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If player C survives to the end of the first round, he will definitely kill one of the remaining contestants. Assuming both A and B are still alive, he will have to chose one of them to shoot.
Since B will have a higher chance of killing C, it is reasonable to assume that C will shoot at B and not at A.
B knows this, and when it's his turn to shoot, he will shoot at C rather than at A.
Thus, if both B and C are alive after A's turn, A is guaranteed survival in the first round, plus the first shot in the second at whichever opponent survives the first.
However, if A shoots and kills B, he is sure to be killed by C who will only have one targer to shoot at. If A shoots and kills C, he has a 50% chance of being killed by B with the next shot, without a chance to shoot at B first.
Therefore, it is to A's advantage that both B and C survive his turn. Therefore, he is better off missing deliberately than shooting either of the other participants.
(You can look here for a more statistically thorough solution.) |
