Gambler's ruin - problem 5

Probability Level 2

You walk into Martin Gale's Betting Room with an initial budget of kk

As usual, 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 until you have increased your money to nn, and then you will stop. Here, n>kn>k. Of course you will also have to stop if you lose all your money (i.e. you are ruined).

How many games do you expect to play before you stop?

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