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Thomas comments on LINK: Infinity, probability and disagreement - Less Wrong
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Yes. And there is also a way, to join every looser who does not have the 6 with the 999 winners in a bigger room.
Say, that you find yourself in one of those. How likely it is, that you are the sole looser among nearly 1000 winners?
If you want, you can make it even more extreme. You could have one room with one person, one with two, one with three, etc., each of which contain exactly one loser. Now it seems like the probability of having lost is infinitesimal.