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Abraham and Blaise each have $\$10$. They repeatedly flip a fair coin. If it comes up heads, Abraham gives Blaise $\$1$. If it comes up tails, Blaise gives Abraham $\$1$. What is the expected number of flips until one of them runs out of money?

So I know that the "frog" is on lily pads labeled 0-20, where each lily pad corresponds to Abraham's money. I need to figure out the expected value is of the flips until the frog reaches 0 or 20, given that it's a fair chance to move up or down, and that we start on 10.

Saketh Malyala
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1 Answers1

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I notice that you are an eighth grader and you have solved this gambler's ruin problem by using frog on lily pad (frankly, I don't see how you have obtained the answer) despite the reference by Math1000 not mentioning anything about expected duration of the classical gambler's ruin problem - very impressed.

You may refer to page 17 of the reference below: http://www.johnboccio.com/research/quantum/notes/ruin.pdf

where $a = \$10$ and $z = 10 + 10 = \$20$ for $p=q=0.5$.

Hence equation (34) gives

Dz = 10 (20 - 10) = 100

Regards

thepiercingarrow
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Seow Fan Chong
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