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Vladimir_Nesov comments on No Anthropic Evidence - Less Wrong
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I am missing something. The total probability of being shot while playing is never more than 50%, why would you ever quit?
If you believe that the gun is loaded, you would want to quit, as in that case the probability of dying approaches 100% as you continue playing (see the second paragraph). The puzzle is in interpretation of observing 1000 "heads": in a certain sense it may feel that this implies that the gun is likely loaded, but it actually doesn't, so indeed you won't want to quit, as you won't be able to ever conclude anything about the state of the gun.
I have no idea in what sense (short of the quantum immortality speculations) the gun can be considered likely loaded. 1000 heads means unfair coin, not loaded gun. If you are 100% sure (how un-Bayesian) that the coin is fair, then the past history does not matter. In which case you should keep playing, since your probability of survival is at least 50%, better than in the case of quitting.
Basically it's the same sort of reasoning that gets you quantum suicide - "if the gun is loaded all the 'me' sees all heads, while if the gun is unloaded only a small fraction of me sees all heads, therefore if I see all heads the gun is more likely to be loaded." One simply ignores the fact that the probability of all heads is the same in both cases.
Since the coin flips after the first are made with a different coin, it doesn't matter whether that coin is fair. You probably can conclude that it's unfair, but as long as it's capable of coming down tails at all, the probability of surviving the game indefinitely is still 50%.
But biased coins do not exist short of the total bias of a double-headed coin. Biased coin-flippers do. So since it's you flipping your own coin, 1000 heads means you rigged the game.