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Laura comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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I would be interested in know if your opinion would change if the "predictions" of the super-being were wrong .5% of the time, and some small number of people ended up with the $1,001,000 and some ended up with nothing. Would you still 1 box it?
If a bunch of people have played the game already, then you can calculate the average payoff for a 1-boxer and that of a 2-boxer and pick the best one.