221.Gambler's Ruin With an Edge
★★★random walksSIG
You start with and your friend starts with . Each round you bet , and you win the round with probability 2/3. Play continues until one of you is broke. What is the probability that you end up with all ?
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For a biased walk the ruin probability is built from powers of the odds ratio q/p. Here that ratio is a half.
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