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This page calculates the probability of observing a minimum of K consecutive successes in N binomial trials, where p is the probability of success.

Using the numbers already filled in below, this gives the chances of seeing at least one streak of heads of length at least six in 100 flips of a fair coin. You might see exactly one, more than one, or you might see one of length seven; each are among the ways to qualify "at least one streak of at least six."

You could play with the numbers to calculate, for example, the odds of rolling doubles 20 consecutive times out of 500 rolls with fair dice by changing the parameters in the table below.

Number of trials (N):
Length of streak (K):
Probability of success on one trial (p):

This uses an elegant recursion formula described on this website. Scroll down to the "mathematician's answer" for his derivation. Alas, I don't know his name, so I can't give him more proper credit. I inferred which pronoun to use from his photo on the above site, which shows he's male. Anyway, thanks to him and the discussion on the above for motivating this page.

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