ARE LOTTERIES EFFICIENT?

(Excerpted from True Odds by James Walsh, Merritt Publishing, 1996, Santa Monica, CA. 1-800-638-7597.) Reprinted with permission of Merritt Publishing. All rights reserved.

Because most lottery products have a negative and unchanging expected monetary return, only limited research has been done on the efficiency of lottery markets.

Most academics have studied Lotto games to evaluate the possibility of favorable investment opportunities arising from popular and unpopular numbers.

But numbers chosen at random would follow a more standard binomial distribution. The expected monetary value of this kind of Lotto bet follows well-defined laws of probability and depends on readily available information.

In the April 1995 issue of the journal Economic Inquiry, University of Kentucky professor Frank Scott and Bentley College professor David Gulley argued that players decide whether to play the Lotto based on their reservation price and their assessment of the expected value. The expected value depends on other players' behavior; therefore, each player must generate his or her own forecast of total sales.

The relevant question becomes: Do Lotto players make systematic errors in their forecasts of sales and, therefore, of expected value?

The expected value of a Lotto ticket depends on the structure of the game, the dollar amount rolled over from previous drawings, and the number of tickets purchased by players.

Since players under ordinary circumstances are only willing to buy a limited number of tickets, in any given draw of an actual Lotto game expected value will depend largely on the size of the rollover.

Scott and Gulley claimed that, with a large enough rollover and a small enough level of sales, the expected value of a $1 ticket could be more than $1. The potential for profit from such a situation would likely encourage additional betting, which would reduce the expected value to more than $1. This would be a form of equilibrium.

Scott and Gulley concluded:

...we find that even in the presence of a pleasure component which we are not able to incorporate explicitly, lotto markets tend to be efficient...either of two conclusions is possible.

One is that financial forces do not work towards efficiency, and that whatever direction they do work, they are exactly offset by pleasure forces working in the opposite direction.

Alternatively, it may be that financial forces work towards efficiency and pleasure forces are relatively insignificant. While we are winning to admit that the first alternative is possible, we find the second explanation much more convincing.

Because the state keeps so much of the proceeds in most Lotto games, the economic pursuit of a positive expected value is difficult.

Exploiting a pure profit opportunity is difficult in practice because of the logistical problems encountered in buying a large number of Lotto tickets. Such a strategy is not impossible, however, as was demonstrated in 1993 when an Australian syndicate attempted to make money by covering all the numbers in the Virginia Lotto.

It failed.

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