Elo from LessWrong suggested this problem:
I write a sequence of n heads or tails on paper.
I then start flipping a sequence of n coins. If next coin does not match my sequence, I restart a new sequence of n coins.
What is the rule for the relationship between how many coins I need to flip to get the sequence I have pre-committed to and the length of the sequence of?
Discussion there:
http://lesswrong.com/r/discussion/lw/pg3/open_thread_september_25_october_1_2017/dxlt