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Eliezer_Yudkowsky comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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By assumption, if the person is right to believe they're in a sim, then most of the lottery winners are in sims, so while Omega laughs at them in our world, they win the bet with Omega in most of their worlds.
should have been your clue to check further.
This is a feature of the original problem, isn't it?
Let's say there are 1000 brains in vats, each in their own little world, and a "real" world of a billion people. The chance of a vat-brain winning the lottery is 1, and the chance of a real person winning the lottery is 1 in a million. There are 1000 real lottery winners and 1000 vat lottery winners, so if you win the lottery your chance of being in a vat is 50-50. However, if you look at any particular world, the chances of this week's single lottery winner being a brain in a vat is 1000/1001.
Assume the original problem is run multiple times in multiple worlds, and that the value of pi somehow differs in those worlds (probably you used pi precisely so people couldn't do this, but bear with me). Of all the people who wake up in green rooms, 18/20 of them will be right to take your bet. However, in each particular world, the chances of the green room people being right to take the bet is 1/2.
In this situation there is no paradox. Most of the people in the green rooms come out happy that they took the bet. It's only when you limit it to one universe that it becomes a problem. The same is true of the lottery example. When restricted to a single (real, non-vat) universe, it becomes more troublesome.