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A casino adds $100 to your $100 for a fair-coin game that pays 4:5, and you must wager at least $500 in total before cashing out. How do you maximise your expected earnings?

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B pays A 1 dollar to play. Then 100 fair coins are tossed, and A pays B x dollars if more than 60 land heads and nothing otherwise. For what x is the game fair?

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