Basically, if you are already an entity which has reflectively optimized its decision procedure for Alpha-Omega situations, then you and Vladimir are making the right choice. But I was not such an entity, and so my choice was the right one for me.

Actually, not. Like I said, your choice there doesn't affect what the envelope contains. If you were rational like me and Vladimir, you wouldn't meet Omega. You'd just receive an envelope with £1 000 000 in it. Funny thing with this envelope-puzzle is that Omega makes refursers and accepters to live in different conditionals. If you end up answering "refuse", you're in the conditional "Alpha decided to send you money". If you answer "accept", you're in the conditional "Alpha decided not to send you money". However, your choice doesn't have any power over these conditionals, regardless of what you'd choose, Alpha's coin toss wouldn't be affected.

And because your choice doesn't affect what the envelope contains, you're not actually winning anything by refusing £10. Your refusal is simply a-causally making Omega appear in front of you after you got £1 000 000 from Alpha. Just like it is making a-causally Omega appear in front of me and Vladimir after we didn't get anything. It doesn't say anything about our chances to win £1 000 000, which were 50-50. And like I noted earlier, because of this, occasionally we receive enveloped that hold 1 000 000, while you occasionally receive empty envelopes.