Truel

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.Citation
last1=Kilgour
first1=D. Marc
last2= Brams
first2=Stephen J.
year=1997
month=December
title=The Truel
journal=Mathematics Magazine
volume=70
issue=5
pages=315-326 ]

Game theory overview

A variety of forms of truels have been studied. 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 and deliberate missing is allowed, the best strategy for the first shooter is to deliberately miss. Since they are 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 them. If the first shooter does not deliberately miss, they will presumably be shot by whichever shooter remained.

If an unlimited number of bullets are used, the players in a truel will generally shoot at each other until only one player is left. The best strategy is generally to aim for the best shooter first, since that minimizes the risk from the second and subsequent shots. Therefore, it is theoretically best to be the worst shot in the hope that the better shots will kill each other leaving you with the worst shot, assuming all shootists know one another's skill.

Truels in popular culture

In one of the most famous spaghetti westerns, "The Good, the Bad and the Ugly", 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 truel is also parodiedFact|date=March 2008 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 ""; all three characters survive.

References

ee also

*Mexican standoff