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Alice and Bob each choose their own coin's chance of heads, and Alice must announce hers first. For which choices by Alice can Bob never expect to win?

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Alice and Bob each choose the heads-probability of their own coin, then both flip. HH: Alice pays Bob $6. TT: Alice pays Bob $4. Otherwise Bob pays Alice $5. Alice must announce her probability before Bob chooses his. For which values of Alice's probability does Bob have non-positive expected value whatever he chooses?

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