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Russian Roulette Probability Question Watch

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    We're playing Russian Roulette with a six-chambered revolver. I have loaded two rounds in adjacent chambers, and fired once. It was a blank, and the cylinder has advanced by one position.

    Would you prefer to fire again straight away, or to spin the chamber before firing?
    Of course, there are natural interesting generalisations which we can talk about once the starter question has been dispatched.
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    Feel free to post your solutions in spoiler tags.
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    desperate times ....
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    (Original post by Swadq)


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    We're playing Russian Roulette with a six-chambered revolver. I have loaded two rounds in adjacent chambers, and fired once. It was a blank, and the cylinder has advanced by one position.

    Would you prefer to fire again straight away, or to spin the chamber before firing?
    Of course, there are natural interesting generalisations which we can talk about once the starter question has been dispatched.
    My answer:

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    You now know that the chamber fired was one of four, which are contiguous. Only one of those four gives rise to the situation that a bullet is in the next chamber. So you have a 25% chance of death with the next shot.

    if you spin the chamber you are back to having a one in three chance of death.

    So stick.
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    Let the 6 respective chambers be C1, C2,...,C6.

    Say C1 was the blank, we now move to C2 - leaving 4 possibilities: C2,C3 with bullets; C3,C4 with bullets; C4,C5 with bullets; C5,C6 with bullets. Thus P(C2 with a bullet) = 1/4

    Now if we spin the chamber, we have 2 bullets remaining in 6 possible chambers, ie a chance of 1/3 of landing on the bullet.

    So stick with C2
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    A few of you have figured out the solution now, so how about thinking about these two problems?

    After a shot is fired, the revolver moves either one chamber forward, or three chambers forward, both with probability 1/2. Now what do you do?
    The two rounds are initially loaded at random, now which option is best?
 
 
 
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