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If, for example, I toss a weighted coin (with a 70% chance of getting heads), how many flips would be needed on average to get a run of 13 heads in a row?

rgk
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    https://math.stackexchange.com/questions/376270/how-many-flips-of-a-fair-coin-does-it-take-until-you-get-n-heads-in-a-row?noredirect=1&lq=1 I believe your answer is here – rgk Jan 12 '20 at 04:50
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    https://stats.stackexchange.com/questions/12174 describes how to solve a generalization of this problem (expected time to realize any specified pattern of heads and tails). A related preliminary question is answered at https://stats.stackexchange.com/questions/338162. – whuber Jan 12 '20 at 13:51

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