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.