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RichardKennaway comments on No Anthropic Evidence - Less Wrong
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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.
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.