Posted by Jason Polak on 25. February 2018 · Write a comment · Categories: probability · Tags:

Consider three cells as so:

A player (the blue disc) starts out in the left-most cell, and discrete time starts. At each step in time, the player has a 1/2 probability of moving left and a 1/2 probability of moving right. If the player chooses to move left but cannot because it is in the left-most cell, then it does nothing, though that still counts as a move. The game ends when the player reaches the right-most cell.

What is the expected number of moves in this game?
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