A casino offers the following game:
You flip a fair coin repeatedly and record the results on slips of paper, one result per slip. At any time you may decide to stop, at which time one of the slips is chosen uniformly at random. You win \$1 if the chosen slip says "Heads".
How much should you be willing to pay to play this game, and what is your strategy?
I heard this puzzle several years ago, I do not know the solution.
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