The drunk one step from the cliff
Asked at SIG, DRW
A drunk stands at position , one step from a cliff at position . Each step he moves toward the cliff (to a lower number) with probability or away from it (to a higher number) with probability . The line extends infinitely away from the cliff. If he ever reaches position , he falls.
What is the probability he eventually falls off the cliff, starting from position ?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.