(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.

Economics and other students of gaming programs have tried to reconcile the risk-seeking behavior implicit in lottery play with the observation that individuals in general display risk aversion.

In this endeavor, economists differentiate two kinds of efficiency in Lotto games: weak-form and strong-form.

Weak-form efficiency requires relatively simple player behavior: They must be able to recognize the potential for abnormal profits. Their collective response then eliminated this potential.

Strong-form efficiency involves more sophisticated player behavior: the ability to forecast the expected value of a Lotto ticket given the information available to them. Strong-form efficiency exists if all bets have expected values equal to one minus the takeout rate.

In their study of state Lottos, Scott and Gulley considered three games in detail:

-In the Kentucky Lotto, expected value varies from $0.09 to $0.58. These figures assume that players realize the announced jackpot is the undiscounted sum of twenty annual payments and are able to calculate present value. If that is so, then the Kentucky Lotto market is weakly efficient. If players use the announced (undiscounted) jackpot, the expected value would vary from $0.18 to $1.17. That suggested they were motivated by non-monetary factors.

-The Massachusetts Megabucks expected values also relied on discounted present value of the jackpot. Only once in six years did the game yield a positive net expected return.

-The Ohio Super Lotto expected values, which ranged from $0.16 to $0.76, indicated weak efficiency. That expected returns were consistently negative suggested a risk-seeking behavior or nonpecuniary returns or both on the part of players.

The significant negative relationship between sales and the residuals indicates that bettors systematically underpredict expected value when rollover is small, and vice versa.

In addition to the monetary return of the bet, there also exists a nonmonetary return (the value derived from watching the numbers being drawn on television, thinking of how any prize money would be spent, etc.).

Market efficiency is a critical concept in economics and finance. Only infrequently do situations arise where relatively clean tests of rational player behavior or market efficiency can be conducted. State-sponsored Lotto games do seem to offer such an opportunity, because the mathematical expectation of a bet depends on, among other things, players' aggregate behavior.

In deciding whether to play, each player must predict how others will behave and then act on that prediction.

A slowdown can generate a gambling Catch 22 for lottery officials. Smaller jackpots generate slower sales. Slower sales generate smaller jackpots.

During the 1990s, most state Lotto games have changed formats, adopting longer odds that lead to more rollovers. The marketing philosophy seems to be that more rollovers create bigger jackpots and disproportionate increases in subsequent sales.

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