Puzzle
A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty standardd six-round revolver, spins it, points it at your head and shoots. …click… You are still alive. He then asks you, “do you want me to spin it again and fire or pull the trigger again right away?” For each option, what is the probability that you’ll be shot?
Solution
With 2 bullets arranged consecutively in a six round revolver, there is only 6 ways to arrange the bullets in the revolver. Here are the six possible ways to arrange two bullets consecutively in a six round revolver.
Additional insight, if you are familiar with Mathematical Probability: There is 6C1 i.e. 6 ways to arrange 2 bullets consecutively. If you wonder why it is not 6C2, here is why: since the two bullets are arranged one right next to the other, the moment you choose a slot for a bullet, the slot for the next is chosen implicitly.
The probability of getting shot in the first round is when the revolver was in arrangement #1 or #4 from the above picture. In other words, there is a 2 out of 6 i.e. 33% chances that you get killed by the gangster when the revolver is spin and fired; in other words, 100% – 33% = 67% chance of surviving.
Once you survive the first round, we can eliminate the arrangements #1 and #4 from the possibilities. Now, there are four ways the revolver could be arranged, and out of those four ways, one way is with a bullet in the current chamber where the revolver’s firing pin is pointing. In other words, once you survive the first firing, there is a 25% chance that you could be killed by the gangster if he pulls the trigger again right away without spinning the cylinder of the revolver; in other words, 100% – 25% = 75% chance of surviving.
Conclusion
The optimal choice to increase your probability of surviving is to let the gangster fire right away. You have a 67% chance of surviving if you spin the revolver, and a 75% chance if you fire right away without spinning. Dare the gangster to fire right away! 😉
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