I don’t see that the scenario is the same. If you one-box everytime in your thought experiment, you are guaranteed to get the million; if you two box everytime, you will certainly not get the million. With Omega, there is a high probability but not certainty.
Also, what you do in the first round causes what happens in the second round, but with Omega, it is debatable whether what you end up doing causes there to be a million dollars or not.
You point out perhaps the only potentially meaningful difference, and it is the main salient point in dispute between one-boxers and two-boxers in the Omega problem.
First subpoint:
With Omega, you are told (by Omega) that there is certainty—that he is never wrong—and you have a large but finite number of previous experiments that do not refute him. Any uncertainty is merely hoped for/dreaded. (There are versions in which there is definite uncertainty, but those are clearly not similar to the OP.)
Second subpoint:
If there is truly, really, actually no uncertainty, then correlation is perfect. It is hard to determine cause and effect in such conditions with no chance to design experiments to separate them. I’d argue that cause is a low-value concept in such a situation.
I don’t see that the scenario is the same. If you one-box everytime in your thought experiment, you are guaranteed to get the million; if you two box everytime, you will certainly not get the million. With Omega, there is a high probability but not certainty.
Also, what you do in the first round causes what happens in the second round, but with Omega, it is debatable whether what you end up doing causes there to be a million dollars or not.
You won’t one-box every time. There is always some chance, however small, that you will two-box, and vice versa.
You point out perhaps the only potentially meaningful difference, and it is the main salient point in dispute between one-boxers and two-boxers in the Omega problem.
First subpoint: With Omega, you are told (by Omega) that there is certainty—that he is never wrong—and you have a large but finite number of previous experiments that do not refute him. Any uncertainty is merely hoped for/dreaded. (There are versions in which there is definite uncertainty, but those are clearly not similar to the OP.)
Second subpoint: If there is truly, really, actually no uncertainty, then correlation is perfect. It is hard to determine cause and effect in such conditions with no chance to design experiments to separate them. I’d argue that cause is a low-value concept in such a situation.