The Truel Problem

Console application to analyze the effectiveness of different strategies of Truel game.

Imagine that you have a three-way duel (or “truel”). The three duelists are named A, B, and C and have accuracy probabilities of a, b, and c with 0 < a < b < c < 1. The rules of the duel are that the duelists fire sequentially in the starting order A, B, C (so the least accurate person fires first, etc., and continuing to fire in that order) and the last person standing wins the duel. If you are duelist A, what strategy should you use to maximize your chance of winning?

Common Strategy Choices

If you ask most people what A’s strategy should be when all 3 duelists are alive, there are two common answers:

1. Always fire at the most accurate duelist (C).
2. Fire randomly (since you are the least accurate it doesn’t matter). To this we’ll add what seems like a bad option:
3. When there are more than two players in the game, fire your shot into the ground, wasting it, otherwise fire on the remaining player.