Consider a gambler who starts with an initial fortune of $1 and then on each successive gam- ble either wins $1 or loses $1 independent of the past with probabilities 0.45 and 0.55 respectively. The gambler's objective is to reach a total fortune of $10, without first getting ruined (running out of money). If the gambler succeeds, then the gambler is said to win the game. In any case, the gambler stops playing after winning or getting ruined, whichever happens first. What is the probabilty that the gambler wins the game?

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