05 Jun '08 22:49

Suppose there is a betting game at the local fairgrounds. In each round of this game, a mouse is freed at the beginning of a circuit and then runs into either hole 1, hole 2, or hole 3 -- each hole with equal chance. Each round before the mouse is freed, you can bet on which hole the mouse will run into. If you are correct, then you get back twice the money you bet. If you are wrong, you lose the money you bet. The minimum bet is 1 dollar. There is no maximum bet. You may play as many rounds as you like, provided of course that you have money to meet the minimum bet for each round.

Now, suppose you have 100 dollars on you, and you go to play this game with the sole objective of leaving with more money than you came with. What is your optimal playing strategy and what can we say about the associated probability of success (again, success is your leaving the game with some amount > 100 dollars)?

I think I have an optimal strategy, but I would like to see if anyone else can come up with something better.

Now, suppose you have 100 dollars on you, and you go to play this game with the sole objective of leaving with more money than you came with. What is your optimal playing strategy and what can we say about the associated probability of success (again, success is your leaving the game with some amount > 100 dollars)?

I think I have an optimal strategy, but I would like to see if anyone else can come up with something better.