Gambler's ruin - problem 3
You walk into Martin Gale's Betting Room with $20.
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 play for a while, and then you are pleasantly surprised to find that you now have $24. You glance at the clock and see it is almost midnight. You decide you will play exactly 4 more games and then go home. How much money do you expect to go home with?
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