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.
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.