a given title was associated with the emperor...
on the other . In England, this game was referred to as cross and pile.
Process
During coin flipping the coin is tossed into the air such that it rotates end-over-end several times. Either beforehand or when the coin is in the air, an interested party calls "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 or was assigned the face-up side is declared the winner. If the outcome is unclear the toss is repeated; for example the coin may, very rarely, land on edge, or fall down a drain.
The coin may be any type as long as it has two distinct sides; it need not be a coin as such.
Fraudulent flipping
It is not very difficult to learn to flip a coin so as to get a reliable intended result, not by controlling the number of flips but by creating the illusion that the coin is flipping. The coin remains at a constant inclination to the vertical and simply rotates, or wobbles, about a vertical axis. The inclination must be sufficient for the coin to occupy most of the sphere that a fairly flipped coin would, while not being so great that the coin is likely to bounce when caught. An inclination around 45 degrees is usually satisfactory.
Another simple way to cheat is simply to peek at the coin as it lands in your hand. Although it seems that this would be easily detectable, in fact, this can be done quickly and convincingly with some practice.
The third common method of fraudulent flipping is to determine which side is up by the feel of the coin. On most American coins, the heads side is smoother than the tails side.
Three-way
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. Note that the three-way flip is 75% likely to work each time it is tried (if all coins are heads or all are tails, which each occurs 1/4 of the time, the flip is repeated until the results differ), and does not require that "heads" or "tails" be called.
A famous example of such a three-way coin flip (choose two out of three) is dramatized in
Friday Night LightsFriday Night Lights is a 2004 drama film which documents the coach and players of a high school football team and the Texas city of Odessa that supports and is obsessed with them. The book on which it was based, Friday Night Lights: A Town, a Team, and a Dream, was authored by H. G...
(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. A legacy of this 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.
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 theoreticGame theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
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
sportA Sport is all forms of physical activity which, through casual or organised participation, aim to use, maintain or improve physical fitness and provide entertainment to participants. Sport may be competitive, where a winner or winners can be identified by objective means, and may require a degree...
s and other
gameA game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements...
s 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
windWind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...
direction, the position of the sun, and other conditions may affect the decision. In team sports it is often the
captainIn team sports, a captain is a title given to a member of the team. The title is frequently honorary, but in some cases the captain may have significant responsibility for strategy and teamwork while the game is in progress on the field...
who makes the call, while the umpire or
refereeA referee is the person of authority, in a variety of sports, who is responsible for presiding over the game from a neutral point of view and making on the fly decisions that enforce the rules of the sport...
usually oversees such proceedings. A competitive method may be used instead of a toss in some situations, for example in basketball the
jump ballA jump ball is a method used to begin or resume play in basketball. It is similar to a face-off in ice hockey or ball-up in Australian rules football...
is employed, while the
faceoffA face-off is the method used to begin play in ice hockey and some other sports. The two teams line up in opposition to each other, and the opposing centres attempt to gain control of the puck after it is dropped between their sticks by an official. One of the referees drops the puck at centre ice...
plays a similar role in ice hockey.
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 soccer matches,
American footballAmerican football is a sport played between two teams of eleven with the objective of scoring points by advancing the ball into the opposing team's end zone. Known in the United States simply as football, it may also be referred to informally as gridiron football. The ball can be advanced by...
games,
Australian rules footballAustralian rules football, officially known as Australian football, also called football, Aussie rules or footy is a sport played between two teams of 22 players on either...
,
volleyballVolleyball is a team sport in which two teams of six players are separated by a net. Each team tries to score points by grounding a ball on the other team's court under organized rules.The complete rules are extensive...
, and other sports requiring such decisions. In the U.S. a specially minted coin is flipped in
National Football LeagueThe National Football League is the highest level of professional American football in the United States, and is considered the top professional American football league in the world. It was formed by eleven teams in 1920 as the American Professional Football Association, with the league changing...
games; the coin is then sent to the
Pro Football Hall of FameThe Pro Football Hall of Fame is the hall of fame of professional football in the United States with an emphasis on the National Football League . It opened in Canton, Ohio, on September 7, 1963, with 17 charter inductees...
, and other coins of the special series minted at the same time are sold to collectors. The
XFLThe XFL was a professional American football league that played for one season in 2001. The league was founded by Vince McMahon, the Chairman of the Board of Directors of WWE...
, a short-lived American football league, attempted to avoid coin tosses by implementing a
faceoffA face-off is the method used to begin play in ice hockey and some other sports. The two teams line up in opposition to each other, and the opposing centres attempt to gain control of the puck after it is dropped between their sticks by an official. One of the referees drops the puck at centre ice...
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, and coin tossing remains the method of choice in American football.
In a soccer 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 introduction of the penalty shoot-out, coin tosses were occasionally needed to decide the outcome of tied matches. The most famous instance of this was the 1968 European Football Championship semi-final between
ItalyThe Italy National Football Team , represents Italy in association football and is controlled by the Italian Football Federation , the governing body for football in Italy. Italy is the second most successful national team in the history of the World Cup having won four titles , just one fewer than...
and the
Soviet UnionThe Soviet Union National Football Team was the national football team of the Soviet Union. It ceased to exist after the break up of the Union...
, which finished 0-0 after extra time. Italy won, and went on to become European champions.
In
cricketCricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...
the toss is often significant, as the decision whether to bat or bowl first can influence the outcome of the game.
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.
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 DraftThe National Football League Draft is an annual event in which the National Football League teams select eligible college football players and it is their most common source of player recruitment. The basic design of the draft is each team is given a position in the drafting order in reverse order...
; 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 BaseballMajor League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
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 playoffA one-game playoff, sometimes known as a pennant playoff or play-in game, is a tiebreaker in certain sports—usually but not always professional—to determine which of two teams, tied in the final standings, will qualify for a post-season tournament...
games that might need to be added to the regular season. Most of these cases did not occur. From the 2009 season, the method to determine home-field advantage was changed.
Fédération Internationale d'EscrimeFédération Internationale d'Escrime is the international governing body of Olympic fencing. It was founded on November 29, 1913 in Paris, France. Today, its head office is in Lausanne, Switzerland...
rules use a coin toss to determine the winner of a
fencingFencing, which is also known as modern fencing to distinguish it from historical fencing, is a family of combat sports using bladed weapons.Fencing is one of four sports which have been featured at every one of the modern Olympic Games...
match that remains tied at the end of a "sudden death" extra minute of competition.
In the
United StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
Asa LovejoyAsa Lawrence Lovejoy was an American pioneer and politician in the region that would become the U.S. state of Oregon. He is best remembered as a founder of the city of Portland, Oregon...
and Francis W. Pettygrove, who owned the claim to the land that would later become
Portland, OregonPortland is a city located in the Pacific Northwest, near the confluence of the Willamette and Columbia rivers in the U.S. state of Oregon. As of the 2010 Census, it had a population of 583,776, making it the 29th most populous city in the United States...
, each wanted to name the new town after their respective hometowns of Boston, Massachusetts and
Portland, MainePortland is the largest city in Maine and is the county seat of Cumberland County. The 2010 city population was 66,194, growing 3 percent since the census of 2000...
; 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.
Canada
In some jurisdictions, a coin is flipped to decide between two candidates who poll equal number of votes in an
electionAn election is a formal decision-making process by which a population chooses an individual to hold public office. Elections have been the usual mechanism by which modern representative democracy operates since the 17th century. Elections may fill offices in the legislature, sometimes in the...
, or two companies tendering equal prices for a project. For example, a coin toss decided a
City of TorontoToronto is the provincial capital of Ontario and the largest city in Canada. It is located in Southern Ontario on the northwestern shore of Lake Ontario. A relatively modern city, Toronto's history dates back to the late-18th century, when its land was first purchased by the British monarchy from...
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). The numerical coincidence is somewhat less remarkable than it appears, because three of the four bids are for a whole number of cents per kilometer.
Australia
In December 2006 Australian television networks
SevenThe Seven Network is an Australian television network owned by Seven West Media Limited. It dates back to 4 November 1956, when the first stations on the VHF7 frequency were established in Melbourne and Sydney.It is currently the second largest network in the country in terms of population reach...
and
TenNetwork Ten , is one of Australia's three major commercial television networks. Owned-and-operated stations can be found in Sydney, Melbourne, Brisbane, Adelaide and Perth, while affiliates extend the network to cover most of the country...
, which shared the broadcasting of the
2007 AFL SeasonThe 2007 AFL Season was the 111th season of the Australian Football League, the highest-level professional Australian rules football league in Australia...
, decided who would broadcast the
Grand FinalThe 2007 AFL Grand Final was an Australian rules football game contested between the Geelong Football Club and the Port Adelaide Football Club, held at the Melbourne Cricket Ground in Melbourne on 29 September 2007. It was the 111th annual Grand Final of the VFL/AFL, staged to determine the...
with the toss of a coin. Network Ten won.
United Kingdom
In the United Kingdom, if a local or national election has resulted in a tie where candidates receive exactly the same number of votes after 3 recounts, then the winner can be decided either by drawing straws/lots, coin flip, or drawing a high card in pack of cards
http://news.bbc.co.uk/1/hi/in_depth/uk_politics/2000/local_elections/736660.stmhttp://answers.google.com/answers/threadview/id/13729.html.
In more casual settings, coin flipping is used simply to resolve arguments between friends or family members, or for amusement.
Physics
Experimental and theoretical analysis of coin tossing has shown that the outcome is predictable, to some degree at least, if the initial conditions of the toss (position,
velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
and
angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
) are known.
Coin tossing may be modeled as a problem in
Lagrangian mechanicsLagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. It was introduced by the Italian-French mathematician Joseph-Louis Lagrange in 1788....
.
The important aspects are the tumbling motion of the coin, the precession (wobbling) of its axis, and whether the coin bounces at the end of its trajectory.
The outcome of coin flipping has been studied by
Persi DiaconisPersi Warren Diaconis is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University....
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 tossing is fair to two decimals but not to three. That is, typical flips show biases such as .495 or .503."
In studying coin flipping, to observe the rotation speed of coin flips, Diaconis first used a
strobe lightA strobe light or stroboscopic lamp, commonly called a strobe, is a device used to produce regular flashes of light. It is one of a number of devices that can be used as a stroboscope...
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 0.51, though a subsequent attempt to verify this experimentally gave ambiguous results. Stage magicians and gamblers, with practice, are able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.
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.
Counterintuitive properties
Human intuition about
conditional probabilityIn probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....
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 likely that THH will precede HHT. (See
Penney's gamePenney's game is a binary sequence generating game between two players. At the start of the game, the two players agree on the length of the sequences to be generated. This length is usually taken to be three, but can be any larger number...
)
Mathematics
The mathematical abstraction of the statistics of coin flipping is described by means of the
Bernoulli processIn probability and statistics, a Bernoulli process is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables Xi are identical and independent...
; a single flip of a coin is a
Bernoulli trialIn the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure"....
. 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 fairIn statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of...
.
Coin flipping in telecommunications
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 telecommunications and
cryptographyCryptography is the practice and study of techniques for secure communication in the presence of third parties...
, the following algorithm can be used:
- Alice chooses an outcome for an imaginary coin flip, such as "tail", and she produces a random string such as "ljngjkrjgnfdudiudd"
- She computes a SHA-1 hash of the string "tail ljngjkrjgnfdudiudd", which is 89959180eeb6f4554a5da73948bf5a7c178f6e48
- She shows Bob the string "89959180eeb6f4554a5da73948bf5a7c178f6e48" and asks him: "head or tail"?
- Bob says, for instance, "head".
- Alice tells him he's just lost, and proves it by showing the string "tail ljngjkrjgnfdudiudd".
- Bob can check that Alice didn't lie by computing the SHA-1 of the string.
In lotteries
The
New ZealandNew Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...
lotteryA lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments...
game Big Wednesday 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 Chance winner's prize.
Use in clarifying feelings
A technique attributed to
Sigmund FreudSigmund Freud , born Sigismund Schlomo Freud , was an Austrian neurologist who founded the discipline of psychoanalysis...
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 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."
In fiction
George RaftGeorge Raft was an American film actor and dancer identified with portrayals of gangsters in crime melodramas of the 1930s and 1940s...
became famous as the coin-flipping gangster "Guino Rinaldo" in the 1932
Howard HawksHoward Winchester Hawks was an American film director, producer and screenwriter of the classic Hollywood era...
/
Howard HughesHoward Robard Hughes, Jr. was an American business magnate, investor, aviator, engineer, film producer, director, and philanthropist. He was one of the wealthiest people in the world...
film
ScarfaceScarface is a 1932 American gangster film starring Paul Muni and George Raft, produced by Howard Hughes, directed by Howard Hawks and Richard Rosson, and written by Ben Hecht based on the 1929 novel of the same name by Armitage Trail...
(1932).
Bugs BunnyBugs Bunny is a animated character created in 1938 at Leon Schlesinger Productions, later Warner Bros. Cartoons. Bugs is an anthropomorphic gray rabbit and is famous for his flippant, insouciant personality and his portrayal as a trickster. He has primarily appeared in animated cartoons, most...
parodies Raft in the classic 1946 animated short film
Racketeer RabbitRacketeer Rabbit is a 1946 animated short film in the Looney Tunes series produced by Warner Bros. Cartoons, Inc. It stars Bugs Bunny, who duels with a pair of racketeers or gangsters, Rocky and Hugo forerunners who resemble Edward G. Robinson and Peter Lorre...
. Raft himself later parodied his own gangster persona as the character "Spats Colombo" in
Billy WilderBilly Wilder was an Austro-Hungarian born American filmmaker, screenwriter, producer, artist, and journalist, whose career spanned more than 50 years and 60 films. He is regarded as one of the most brilliant and versatile filmmakers of Hollywood's golden age...
's 1959 comedy
Some Like It HotSome Like It Hot is an American comedy film, made in 1958 and released in 1959, which was directed by Billy Wilder and starred Marilyn Monroe, Tony Curtis, Jack Lemmon and George Raft. The supporting cast includes Joe E. Brown, Pat O'Brien and Nehemiah Persoff. The film is a remake by Wilder and I....
: Raft sees another mobster flipping a coin and responds, "Where did you pick up that cheap trick?" Raft's coin-tossing established a distinctive motif used in numerous later gangster movies.
In the
1939 filmThe year 1939 in motion pictures can be justified as being called the most outstanding one ever, when it comes to the high quality and high attendance at the large set of the best films that premiered in the year .- Events :Motion picture historians and film often rate...
Mr. Smith Goes to WashingtonMr. Smith Goes to Washington is a 1939 American drama film starring Jean Arthur and James Stewart about one man's effect on American politics. It was directed by Frank Capra and written by Sidney Buchman, based on Lewis R. Foster's unpublished story. Mr...
, a
state governorIn the United States, the title governor refers to the chief executive of each state or insular territory, not directly subordinate to the federal authorities, but the political and ceremonial head of the state.-Role and powers:...
has to select an interim
SenatorThe United States Senate is the upper house of the bicameral legislature of the United States, and together with the United States House of Representatives comprises the United States Congress. The composition and powers of the Senate are established in Article One of the U.S. Constitution. Each...
, and he is being pressured by two opposing factions to choose between their respective candidates, Mr. Hill and Mr. Miller. Unable to choose, he flips a coin in the privacy of his office, but it falls against a book and lands on edge. Consequently, he makes neither choice and chooses Mr. Smith.
In the climax of
SholaySholay is a 1975 Indian action-adventure film produced by G.P. Sippy and directed by his son Ramesh Sippy. It is considered among the greatest films in the history of Indian cinema. Released on 15 August 1975, it stars Dharmendra, Amitabh Bachchan, Hema Malini, Sanjeev Kumar, Jaya Bhaduri and...
, Veeru and Jaidev decide their next strategy over their encounter with the villains by tossing a coin (they are in habit of deciding over the affairs between themselves this way). It is revealed at the end that the coin used by him is actually a trick coin that always come up
heads.
The 1972 movie adaptation of
Graham GreeneHenry Graham Greene, OM, CH was an English author, playwright and literary critic. His works explore the ambivalent moral and political issues of the modern world...
's novel
Travels with My AuntTravels with My Aunt is a novel written by English author Graham Greene.The novel follows the travels of Henry Pulling, a retired bank manager, and his eccentric Aunt Augusta as they find their way across Europe, and eventually even further afield...
ends with a coin toss that will decide the future of one of the characters. The movie ends with the coin in mid-air, leaving their fate unresolved.
Two-FaceTwo-Face is a fictional comic book supervillain who appears in comic books published by DC Comics. and is an enemy of Batman. The character first appeared in Detective Comics #66 , and was created by Bob Kane and Bill Finger....
, the
comic bookA comic book or comicbook is a magazine made up of comics, narrative artwork in the form of separate panels that represent individual scenes, often accompanied by dialog as well as including...
supervillainA supervillain or supervillainess is a variant of the villain character type, commonly found in comic books, action movies and science fiction in various media.They are sometimes used as foils to superheroes and other fictional heroes...
(most famously as a member of
BatmanBatman is a fictional character created by the artist Bob Kane and writer Bill Finger. A comic book superhero, Batman first appeared in Detective Comics #27 , and since then has appeared primarily in publications by DC Comics...
's
rogues galleryA rogues gallery is a police collection of pictures or photographs of criminals and suspects kept for identification purposes...
), has a double-headed coin with one side defaced—a parallel to his actual character, because one side of his face is deformed—which he relies upon for all of his decisions. He will do evil if it lands on the defaced side, and good on the other side. The coin is also representative of alter-ego Harvey Dent's obsession with
dualismDualism denotes a state of two parts. The term 'dualism' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general or common usages. Dualism can refer to moral dualism, Dualism (from...
and the number 2. In the movie
The Dark KnightThe Dark Knight is a 2008 superhero film directed, produced and co-written by Christopher Nolan. Based on the DC Comics character Batman, the film is part of Nolan's Batman film series and a sequel to 2005's Batman Begins...
, the coin starts out clean, and Harvey Dent uses this trick coin to seemingly leave important decisions to chance ("Heads I go through with it"). The coin is later blackened on one side in the explosion that kills his fiancée,
Rachel DawesRachel Dawes is a fictional character who first appeared in Christopher Nolan's 2005 feature film, Batman Begins. She was portrayed in that film by Katie Holmes and as a child in flashback scenes by Emma Lockhart. Katie Holmes also voiced Rachel in the Batman Begins video game. Maggie Gyllenhaal...
. In
Batman ForeverBatman Forever is a 1995 American superhero film directed by Joel Schumacher and produced by Tim Burton. Based on the DC Comics character Batman, the film is a sequel to Batman Returns , with Val Kilmer replacing Michael Keaton as Batman...
however, he would sometimes flip several times till he got the side he wanted.
In
The Twilight ZoneThe Twilight Zone is an American anthology television series created by Rod Serling, which ran for five seasons on CBS from 1959 to 1964. The series consisted of unrelated episodes depicting paranormal, futuristic, dystopian, or simply disturbing events; each show typically featured a surprising...
episode "
A Penny for Your Thoughts"A Penny for Your Thoughts" is an episode of the television series The Twilight Zone.-Synopsis:Hector B. Poole, a timid bank clerk, gains telepathic powers after tossing a coin that miraculously stands on its edge...
," the main character buys a newspaper, and flips a coin into the collection pan, where it lands on its edge. As a consequence, he can hear people's thoughts, but at the end of the day he knocks the coin off its edge when dropping another coin into the pan, which causes him to lose his
telepathicTelepathy , is the induction of mental states from one mind to another. The term was coined in 1882 by the classical scholar Fredric W. H. Myers, a founder of the Society for Psychical Research, and has remained more popular than the more-correct expression thought-transference...
ability.
Tom StoppardSir Tom Stoppard OM, CBE, FRSL is a British playwright, knighted in 1997. He has written prolifically for TV, radio, film and stage, finding prominence with plays such as Arcadia, The Coast of Utopia, Every Good Boy Deserves Favour, Professional Foul, The Real Thing, and Rosencrantz and...
's
Rosencrantz & Guildenstern Are DeadRosencrantz and Guildenstern Are Dead is an absurdist, existentialist tragicomedy by Tom Stoppard, first staged at the Edinburgh Festival Fringe in 1966. The play expands upon the exploits of two minor characters from Shakespeare's Hamlet, the courtiers Rosencrantz and Guildenstern...
begins with a series of coin tosses that all come up heads, implying that the characters are suspended in one unchanging moment of time before becoming part of the play.
In the video game
Final Fantasy VIis a role-playing video game developed and published by Square , released in 1994 for the Super Nintendo Entertainment System as a part of the Final Fantasy series. Set in a fantasy world with a technology level equivalent to that of the Second Industrial Revolution, the game's story focuses on a...
brothers Edgar and Sabin flip a coin in order to determine who succeeds the throne of Figaro. It is later revealed that Edgar used a double-headed coin in order to win, allowing Sabin to live without the burden of the kingdom. This coin is also seen if Edgar is present in the first encounter with the gambler Setzer, who is highly amused by it when it is used to trick him into providing his airship.
In the video game "Shenmue 2" gang leader Wuying Ren carries a double-sided coin in each pocket, asking for a head or tail call before pulling the coin out and flipping the coin. This process guarantees him victory in the outcome of the coin toss, usually forcing protagonist Ryo into a dangerous situation. The trickery behind this method is revealed as the characters part ways at the end of the game.
In
FuturamaFuturama is an American animated science fiction sitcom created by Matt Groening and developed by Groening and David X. Cohen for the Fox Broadcasting Company. The series follows the adventures of a late 20th-century New York City pizza delivery boy, Philip J...
episode
The Farnsworth Parabox"The Farnsworth Parabox" is the fifteenth episode of the fourth production season of Futurama. It first aired June 8, 2003, as the tenth episode in the fifth broadcast season. The episode was written by Bill Odenkirk and directed by Ron Hughart.- Plot :...
, Professor Farnsworth
creates a parallel universe"The Farnsworth Parabox" is the fifteenth episode of the fourth production season of Futurama. It first aired June 8, 2003, as the tenth episode in the fifth broadcast season. The episode was written by Bill Odenkirk and directed by Ron Hughart.- Plot :...
. The only difference between
our universe and the other is that every time someone flipped a coin, it landed on the opposite side. This leads to extremely different worlds and humorous confusion.
In the American
comedyComedy , as a popular meaning, is any humorous discourse or work generally intended to amuse by creating laughter, especially in television, film, and stand-up comedy. This must be carefully distinguished from its academic definition, namely the comic theatre, whose Western origins are found in...
film
Mouse Hunt, out-of-work brothers Lars and Ernie toss a coin to decide who gets to sleep in the only bed in the inherited house. The coin ends up spinning on the floor and coming to rest on edge—an extremely rare and unlikely occurrence—so the brothers share the bed.
The
Hong KongHong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...
-made film
Shaolin SoccerShaolin Soccer is a 2001 Hong Kong comedy film co-written, directed by and starring Stephen Chow. A former Shaolin monk reunites his five brothers, years after their master's death, to apply their superhuman martial arts skills to play soccer and bring Shaolin kung fu to the masses.In 2008 a...
contains a scene in which one of Sing's brothers is being asked to join Sing's soccer team, and he refuses because he mathematically predicts the team will fail; he uses a coin toss to demonstrate his point, saying it has zero chance of landing on its edge. When the coin is carelessly dropped later in the scene, the brother is amazed to discover that it has, indeed, landed on its edge and become stuck inside a small crack in the asphalt.
The DVD of
Final Destination 3Final Destination 3 is a 2006 supernatural slasher film, and the third film in the Final Destination series. The film was directed and written by James Wong, who co-wrote and directed the first film, and was produced by Craig Perry. It was released in North America on February 10, 2006...
has a special feature allowing the viewer to flip a coin apparently to determine the outcome of the movie; however, the outcome is fixed to maintain the plot, and the coin flip is ignored.
Isaac AsimovIsaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...
's short story
The Machine that Won the WarThe Machine that Won the War is a science fiction short story by Isaac Asimov. The story first appeared in the October 1961 issue of The Magazine of Fantasy & Science Fiction, and was reprinted in the collections Nightfall and Other Stories and Robot Dreams...
ends with a character revealing that he made his decisions based on coin tosses.
The final episode of the American television series
JAGJAG is an American adventure/legal drama television show that was produced by Belisarius Productions, in association with Paramount Network Television and, for the first season only, NBC Productions...
ends with an incomplete coin flip.
In an episode of
Malcolm in the MiddleMalcolm in the Middle is an American television sitcom created by Linwood Boomer for the Fox Network. The series was first broadcast on January 9, 2000, and ended its six-and-a-half-year run on May 14, 2006, after seven seasons and 151 episodes...
, Malcolm decides to flip a coin in order to resolve a dispute about keeping a potentially offensive cardboard cut-out up in the store that he works in (citing that logic wasn't good enough). The coin is shown to land on its side, leaving Malcolm uncertain what to do.
In the book
No Country for Old MenNo Country for Old Men is a 2005 novel by U.S. author Cormac McCarthy. Set along the United States–Mexico border in 1980, the story concerns an illicit drug deal gone wrong in a remote desert location. The title comes from the poem "Sailing to Byzantium" by William Butler Yeats...
(and
the film made of itNo Country for Old Men is a 2007 American crime thriller directed by Joel Coen and Ethan Coen, and starring Tommy Lee Jones, Javier Bardem, and Josh Brolin. The film was adapted from the Cormac McCarthy novel of the same name...
), Anton Chigurh, the story's villain, occasionally flips coins for potential victims to decide whether or not to kill them. He allows people to place their life in the hands of
divine providenceKarma in Indian religions is the concept of "action" or "deed", understood as that which causes the entire cycle of cause and effect originating in ancient India and treated in Hindu, Jain, Buddhist and Sikh philosophies....
, and those who refuse to choose are killed anyway, for their obstinacy and refusal to submit to Fate. The meaning of Chigurh's coin-flipping is left ambiguous (in both the book and the film), and has led to considerable discussion: commentators suggest, for example, that Chigurh views himself as simply following the will of the universe, or is "merely cruel," or that it is an inevitable outgrowth of his (perceived) atheism or that Chigurh is in fact a stand-in for fate, or alternatively that his adherence to chance is a way for him to deny responsibility for his actions or to displace that responsibility onto his victims.
In the manga/anime of Hunter x Hunter by
Yoshihiro Togashiis a Japanese manga artist. He began drawing manga at an early age; while he attended college, the publisher Shueisha recognized his talent. Togashi has authored numerous manga series in different genres during the past three decades...
, a servant of the Zaolydeck family challenges Gon and his companions, Leorio and Kurapica, to a game involving a coin flip. The game is simple: Yoshihiro flips the coin in the air and quickly snatches it before the coin falls, then Gon or his companions have to say which hand the employee caught the coin with. This proves to be incredibly difficult due to the unrealistic speed of the coin flipper's hands. Gon is very observant and is occasionally able to guess right.
See FlipismFlipism, sometimes written as "Flippism," is a pseudophilosophy under which all decisions are made by flipping a coin. It originally appeared in the Disney comic "Flip Decision" by Carl Barks, published in 1953...
.
In
ScrubsScrubs is an American medical comedy-drama television series created in 2001 by Bill Lawrence and produced by ABC Studios. The show follows the lives of several employees of the fictional Sacred Heart, a teaching hospital. It features fast-paced screenplay, slapstick, and surreal vignettes...
episode
"My Best Friend's Baby's Baby and My Baby's Baby", protagonist J.D. and Kim cannot decide whether or not to keep their baby after an accidental pregnancy. When all else fails, they flip a coin, which ironically lands on its edge.
In the mentalist episode blood in, blood out during season 2 Patrick Jane CBI consultant wins a wager by flipping a coin and it landing on heads 20 times in a row.
External links
- Heads or Tails? (A discussion of the predictability of a coin toss; with references)
- The Not So Random Coin Toss (Brief blurb about Persi Diaconis' work, with a photograph of the coin-tossing machine)
- Dynamical Bias in the Coin Toss (by Persi Diaconis, Susan Holmes, and Richard Montgomery; very detailed)
- Whether divination by drawing lots is unlawful? (From the Summa Theologica
The Summa Theologiæ is the best-known work of Thomas Aquinas , and although unfinished, "one of the classics of the history of philosophy and one of the most influential works of Western literature." It is intended as a manual for beginners in theology and a compendium of all of the main...
of Thomas AquinasThomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...
)
- The Casting of Lots (Discussion of making decisions by chance outcomes throughout history)
- Coin Tossing — mathworld.com (Contains information about counterintuitive properties of coin tossing)
- Leads in Coin Tossing by Fiona Maclachlan, The Wolfram Demonstrations Project.