Imagine someone named Omega offers to play a game with you. Omega has a bag, and they swear on their life that exactly one of the following statements is true:
They put a single piece of paper in the bag, and it has “1” written on it.
They put 10 trillion pieces of paper in the bag, numbered “1”, “2″, “3”, etc. up to ten trillion.
Omega then has an independent neutral third party reach into the bag and pull out a random piece of paper which they then hand to you. You look at the piece of paper and it says “1” on it. Omega doesn’t get to look at the piece of paper, so they don’t know what number you saw on that paper.
Now the game Omega propose to you is: If you can guess which of the two statements was the true one, they’ll give you a million dollars. Otherwise, you get nothing.
Which do you guess? Do you guess that the bag had a single piece of paper in it, or do you guess that the bag had 10 trillion pieces of paper in it?
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.