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.