Gambler's ruin (unfair)
Player M has $1 and player N has $2. Each round the winner takes $1 from the loser; M wins each round with probability . They play until someone is broke. What is the probability M ends up with all $3? (to 3 decimals)
Show hints (2)+
- Set up absorption equations on states {0,1,2,3}.
- Solve the two linear equations for .
Answer
Reveal answer →Final answer
0.5714 (± 0.005)
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