Suppose you are playing a game with a friend in which you bet ? dollars on...

Suppose you are playing a game with a friend in which you bet ? dollars on the flip of a fair coin: if the coin lands tails you lose your ? dollar bet, but if it lands heads, you get 2? dollars back (i.e., you get your ? dollars back plus you win ? dollars).

Let ? = "the amount you gain or lose."

(a) What is the expected return ?(?) on this game? (Give your answer in terms of ?)

Now, after losing a bunch of times, suppose you decide to improve your chances with the following strategy: you will start by betting $1, and if you lose, you will double your bet the next time, and you will keep playing until you win (the coin has to land heads sometime!).

Let ? = "the amount you gain or lose with this strategy".

(b) What is the expected return ?(?) with this strategy? (Hint: think about what happens for each of the cases of ?=1,2,3… flips).

(c) Hm ... do you see any problem with this strategy? How much money would you have to start with to guarantee that you always win?

(d) Suppose when you apply this strategy, you start with $20 and you quit the game when you run out of money. Now what is ?(?)?

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Expert Solution

orchestra answered 10 months ago

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