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Bob feels that Fermat's method is unfair. He argues that the game should terminate after someone has 5 points. Therefore, Alice only has three ways

Bob feels that Fermat's method is unfair. He argues that the game should terminate after someone has 5 points. Therefore, Alice only has three ways to win ("A", "BA", "BBA"), and Bob has one way to win ("BBB").Therefore, the pot should be split in 3:1. What do you think about Bob's argument? Is it correct or wrong? Explain:

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