Question

A, B, and C are to fight a three-cornered pistol duel. All know that A's chance of hitting his target is 0.3, C's is 0.5, and B never misses. They are to fire at their choice of target in succession in the order A, B, C, cyclically (but a hit man loses further turns and is no longer shot at) until only one man is left unhit. What should A's strategy be?

Answer 1

A's best strategy in the three-cornered pistol duel is to intentionally miss on his first turn to improve his chances against B, who never misses.

Step-by-step explanation:

The question involves determining A's best strategy in a three-cornered pistol duel given the probabilities of hitting the target for each participant. As stated, A has a 0.3 probability of hitting his target, C has a 0.5 probability, and B never misses.

A should aim at the ground (intentionally miss), which forces B to fire at C, because B is sure to hit and eliminate one competitor. If B hits C, A will have a 1-on-1 duel with B, giving A a chance to fire again before B can return fire. If C misses A afterward, A stands a better chance than in a direct exchange of fire considering their hit probabilities.

A's goal should be to increase his chances of survival in the duel. Since B never misses, A should try to eliminate B as quickly as possible. However, if A targets B first, C has a higher chance of hitting A in the next round. Therefore, A's strategy should be to target C in the first round, increasing his chances of survival.

If A hits C, then A has a higher chance of winning against B in the second round. If A misses C, it's better for A if C hits B, as this increases A's chances of winning against C in the next round.