http://online.wsj.com/article/SB1000142 ... inance_PF4
Wikipedia describes the St. Petersburg Paradox as:
How much would you pay to play this game, given that you could only ever play it once?Consider the following game of chance: you pay a fixed fee to enter and then a fair coin is tossed repeatedly until a tail appears, ending the game. The pot starts at 1 dollar and is doubled every time a head appears. You win whatever is in the pot after the game ends. Thus you win 1 dollar if a tail appears on the first toss, 2 dollars if a head appears on the first toss and a tail on the second, 4 dollars if a head appears on the first two tosses and a tail on the third, 8 dollars if a head appears on the first three tosses and a tail on the fourth, etc.
My knee jerk reaction was that I would pay very little, since the probability of making "at least X dollars" is fairly low, where X is a significant amount of money to me. For example, the odds are:
100% chance of getting at least $1
50% chance of getting at least $2
25% chance of getting at least $4
12.5% chance of getting at least $8
1.49E-06% chance of getting at least $67,108,864
(note that the last probability listed above is roughly the same odds as being hit by a meteorite sometime during your lifetime)
But another way of looking at this is that your "expected return" is actually infinity dollars. That's because the expected value of playing is:
0.5*1 + 0.25*2 + 0.125*4 + ... + 1.49E-06%*67,108,864 + ...
= 0.5 + 0.5 + 0.5 + ... + 0.5 + ...
How much would you pay to potentially have infinite money?