I'll disregard my earlier comment and assume the latter interpretation for now.

So here are the things that can (and can't) happen:

1. Alpha puts £1 000 000 in the envelope.
   1. Omega has predicted you will refuse the £10 and that there is £1 000 000 in the envelope.
      1. You refuse the £10, and find £1 000 000 in the envelope.
      2. You accept the £10 — contradiction, won't happen.
   2. Omega has predicted you will accept the £10 and that the envelope is empty — contradiction, won't happen.
2. Alpha puts nothing in the envelope.
   1. Omega has predicted you will refuse the £10 and that there is £1 000 000 in the envelope — contradiction, won't happen.
   2. Omega has predicted you will accept the £10 and that the envelope is empty.
      1. You refuse the £10 — contradiction, won't happen.
      2. You accept the £10, and find nothing in the envelope.

So, starting with Alpha's coin flip, here are the only possible paths:

1. Alpha puts £1 000 000 in the envelope. Omega has predicted you will refuse the £10 and that there is £1 000 000 in the envelope. You refuse the £10, and find £1 000 000 in the envelope.
2. Alpha puts nothing in the envelope. Omega has predicted you will accept the £10 and that the envelope is empty. You accept the £10, and find nothing in the envelope.
3. Alpha puts £1 000 000 in the envelope. Omega predicts that if it were to offer you this puzzle (while honestly making the given prediction), you would accept the £10, so it has no choice but to leave you alone. You find £1 000 000 in the envelope.
4. Alpha puts nothing in the envelope. Omega predicts that if it were to offer you this puzzle (while honestly making the given prediction), you would reject the £10, so it has no choice but to leave you alone. You find nothing in the envelope.

Unlike in Newcomb's problem, in this case Omega's prediction is irrelevant to what Alpha actually did. The envelope either contains £1 000 000 or nothing, and you're going to receive it as-is, no matter what Omega says about your future actions. If the envelope has £1 000 000 in it, and you're the sort of person who would accept the £10, then Omega will not offer you this conundrum, because it couldn't honestly state the prediction as given — it would just leave you alone with your new riches. Same if the envelope is empty and you are the sort of person who would reject the £10. Your strategy affects nothing other than whether Omega will show up in the first place.

Conclusion: be the sort of person who would accept the £10. It won't affect whether you'll receive the envelope or what you find in it, and if it is empty, at least you'll get that £10 as a consolation prize.

(And now I'll read the rest of the thread to see if smarter people agree with me.)