Gambling motivation and involvement: A review of social

utility for a person who owns only 1000 dollars than it has for a person who owns
1,000,000 dollars. For the former person, 500 dollars is a substantial increase in
wealth, for the latter it is a drop in the ocean.
This is illustrated by the solid line in Figure 1: the Bernoulli logarithmic function
(also called the von Neuman-Morgenstern utility function). Although w1 and w2
are additions of equal sums of monetary (or other) value to an individual’s wealth,
w2 causes a lesser increase (b) in utility than w1 (a). As noted by Bernoulli, this has
further implications for gambling than the rather contrived bet of the St. Petersburg
Paradox. Let us assume that a person, who has a wealth of 10,000 dollars, is offered
the opportunity to bet 1000 dollars on a gamble in which he has an equal chance
of losing or doubling his stake. According to Bernoulli’s theory, the 1000 dollars
he might win has less expected utility value than the 1000 dollars he might lose.
Therefore, “everyone who bets any part of his fortune, however small, on a mathematically
fair game of chance acts irrationally” [139 p.29 ]. Of course, if the odds are
against the gambler, it is even more irrational to stake money. Thus, while Gabriel
Cramer and Daniel Bernoulli apparently solved the St. Petersburg Paradox, there
remained enigmas in gambling behavior for economists who adhered to the notion
of “economic man” as rational and utility-maximizing.
RELEvancE tO pRObLEm GambLinG StudiES
The theories of the early economists on gambling have little relevance to gambling
studies of today. The theories have been described here to provide a background for
later developments in economic theory.
Classical expected utility theory
The question of why rational people chose to gamble remained unsolved in economics
for more than 200 years. Various solutions were attempted, but proved to
be inadequate. It was particularly difficult to account for the fact that often people
both gamble and buy insurance, the first being a risk-seeking activity and the second
suggesting an aversion to risk. It was not until 1948 that a widely accepted solution
was presented by Milton Friedman and Leonard Savage [140]: the marginal utility
of wealth does not diminish uniformly, see the dashed line in Figure 1 (“Friedman-
Savage function”).
26 G A M B L I N G M O T I VAT I O N A N D I N V O LV E M E N T