Eight men, including Colonel Mustard, sit at a round table, for a modified game of Russian roulette. They are using a six chamber revolver which has been loaded with 5 bullets.

The game begins by one of the men reaching into a hat, and randomly drawing the name of the first player.

If the first player survives his turn, the gun is handed to his adjacent clockwise neighbor, and his name is immediately returned to the hat.

If the first player loses, his name is thrown away, and the men pull from the hat, and choose the name of the next player.

The game is continued in such a way until either all five bullets have fired, OR a player survives his turn, but no longer has an adjacent clockwise neighbor to pass the gun to.

What is the probability that the Colonel will survive the game?

(Note that the chamber is spun every time a player takes his turn).

The hard part is the probability that a person has an empty chair to his right given there are E empty seats.  Call this P(E).  I havent found this yet.
That way we can find the probability the game will end early given an empty chamber.

The rest is pretty easy as it comes down to geometric series (empty chambers.)

Posted by Jer on 2010-06-08 14:38:31