Games and stopping · Random walk · difficulty 3 of 5
One step from the edge
A walker stands one step from the edge of a cliff. Each step, independently, they move one step away from the edge with probability 2/3 and one step toward it otherwise. Reaching the edge means falling. There is no limit on the number of steps. What is the probability that they eventually fall?
Answer with a probability. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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