All you need to consider are the six possible bullet configurations

B B B E E E -> player 1 dies E B B B E E -> player 2 dies E E B B B E -> player 1 dies E E E B B B -> player 2 dies B E E E B B -> player 1 dies B B E E E B -> player 1 dies

One therefore has a 2/3 probability of winning (and a 1/3 probability of dying) by shooting second. I for one would prefer this option.

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