Medium · Stochastic Processes & Markov Chains · Numerical · ~10 min · #23
Gambler's Ruin with an Edge
You start with $3 and repeatedly bet $1. Each bet wins with probability and loses with probability . You stop when you reach $10 or go broke.
What is the probability that you reach $10? Give your answer to at least three decimal places.
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Difference equationsAbsorbing Markov chainsGambler's ruin
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