# A good estimate on the probability of getting X “heads” in a row out of N coin flips?

Let's say I flip a coin $N$ times. What is a good upper bound on the probability that I will, at some point during these $N$ flips, get $X$ "heads" in a row?

What is the probability that this will happen $K$ times?

(Example: If my flips are $HTHTHHHHTT$ then I got 3 heads in a row $K=2$ times)

The coin might be biased.

Thanks!

• What is the probability of flipping a "head"? Is it $0.5$? – Pedro Jun 4 '15 at 13:07
• It can be a biased coin. I clarified, thanks. – abacus Jun 4 '15 at 13:09
• I.e., a bound on the exact answer (with $m = X$). – r.e.s. Jun 4 '15 at 14:09