Seems like you could come up with a recursive formula to compute the expected number of steps to reach hedge N. Along the lines of how you compute the expected

Seems like you could come up with a recursive formula to compute the expected number of steps to reach hedge N. Along the lines of how you compute the expected number of coin flips to get K heads in a row. I'm too lazy to figure it out right now though, so there may be some nuance I'm missing.