I think Randall's strategy can be made a little less abstract, and simpler:
I pick any distribution that has non-zero probability over any subset of the reals. Use it to pick a number. If the revealed number is higher, guess lower, and vice-versa. Ta-da! You win 50% + epsilon/2.
I think. There's still just a whiff of paradox there, but maybe that's just me.
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winterfish
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Date: 2010-03-28 03:59 am (UTC)I pick any distribution that has non-zero probability over any subset of the reals. Use it to pick a number. If the revealed number is higher, guess lower, and vice-versa. Ta-da! You win 50% + epsilon/2.
I think. There's still just a whiff of paradox there, but maybe that's just me.