Gambler's Ruin

Senior Quant · Brainteasers & Logic

Symmetric random walk starting at k=5, barriers at 0 and N=10. What is P(reach N before 0)?

Question

A symmetric random walk on

\mathbb{Z}

starts at 0. What is the probability of ever returning to 0? If the walk has drift

p > 1/2

, does it return? State the gambler's ruin result: starting at

k

with absorbing barriers at 0 and

N

, what is the probability of reaching

N

before 0?

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