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mwengler comments on The Ultimate Newcomb's Problem - Less Wrong
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What? I can't even parse that.
There IS a number in the box which is the same as the one at the Lottery Bank. The number either is prime or it is composite.
According to the hypothetical, if I two-box, there is a 99.9% correlation with Omega putting a composite number in his box, in which case my payooff is $2,001,000. There is a 0.1% correlation with Omega putting a prime number in the box in which case my payoffis $1,001,000. If the correlation is a good estimate of probability, then my expected payoff from two-boxing is $2million more or less. If I one-box, blah blah blah expected payoff is $1million.
Sorry for my poor phrasing. The Number Lottery's number is randomly chosen and has nothing to do with Omega's prediction of you as a two-boxer or one-boxer. It is only Omega's choice of number that depends on whether it believes you are a one-boxer or two-boxer. Does this clear it up?
Note that there is a caveat: if your strategy for deciding to one-box or two-box depends on the outcome of the Number Lottery, then Omega's choice of number and the Lottery's choice of number are no longer independent.