PlaidX comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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How about if the wager is that anybody in any room can guess the outcome of the coinflip, and if they get it right they win 1$ and if they get it wrong they lose 2$?
If you still think it's 50% after waking up in a green room, you won't take the bet, and you'll win 0$, if you think it's 90% you'll take the bet and come out 14$ ahead on balance, with two of you losing 2$ each and 18 of you getting $1.
Doesn't this show anthropic reasoning is right as much as the OP shows it's wrong?