I was a little confused when I read the section on the St. Petersburg Lottery, so I looked around to see what it was all about. In order to find the expected v

I was a little confused when I read the section on the St. Petersburg Lottery, so I looked around to see what it was all about. In order to find the expected value, you simply multiply the probability of the event by its expected payout. Then to find the total expected value, you sum all of the possible outcomes. So the probability of the first flip being tails (1/2) times the payout ($1), gives the expected value of that flip ($0.50). The rest of the flips follow in a similar way: 2nd (1/4)x($2)=0.50, 3rd (1/8)x($2)=0.50, 4th (1/16)x($4)=0.50, etc. If you take the sum of these values to an infinite number of flips (.50+.50+.50+...), you end up with an expected value of infinity. On the other hand, even if the bank is ridiculously wealthy [1] (i.e. US GDP), the expected payout is ridiculously small. That, to me, is the crux of the fallacy. It reminds me of the legend of the creator of chess who asked for one grain of rice for the first square of the chessboard, two for the second, four for the third, etc. which becomes greater than the world production of rice after a few dozen squares. [1]http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_St._Petersburg_lotteries http://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_S...