# Will you prefer to go first or second if you are given a choice ?

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You are stuck with a gangster who likes to play it rough. The only way to survive is to accept his invitation to play Russian Roulette.

He presents a revolver in which, three bullets have been placed consecutively. Now he spins the chamber cylinder of the gun. The cylinder wont be spun again. The gun will be passed between both of you till the gun fires and one of you is dead.

Will you prefer to go first or second if you are given a choice ?

posted Jul 27, 2015

Going second will double your chance of survival.
As the bullets are in consecutive chambers, lets call them chamber 1, 2 and 3.

If the starting chamber is 1, 2, 3 or 5 will be fatal for whoever goes first.
If the starting chamber is 4 or 6 will be fatal for whoever goes second.

Answer: choose to go second, you have a 4/6 or 2/3 chance of winning.

Let us label the chambers for our convenience as C1, C2... C6.
Now, when the cylinder is spun, there can be the following six outcomes.
1. If C1 is fired first: Player 1 dies.
2. If C2 is fired first: Player 1 dies.
3. If C3 is fired first: Player 1 dies.
4. If C4 is fired first: Player 2 dies (First shot, player 1, C4 empty. Second shot player 2, C5, empty. Third shot player 1, C6 empty. Fourth shot player 2, C1 not empty.)
5. C5 is fired first: Player 1 dies (First shot, player 1, C5 empty. Second shot player 2, C6, empty. Third shot player 1, C1 not empty.)
6. C6 is fired first: Player 2 dies (First shot, player 1, C6 empty. Second shot, player 2, C1, not empty)
Therefore, if you choose to go second, you have a 4/6 or 2/3 chance of winning.

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