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!