Truel. A truel is like a duel except there are three players involved. We will c

Question

Truel. A truel is like a duel except there are three players involved. We will call them player A, player B, and Player C. Each player comes with his probability of hitting a target. Player A hits a target with probabilitypA=0.9, Player B with probability pB=0.7 and Player C with probability pC=0.2. The game is played by rounds. At each round the players shoot at each other simultaneously, hence their speed doesn’t matter. The truel is over when ONLY ONE player is still alive or if all three of them are dead. We assumed that each player has infinitely many bullets. No collaboration between players is allowed. No players shoots in the air or misses a round.

What is the expected number of rounds given A won? Same question if B won, C won or nobody won?

Find the probabilities of winning for A,B,C or nobody winning for general probabilities pA, pB, pC.

Explanation / Answer

The question is not clearly defined according to me, because here it is not mentioned how many times a person can fire bullet in each round, most important part is that one,because if any one can fire only one bullet in each round then the answer will be different from the case if anyone can fire more than one bullet in each round.

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