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>>>Previous history has no effect on future outcomes. A fair coin could come up heads a billion times in a row as well. The next flip will still be 0.5.

You hit the nail on the head here - a fair coin would. But if there are unfair coins, things start to change. If we know there's an unfair coin, and we see an unusual run, we should consider that it may be that coin.

Think of this: increase the flips to 1000, and you're still getting heads each time. Would you bet on the next being heads or tails?



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