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Suppose I have a biased coin with probability of heads p, and tails q=(1-p). It is then used in a game which lasts at most N tosses, and start with a stake of £1. Each time the coin is tails my money is doubled. The first time it comes down heads my money is reduced to £1, and the second time it comes down heads, I lose all my money. The game ends after N tosses, or after the second head. What is the expectation of my money at the end of the game?

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    Sounds like [Gambler's ruin](http://en.wikipedia.org/wiki/Gambler's_ruin#Unfair_coin_flipping) to me.2011-04-17
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    @Undercover Mathematician In the gambler's ruin problem, there is no limit on the number of coin tosses. So this problem is not quite the same.2011-04-17
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    Ah, you're right. Thanks!2011-04-17

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