The way the scenario is given, player is informed that Omega and Omicron’s numbers coincide, but needs to decide for themselves what that implies for whether that number is prime or composite. So if the player is EDT, that player will always two box in this scenario.
I think the sequence of events goes like this:
Omega knows it is about to encounter an EDT, and so starts to simulate them.
The simulated EDT reasons “I should take both boxes, because this makes X composite, which pays more than making X prime by taking one box (the extra $1k being inconsequential)”
Omega, seeing that EDT would take both boxes, thus decides put a composite number in the box.
Omicron selects a random number. It just so happens that the number it selected was coincidentally X.
EDT arrives at the scenario and, as predicted by Omega, takes both boxes.
Omega does not pay 1M (but EDT gets to keep the 1K).
The way the scenario is given, player is informed that Omega and Omicron’s numbers coincide, but needs to decide for themselves what that implies for whether that number is prime or composite. So if the player is EDT, that player will always two box in this scenario.
I think the sequence of events goes like this:
Omega knows it is about to encounter an EDT, and so starts to simulate them.
The simulated EDT reasons “I should take both boxes, because this makes X composite, which pays more than making X prime by taking one box (the extra $1k being inconsequential)”
Omega, seeing that EDT would take both boxes, thus decides put a composite number in the box.
Omicron selects a random number. It just so happens that the number it selected was coincidentally X.
EDT arrives at the scenario and, as predicted by Omega, takes both boxes.
Omega does not pay 1M (but EDT gets to keep the 1K).
Omicron pays 2M.