The Favoured Gambler
A gambler starts with $3. Each round she bets $1 and wins it with probability 2/3 or loses it with probability 1/3, independently. She stops when she reaches $0 or $6. What is the probability that she reaches $6? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Roll Until Six 3.0/10
Source: Gambler's ruin with unequal odds, classical since Huygens and de Moivre. Statement written for AxiomIQ.