Truel
Encyclopedia
A truel is a neologism for a duel
between three opponents, in which players can fire at one another in an attempt to eliminate them while surviving themselves.
. Features that determine the nature of a truel include
There is usually a general assumption that each player in the truel wants to survive, and will behave logically in a manner that maximizes individual probabilities of survival.
In the widely studied form, the three have different probabilities of hitting their target.
If a single bullet is used, the probabilities of hitting the target are equal and deliberate missing
is allowed, the best strategy for the first shooter is to deliberately miss. Since he is now disarmed, the next shooter will have no reason to shoot the first one and so will shoot at the third shooter. While the second shooter might miss deliberately, there would then be the risk that the third one would shoot him. If the first shooter does not deliberately miss, he will presumably be shot by whichever shooter remained.
If an unlimited number of bullets are used, then deliberate missing may be the best strategy for a duelist with lower accuracy than both opponents.
If both have better than 50% success rate, he should continue to miss until one of his opponents kills the other.
Then he will get the first shot at the remaining opponent.
But if the "middle" opponent is weak, it can better to team up with him until the strongest is eliminated.
The details depend on the firing order. For example, if the order is P, Q, R, with respective probabilities
and it is R's turn, R should waste his shot if:
but not do so if:
In between, R should waste his shot if:
's play "Fat King Melon" (1927). An extensive bibliography has been compiled by D. Marc Kilgour . The word "truel" was introduced in Martin Shubik
's 1964 book "Game Theory and Related Approaches to Social Behavior", page 43, and independently in Richard Epstein's 1967 book "Theory of Gambling and Statistical Logic", page 343.
, the final showdown is played out to be a climactic truel between the three main characters: Blondie ("The Good")
, Angel Eyes ("The Bad"), and Tuco ("The Ugly"). The standoff remains a signature piece for director
Sergio Leone
and one of the best-known scenes in film history
.
The climactic ending to the 1992 film Reservoir Dogs
has a truel between the characters Mr. White, Nice Guy Eddie, and Joe Cabot in which only one survives.
The truel is also parodied
at the climax of the film Dead Again
.
A truel with swords is fought between Jack Sparrow, Will Turner
, and James Norrington
in the 2006 film Pirates of the Caribbean: Dead Man's Chest
; all three characters survive.
The short film Truel explores
the idea of a three-way duel.
Duel
A duel is an arranged engagement in combat between two individuals, with matched weapons in accordance with agreed-upon rules.Duels in this form were chiefly practised in Early Modern Europe, with precedents in the medieval code of chivalry, and continued into the modern period especially among...
between three opponents, in which players can fire at one another in an attempt to eliminate them while surviving themselves.
Game theory overview
A variety of forms of truels have been studied in game theoryGame theory
Game 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...
. Features that determine the nature of a truel include
- the probability of each player hitting their chosen targets (often not assumed to be the same for each player)
- whether the players shoot simultaneously or sequentially, and, if sequentially, whether the shooting order is predetermined, or determined at random from among the survivors;
- the number of bullets each player has (in particular, whether this is finite or infinite);
- whether or not intentionally missing is allowed.
There is usually a general assumption that each player in the truel wants to survive, and will behave logically in a manner that maximizes individual probabilities of survival.
In the widely studied form, the three have different probabilities of hitting their target.
If a single bullet is used, the probabilities of hitting the target are equal and deliberate missing
Delope
Delope is the practice of throwing away one's first fire in a duel, in an attempt to abort the conflict. According to most traditions the deloper must first allow his opponent the opportunity to fire after the command is issued by the secondary, without hinting at his intentions...
is allowed, the best strategy for the first shooter is to deliberately miss. Since he is now disarmed, the next shooter will have no reason to shoot the first one and so will shoot at the third shooter. While the second shooter might miss deliberately, there would then be the risk that the third one would shoot him. If the first shooter does not deliberately miss, he will presumably be shot by whichever shooter remained.
If an unlimited number of bullets are used, then deliberate missing may be the best strategy for a duelist with lower accuracy than both opponents.
If both have better than 50% success rate, he should continue to miss until one of his opponents kills the other.
Then he will get the first shot at the remaining opponent.
But if the "middle" opponent is weak, it can better to team up with him until the strongest is eliminated.
The details depend on the firing order. For example, if the order is P, Q, R, with respective probabilities
and it is R's turn, R should waste his shot if:
but not do so if:
In between, R should waste his shot if:
History
The earliest known mention of three-person "duels" appears to have been in A. P. HerbertA. P. Herbert
Sir Alan Patrick Herbert, CH was an English humorist, novelist, playwright and law reform activist...
's play "Fat King Melon" (1927). An extensive bibliography has been compiled by D. Marc Kilgour . The word "truel" was introduced in Martin Shubik
Martin Shubik
Martin Shubik is an American economist, who is Professor Emeritus of Mathematical Institutional Economics at Yale University. He was educated at the University of Toronto and Princeton University...
's 1964 book "Game Theory and Related Approaches to Social Behavior", page 43, and independently in Richard Epstein's 1967 book "Theory of Gambling and Statistical Logic", page 343.
Truels in popular culture
In one of the most famous spaghetti westerns, The Good, the Bad and the UglyThe Good, the Bad and the Ugly
The Good, the Bad and the Ugly is a 1966 Italian epic spaghetti western film directed by Sergio Leone, starring Clint Eastwood, Lee Van Cleef, and Eli Wallach in the title roles. The screenplay was written by Age & Scarpelli, Luciano Vincenzoni and Leone, based on a story by Vincenzoni and Leone...
, the final showdown is played out to be a climactic truel between the three main characters: Blondie ("The Good")
Man with No Name
The man with no name is a stock character in Western films, but the term usually applies specifically to the character played by Clint Eastwood in Sergio Leone's "Dollars Trilogy."...
, Angel Eyes ("The Bad"), and Tuco ("The Ugly"). The standoff remains a signature piece for director
Film director
A film director is a person who directs the actors and film crew in filmmaking. They control a film's artistic and dramatic nathan roach, while guiding the technical crew and actors.-Responsibilities:...
Sergio Leone
Sergio Leone
Sergio Leone was an Italian film director, producer and screenwriter most associated with the "Spaghetti Western" genre.Leone's film-making style includes juxtaposing extreme close-up shots with lengthy long shots...
and one of the best-known scenes in film history
History of film
The history of film is the historical development of the medium known variously as cinema, motion pictures, film, or the movies.The history of film spans over 100 years, from the latter part of the 19th century to the present day...
.
The climactic ending to the 1992 film Reservoir Dogs
Reservoir Dogs
Reservoir Dogs is an American crime film marking debut of director and writer Quentin Tarantino. It depicts the events before and after a botched diamond heist, but not the heist itself. Reservoir Dogs stars an ensemble cast: Harvey Keitel, Steve Buscemi, Tim Roth, Michael Madsen, Chris Penn, and...
has a truel between the characters Mr. White, Nice Guy Eddie, and Joe Cabot in which only one survives.
The truel is also parodied
Parody
A parody , in current usage, is an imitative work created to mock, comment on, or trivialise an original work, its subject, author, style, or some other target, by means of humorous, satiric or ironic imitation...
at the climax of the film Dead Again
Dead Again
Dead Again is a 1991 psychological thriller/neo-noir directed by Kenneth Branagh, starring Branagh and his then-wife Emma Thompson. Andy García, Derek Jacobi and Robin Williams are also featured.-Plot summary:...
.
A truel with swords is fought between Jack Sparrow, Will Turner
Will Turner
William "Will" Turner, Jr. is a central character in the first three titles of the Pirates of the Caribbean film series produced by Walt Disney Pictures. He is played by Orlando Bloom . Will is a blacksmith's apprentice working in Port Royal...
, and James Norrington
James Norrington
James Norrington, CB is a fictional character in Disney's Pirates of the Caribbean film series. He is played by English actor Jack Davenport.-Character history:...
in the 2006 film Pirates of the Caribbean: Dead Man's Chest
Pirates of the Caribbean: Dead Man's Chest
Pirates of the Caribbean: Dead Man's Chest is a 2006 adventure fantasy film and the second film of the Pirates of the Caribbean series, following Pirates of the Caribbean: The Curse of the Black Pearl . It was directed by Gore Verbinski, written by Ted Elliott and Terry Rossio, and produced by...
; all three characters survive.
The short film Truel explores
the idea of a three-way duel.