I'm playing a game where I'm tossing a fair coin. When it's heads I gain a dollar. When it's tails I lose a dollar. I play until I have +24 or -36

Question

I'm playing a game where I'm tossing a fair coin. When it's heads I gain a dollar. When it's tails I lose a dollar. I play until I have +24 or -36. What's the probability of each condition?

I'm comparing answers to chatgpt.

Answer 1

You don't need to simulate to get the answers.

• The ambit of the game is $24-(-36) =60$

• Since the odds are even, the up/down relationship will be linear, and the two ends represent the extremities of a straight line

• It is evident that the nearer you are to your goal, the higher your probability of achieving it.

• Thus the probability of success is equal to the fraction of the ambit from ruin, and vice-versa.

• You can solve any gambler's ruin problem with even odds similarly.