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?

I just ran to the convenience store for some munchies and realized that there is a "game of chance" that is similar to this "game" in the aspects that confused you -- the lottery.

In the lottery you buy in (buy a ticket) after which you become irrelevant until the payout phase. The operator runs the game alone except for a witness, which may or may not be you, whose only purpose is to keep him honest. If there is no payoff on the first round, the payoff for the next round is increased (but usually by much less than by doubling it)

There are differences, though.

In a lottery, the buy-in (the cost of the ticket) is fixed, and the payout is determined. In this game, the pay-out is (basically) fixed, and we have to determine the buy-in.

In a lottery, you have to buy in again each round. In this game, the buy-in for all later rounds must be included in the initial buy-in

In a lottery, the increased jackpot comes from the buy-ins from those who played and lost in the last round. In this game, these must also come out of the initial buy-in

Posted by TomM on 2002-10-09 20:08:27