Mathematics Problem Of the Week

Fall 2001

POW #7

Paintball Duel

Brian, Caldwell and Dennis are paintball enthusiasts who decide to set up a three-way duel. They put their names in a hat and agree to shoot in the order that names are drawn (at random) from the hat. Once the order has been determined, it will be repeated until the game is over. When it's one player's turn, he may choose one opponent at whom to fire and once a player has been hit he is out of the game. Assume that Brian always hits the person he is aiming at, Caldwell is successful on 80% of his shots, and Dennis hits his target on just 50% of his shots. The winner is the player left after his two opponents have been hit.

If we assume that each player chooses a target to try to maximize the probability that he wins the duel, who has the best chance of surviving? Support your answer with appropriate probabilistic calculations for each player, but be careful, the obvious strategy may not be the best.

Due Friday, November 2^nd at Noon.