Gambler's ruin - problem 7

You walk into Martin Gale's Betting Room with an initial budget of \(k\)

Again, 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 to keep playing, meaning that the only thing that will cause you to stop is losing all your money. How many games do you expect to play before you stop?

Note: As in problem 6 of this series, you may assume Martin's budget is infinite.

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