As formulated, zero -- under the rules you posted you never win anything. Is there an unstated assumption that you can stop the game at any time and exit with your stake?
I guess I didn't formulate the rules clearly enough--if the coin lands on tails, you exit with the stake. For example, if you play and the sequence is HEADS -> HEADS -> TAILS, you exit with $4. The game only ends when tails is flipped.
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