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?
As TomM pointed out, any finite number is a "fair" price for the game. The question, though, really comes down to whether you can afford to lose $100. If the game can be repeated over and over, it comes down to the odds that you will clear out your bank account before you hit a big payoff.
This is kind of one of those cases where "pure" mathematics and the real world butt heads. An analogous question might be, "Would you pay $100 for a one-in-a-billion chance at $1 trillion?" Your expected payout is $1000, but that doesn't mean you should bet the farm...
My take
