(Solution) - Suppose that on each play of a certain game a -(2025 Original AI-Free Solution)

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Suppose that on each play of a certain game, a person will either win one dollar with probability 2/3 or lose one dollar with probability 1/3. Suppose also that the person?s goal is to win two dollars by playing this game. How large an initial fortune must the person have in order for the probability to be at least 0.99 that he will achieve his goal before he loses his initial fortune?