Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

420 probability/roulette.p

You are in a game of Russian roulette, but this time the gun (a 6
shooter revolver) has three bullets _in_a_row_ in three of the
chambers. The barrel is spun only once. Each player then points the
gun at his (her) head and pulls the trigger. If he (she) is still
alive, the gun is passed to the other player who then points it at his
(her) own head and pulls the trigger. The game stops when one player
dies.

Now to the point: would you rather be first or second to shoot?

probability/roulette.s

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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