How about simply multiplying? Treat Omega as a fair coin toss. 50% of a million is half-a-million, and that’s vastly bigger than a thousand. You can ignore the question of whether omega has filled the box, in deciding that the uncertain box is more important. So much more important, that the chance of gaining an extra 1000 isn’t worth the bother of trying to beat the puzzle. You just grab the important box.
How about simply multiplying? Treat Omega as a fair coin toss. 50% of a million is half-a-million, and that’s vastly bigger than a thousand. You can ignore the question of whether omega has filled the box, in deciding that the uncertain box is more important. So much more important, that the chance of gaining an extra 1000 isn’t worth the bother of trying to beat the puzzle. You just grab the important box.