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In other words, the subjective perception of a copy of you in a typical parallel universe is a seemingly random sequence of wins and losses, behaving as if generated through a random process with probabilities of 50% for each outcome. This experiment can be made more rigorous if you take notes on a piece of pater, writing "1" every time you win and "0" every time you lose, and place a decimal point in front of it all. For example, if you lose, lose, win, lose, win,win,win, lose,lose and win, you'd write ".0010111001." But this is just what real numbers between zero and one look like when written out in binary, the way computers usually write them on the hard drive! If you imagine repeating the Quantum Cards experiment infinitely many times, your piece of paper would have infinitely many digits written on it, so you can match each parallel universe with a number between zero and one. Now what Borel's theorem proves is that almost all of these numbers have 50% of their decimals equal to 0 and 50% equal to 1, so this means that almost all of the parallel universes have you winning 50% of the time and losing 50% of the time.
It's not just that the percentages come out right. The number ".010101010101..." has 50% of its digits equal to 0 but clearly isn't random, since it has a simple pattern. Borel's theorem can be generalized to show that almost all numbers have random-looking digits with no patterns whatsoever. This means that in almost all Level III parallel universes, your sequence of wins and losses will also be totally random, without any pattern, so that all that can be predicted is that you'll win 50% of the time.
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Max Tegmark (Our Mathematical Universe: My Quest for the Ultimate Nature of Reality)