# Clue to Puzzle #51: Three Way Duel or Truel

51. Alice, Bob, and Cheri, three smart people, arrange a three-way duel. Alice is a poor shot, hitting her target only 1/3 of the time on average. Bob is better, hitting his target 2/3 of the time. Cheri is a sure shot hitting 100% of the time. They take turns shooting, first Alice, then Bob, the Cheri, then back to Alice, and so on until one is left. What is Alice's best course of action? And her chances of survival?
We assume that all players act rationally, that is to say Cheri and Bob will target each other until one dies as they represent the greatest threat to each other. This part of the game is somewhat out of Alice's control. Alice can control who she shoots at or even if she shoots at anyone at all.

Since Bob and Cheri are targeting each other, nobody is targeting Alice, necessarily Alice will end up in a 2 way duel with one of the others. It's about how she can best survive this.

Obviously she would rather face Bob than Carol. But also think about the order in which people fire. Who goes next after someone dies?

Attach some values to these competing factors and Bob's your late uncle.

If you want a little more help I have written a simulator for different scenarios hidden below. click here to view it

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