Are Lotteries Fair? Lotteries have become part of the American way of life. Most states
now have legal lotteries, including multi—state lotteries such as Power-
ball and the Big Game. National statistics show that per capita [average
per person] lottery spending is approaching $2130 per year. Since many
people do not play lotteries at al]. this means that active players tend to
spend much more than $200 per year. The mathematics of lottery odds involves counting the various
combinations of numbers that are winners. While these calculations can
become complex. the essential conclusion is always the same: The
probability of winning a big prize is infinitesimally small. Advertise-
ments may make lotteries sound like a good deal, but the expected value
associated with a lottery is always negative [in average, those who play
regularly can expect to lose about half of what they spend. Lottery proponents point to several positive aspects. For example,
lotteries produce billions of dollars of revenue that states use for education,
recreation. and environmental initiatives. This revenue allows states to
keep tax rates lower than they would be otherwise. Proponents also point
out that lottery participation is voluntary and enjoyed by a representative
cross~section of society. Indeed. a recent Gallup poll shows that three-
fourths of Americans approve of state lotteries [two-thirds approve ot’legal
gambling in general). This favorable picture is part of the marketing and public relations
of state lotteries. For example, Colorado state lottery officials ofi’er
statistics on the age, income, and education of lottery players compared
to the general population (Figure 6.16], 1Within a few percentage points.
the age of lottery players parallels that of the population as a whole. Similarly, the histogram
for the income of lottery players gives the impression that lottery players as a whole are