Saint Petersburg paradox a puzzle about gambling that motivated the distinction between expected return and expected utility. Daniel Bernoulli published it in a St. Petersburg journal in 1738. It concerns a gamble like this: it pays $2 if heads appears on the first toss of a coin, $4 if heads does not appear until the second toss, $8 if heads does not appear until the third toss, and so on. The expected return from the gamble is (½)2 ! (¼)4 ! (1/8)8 ! . . . , or 1 ! 1 ! 1 ! . . . , i.e., it is infinite. But no one would pay much for the gamble. So it seems that expected returns do not govern rational preferences. Bernoulli argued that expected utilities govern rational preferences. He also held that the utility of wealth is proportional to the log of the amount of wealth. Given his assumptions, the gamble has finite expected utility, and should not be preferred to large sums of money. However, a twentieth-century version of the paradox, attributed to Karl Menger, reconstructs the gamble, putting utility payoffs in place of monetary payoffs, so that the new gamble has infinite expected utility. Since no one would trade much utility for the new gamble, it also seems that expected utilities do not govern rational preferences. The resolution of the paradox is under debate. See also DECI- SION THEORY, EMPIRICAL DECISION THEORY. P.We.