Three-Way Duel With Rational Players
Alice, Bob, and Chad are in a three-way duel. They take turns shooting in the fixed order Alice, Bob, Chad, repeating until only one person remains. Their guns have the following hit probabilities:
- Alice:
/3$
- Bob:
/3$
- Chad: $ (never misses)
If a shot misses the target, it hits no one. Each player plays optimally to maximize their own probability of survival. On each turn, a player may choose to shoot at either opponent -- or choose not to shoot at all.
Under optimal play from all three players, what is the probability that Alice is the last one standing?
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