You could have that conversation, but you don’t have to. The argument for assigning 50% to red is that it’s the only question Omega has asked you. There are several ways out of that. The first one is that the moment he offers you a 25% bet I would update to presume that 3:1 is not a positive e.v. bet, with a new number of perhaps 12.5% with a range of 0% to 25% with symmetric distribution. Similarly, if he offered me three to one that it wasn’t red, I would presume that it probably will be. On a similar note, when he asks about blue (even without any bets involved) I can’t see answering higher than 33.3%.
Contrast this with Alicorn watching this incident and offering me 3:1 after Omega asks my probability for red and I say 50%. I still have to update for Alicorn’s opinion, but I might or might not accept that bet.
You could have that conversation, but you don’t have to. The argument for assigning 50% to red is that it’s the only question Omega has asked you. There are several ways out of that. The first one is that the moment he offers you a 25% bet I would update to presume that 3:1 is not a positive e.v. bet, with a new number of perhaps 12.5% with a range of 0% to 25% with symmetric distribution. Similarly, if he offered me three to one that it wasn’t red, I would presume that it probably will be. On a similar note, when he asks about blue (even without any bets involved) I can’t see answering higher than 33.3%.
Contrast this with Alicorn watching this incident and offering me 3:1 after Omega asks my probability for red and I say 50%. I still have to update for Alicorn’s opinion, but I might or might not accept that bet.