JGWeissman comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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They are not equivalent. If one green room copy is chosen at random, then the game will be played exactly once whether the coin flip resulted in heads or tails. But if every green room copy plays, the the game will be played 18 times if the coin came up heads and 2 times if the coin came up tails.