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Vladimir_Nesov comments on Omega's subcontracting to Alpha - Less Wrong
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You are setting the conditions for appearance of Omega. The best conditions for Omega to appear are those where you take its money, since it's good for nothing else.
By refusing the £10, you maximize the amount of money that the agents who see Omega get, by moving Omega around. It's similar to trying to become a lottery winner by selling to existing lottery winners the same dietary supplement you take, since this makes the takers of this dietary supplement more likely to be lottery winners.
(Added this paragraph to the top-level comment.)
I'm not 100% sure but it seems like you and Jonii are calculating correctly. It's just ironic that if the situation as described happens to you, it means you were unlucky and there's no money in Alpha's envelope, whereas if it happens to someone like me, it means I was lucky and the £1000000 is there.