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Old 06-17-2018, 02:27 PM   #1
Akea
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Gambling Question pls Help

Can you help me with this question pls

Assume that a gambler plays a fair game where he can win or lose 1 dollar in each round . His initial stock is 200 dollar. He decides a priory to stop gambling at the moment when he either has 500 dollars or 0 dollars in his stock. Time is counted by the number of rounds played.
i) show that the probability that he will never stops gambling is zero
ii ) Compute the probability that at the time when he stops gambling he has 500 dollars , and the probability that he has zero dollars
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Old 06-17-2018, 03:13 PM   #2
whosnext
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Re: Gambling Question pls Help

This sounds like a school homework problem. If so, I imagine that you are learning about random walks, markov processes, and the like.

In any event, there is a large body of work done in these areas that is relevant to your question.

I suggest you tell us what you have done so far in trying to answer the question and then someone would have a better idea of how to help you.
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Old 06-18-2018, 04:43 AM   #3
nickthegeek
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Re: Gambling Question pls Help

Quote:
Originally Posted by Akea View Post
Can you help me with this question pls

Assume that a gambler plays a fair game where he can win or lose 1 dollar in each round . His initial stock is 200 dollar. He decides a priory to stop gambling at the moment when he either has 500 dollars or 0 dollars in his stock. Time is counted by the number of rounds played.
i) show that the probability that he will never stops gambling is zero
ii ) Compute the probability that at the time when he stops gambling he has 500 dollars , and the probability that he has zero dollars
Although I agree with whosenext, these questions can be answered even without any previous knowledge about random walks and risk of ruin, but just with some logic.

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