# Gambler's ruin - problem 2

Probability Level 3

You walk into Martin Gale's Betting Room with $2. You can play the following game any number of times (if you have what it costs) • You pay Martin a dollar. • Martin tosses a fair coin • If the coin comes up heads Martin pays you two dollars. If it comes up tails, you get nothing. You decide that you will play for a while, but if you ever get up to$5 you will cash out and go home. And, naturally, if you are left with no money then also you will go home.

What is the expected number of games you will play before you stop?

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