We play a game as follows:
I place one dollar on the table. I repeatedly flip a coin. Each time the coin comes up heads, I double the money on the table. The first time the coin comes up tails, you take the money and the game is over.
What's a fair admission price for the game?
Would you play the game with me for $100?
Well, if you look at it from the 'house' point of view: The chance for the player to get anything more than 2$ is less than 50% In fact, the chance of winning x$ is 1/x. If the house can clearly stipulate rules such as, only 10 flips for instance, giving a jackpot of 1024$ Stating then that you can play the game for any amount more than 2$ (no, make that just a bit more) and less than 1024$ is a matter of market research. For instance, setting the buy in price to 10$ would require more than 3 consecutive successful flips (1/16 chance of winning anything) Thus the house will definately make money in the end... It would just require that magic number that would make the player say "Wow, I can pay 10$ for this game, but I can win 1024$ !!" The upper limit could obviously be lifted, to get a higher payout, but that would just be unfair...
The house
