How Much is this gamble worth?

The St. Petersburg gamble is played as follows: A fair coin will be tossed, and if it is HEADS, you win $2 and the game is over. If it is TAILS, the coin is tossed again, and now if it is HEADS, you win $4. If TAILS, it is tossed again, and this time HEADS pays $8. The gamble doubles in value each time TAILS occurs, but once HEADS occurs, it pays off and the game is over. This gamble could go on forever and ever, doubling its payoff for each TAILS. However, the probability of ending at $2 is 1/2;the probability of ending at $4 is 1/4; the probability of ending at $8 is 1/8; and the probability halves each time, just as the winning doubles.

What is the most you would pay (in dollars) for the chance to play the St. Petersburg gamble once?
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