Adam Smith on Lotteries

In many places, lotteries are the only legal form of gambling. And even then, only the government is allowed to run them. This may be because lottery profit margins are often 30 percent or more. Casinos average about 5 percent. Lotteries are the worst possible deal for gamblers.

Why do people still play lotteries, then? It’s because humans have an inherent cognitive bias to overestimate the odds of success, and underestimate the odds of failure. This is a useful cognitive defect, because it encourages risk-taking. It was evolutionarily useful back in our hunter-gatherer days. And it remains so today; there would be far less entrepreneurship if people saw odds more clearly. But there are drawbacks. Lotteries are among them.

I didn’t know there were state-run lotteries in 1776, but apparently there were, because Adam Smith explains what a bad deal they are in The Wealth of Nations:

The world neither ever saw, nor ever will see, a perfectly fair lottery; or one in which the whole gain compensated the whole loss; because the undertaker could make nothing by it. In the state lotteries the tickets are not really worth the price…

Many people think that buying more tickets improves one’s odds of winning. But Smith saw that this was not a wise strategy:

There is not, however, a more certain proposition in mathematics, than that the more tickets you adventure upon, the more likely you are to be a loser. Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets the nearer you approach to this certainty.

(Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, 124-25.)