I play $n$ games of chess against my friend. I have a probability $p$ of winning, my friend a probability of $1-p$ of winning a single game. Assume games are independent.
What is the probability that one of us wins $x$ successive frames in the $n$ games, where $ x \leq n$?
I thought about using the geometric distribution of some sorts as this seems natural, given we're on about successive trials, but I've not got anywhere with it.