Yes that was my reasoning too. The situation presumably goes:
Omicron chooses a random number X, either prime or composite
Omega simulates you, makes its prediction, and decides whether X’s primality is consistent with its prediction
If it is, then:
Omega puts X into the box
Omega teleports you into the room with the boxes and has you make your choice
If it’s not, then...? I think the correct solution depends on what Omega does in this case.
Maybe it just quietly waits until tomorrow and tries again? In which case no one is ever shown a case where the box does not contain Omicron’s number. If this is how Omega is acting, then I think you can act as though your choice affects Omircon’s number, even though that number is technically random on this particular day.
Maybe it just picks its own number, and shows you the problem anyway. I believe this was the assumption in the post.
The fact that the 2 numbers are equal is not always true, it is randomly true on this day.
Yes that was my reasoning too. The situation presumably goes:
Omicron chooses a random number X, either prime or composite
Omega simulates you, makes its prediction, and decides whether X’s primality is consistent with its prediction
If it is, then:
Omega puts X into the box
Omega teleports you into the room with the boxes and has you make your choice
If it’s not, then...? I think the correct solution depends on what Omega does in this case.
Maybe it just quietly waits until tomorrow and tries again? In which case no one is ever shown a case where the box does not contain Omicron’s number. If this is how Omega is acting, then I think you can act as though your choice affects Omircon’s number, even though that number is technically random on this particular day.
Maybe it just picks its own number, and shows you the problem anyway. I believe this was the assumption in the post.