The answer is dependong on what Omega would have done if he had predicted that you will refuse the 10 iff there is nothing in Alpha’s envelope. Two possibilities :
Omega1 would have brought you the envelope anyway, but said nothing else
Omega2 wouldn’t have bothered to come, since there’s no paradox involved.
When dealing with Omega1, take the £10, yay, free money ! (there wasn’t anything in the envelope anyway, otherwise Omega wouldn’t have visited you, the taker-of-free-money—see Vladimir’s explanation)
The post as stated doesn’t tell us which Omega we’re dealing with, so I would have to guess. I’d say Omega2 (so I wouldn’t take the coin), but any information about Omega may switch that the other way.
When dealing with Omega2, don’t take the £10, ’cause Omega2 doesn’t visit takers-of-free-money when the envelope is full, and you want omega to be visiting you!
The answer is dependong on what Omega would have done if he had predicted that you will refuse the 10 iff there is nothing in Alpha’s envelope. Two possibilities :
Omega1 would have brought you the envelope anyway, but said nothing else
Omega2 wouldn’t have bothered to come, since there’s no paradox involved.
When dealing with Omega1, take the £10, yay, free money ! (there wasn’t anything in the envelope anyway, otherwise Omega wouldn’t have visited you, the taker-of-free-money—see Vladimir’s explanation)
The post as stated doesn’t tell us which Omega we’re dealing with, so I would have to guess. I’d say Omega2 (so I wouldn’t take the coin), but any information about Omega may switch that the other way.
When dealing with Omega2, don’t take the £10, ’cause Omega2 doesn’t visit takers-of-free-money when the envelope is full, and you want omega to be visiting you!
Omega didn’t bring you the envelope. It arrived before he got there.