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You double your bet after every loss on a fair coin, starting at $1 and stopping at the first win, with a $63 bankroll. What is your expected profit?

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In a game on a fair coin where Heads doubles your bet and Tails loses it, you bet $1, then $2 after a loss, then $4 and so on until you finally win, then stop. You have a total bankroll of $63 for this strategy. What is your expected profit? Candidates report this question with different numbers from one sitting to the next.

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