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Jonathan has a coin that may be biased, but he doesn't think so. You disagree with him though, and he challenges you to a bet.

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Jonathan has a coin that may be biased, but he doesn't think so. You disagree with him though, and he challenges you to a bet. You start off with Xo dollars. You and Jonathan then play multiple rounds, and each round, you bet an amount of money of your choosing, and then coin is tossed. Jonathan will match your bet, no matter what, and if the coin comes up heads, you win and you take both yours and Jonathan's bet, and if it comes up tails, then you lose your bet.(a) Now suppose you actually secretly know that the bias of the coin is ?

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