Jump frog, jump!

An infinite line of stepping stones stretches out into an infinitely large lake.

A frog starts on the second stone from the shore.

Every second, he takes a jump to a neighboring stone. He has a 60% chance of jumping one stone closer to the shore and a 40% chance of jumping one stone further away from the shore.

What is the expected value for the number of jumps he will take before reaching the first stone (the one closest to the shore)?


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