>You pay me a certain amount of money at the beginning. I flip a coin. If "tail" appears, the game ends - you get nothing in exchange for you initial bet. If "head" appears, I pay you $1, and the game continues. If "head" appears for the second time,I pay you $2. The third time, $4, the fourth time $8, etc. - but as soon as "tail" appears, the game is over.
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>How much would you be willing to pay to play this game?
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>Hilmar.

I think I hadn't made it clear that the payments are additive. For instance, if "head" appears thrice, you get $1 + $2 + $4 = $7.

Well, since nobody responded in many days anyway, I will give an analysis. The probability of getting "head" the first time is 1/2; making a value of 1/2 * $0.50. For the second "head", the probability is 1/4, the total value is 1/4 * $2 = $0.50. For the third head, the total value is 1/8 * $4 = $0.50.

The total value of the game, in dollars, is 1/2 + 1/2 + 1/2 ... that is, infinite.

Of course, playing the game a single time, you will get a finite amount of money. It is only the average that is infinite. Strange, huh?

Hilmar.