This analogy is perhaps easier to understand the concept that I am curious about: Using the coin flipping analogy suppose we're going to run a test of ten coin flips. Logically speaking you would expect that there would be about an even 5 heads and 5 tails turn out, right? Now suppose that by some strange chance your first 5 flips are all heads.
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the odds of getting more and more in a row become more scarece, but that doesn't make each individual flip any more or less likely. Each flip still leaves a 50/50 chance that it will be heads or tails. Just like if you are playing poker with, say, 7 people, you will always have a 1 in 7 chance of having a better hand than the rest.
The statistics you are counting, of having the best hand multiple times in a row, just makes the situation that you ALREADY HAD less and less likely. But it already happened, and created that statistic. Your new hands only add to the previous statistics, but you have the same chance as you had each time before to do well.
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~Christine Lee
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