I think this line of reasoning relies on the Number Lottery's choice of number being conditional on Omega's evaluation of you as a one-boxer or two-boxer.

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.

Those are not the only precommitments one can make for this type of situation.

Of course! I meant to say that Richard's line of thought was mistaken because it didn't take into account the (default) independence of Omega's choice of number and the Number Lottery's choice of number. Suggesting that there are only two possible strategies for approaching this problem was a consequence of my poor wording.