The question is also about what strategy to choose. So I would rather not assume nobody can choose to miss.
I might well be wrong, but my calculation is that the right move for A the first shot is to miss. (If he shoots C dead, and B starts to shoot him, he only has 15/15+50 likelihood to survive. It is better to let B make his try first.)
If we take this into consideration, A first misses, B tries to shoot C and if given the chance C shoots B, so on so forth.
There is some correction needed to my post. So
Case 1: %50 C dead first after A's 100% miss and B's 50%. A's overall survival probability in this case is then 50% * (3/3+3.5) = 23.1% and B is 50%-23.1%=26.9%
Case 2: %50 C survives the first round. B is then 100% dead. A's overall survival p in this case is then 50%*30%=15% and C is 50%-15%=35%.
Overall, A survives 38.1%, B is 26.9% and C is 35%.
I might well be wrong, but my calculation is that the right move for A the first shot is to miss. (If he shoots C dead, and B starts to shoot him, he only has 15/15+50 likelihood to survive. It is better to let B make his try first.)
If we take this into consideration, A first misses, B tries to shoot C and if given the chance C shoots B, so on so forth.
There is some correction needed to my post. So
Case 1: %50 C dead first after A's 100% miss and B's 50%. A's overall survival probability in this case is then 50% * (3/3+3.5) = 23.1% and B is 50%-23.1%=26.9%
Case 2: %50 C survives the first round. B is then 100% dead. A's overall survival p in this case is then 50%*30%=15% and C is 50%-15%=35%.
Overall, A survives 38.1%, B is 26.9% and C is 35%.
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