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?

The expected return would be infinite, if the "house" had an infinite amount of money. This is not the case. The fair price would be $1 (guaranteed) plus .5 dollars times the exponent of the house's money when the house's money is expressed as a power of 2. You can find it by using logs, but I'm not up to date on those, and don't really feel like looking it up. So, unless the house can pay out $(2^199), the game is not fair.

Of course, time becomes a factor based on the number of games played, so it would need to be computerized.... otherwise, I'm not going to stand there for a few million coin flips.... but then I wouldn't play a "fair game" without infinite money either. ;-) Let me know what anyone thinks.

Posted by Ryan on 2003-05-07 08:21:13