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Aha! Bayesian analysis makes it clear.

Posted By: Jeremy Bagai
Date: Sunday, 28 May 2017, at 12:31 a.m.

In Response To: Fun new probability puzzle (Jeremy Bagai)

From my dear friend (non bg player) Joel Henderson:

Suppose you survive the first shot and are about to take the second. If you have the 2-bullet gun, your chance of survival is now 4/6. If you have the either-1-or-3-bullet gun, your chance of survival is now either 5/6 or 3/6 depending, and yes these average to 4/6.

But the fact that you survived the first shot makes it more likely that you actually have the 1-bullet rather than the 3-bullet gun!

This is, of course, exactly the same math as all other (correct) analyses. But this speaks sweetly and clearly to me. :)

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