The Peculiar Scale Economies of Lotto

The best-selling lottery game in the United States is lotto, a parimutuel game of long odds and large jackpots. Unlike in the other popular lottery games (numbers and instant). there is a strong tendency for per-capita lotto sales to increase with the size of the population base. The fact that the jackpot also tends to increase with population size is not a complete explanation, since the probability of winning tends to be inversely proportional to state population. our explanation for why the games are more successful in large states is that players tend to judge the likelihood of winning based on the frequency with which someone wins; then a larger state can offer a game at longer odds but the same perceived probability of winning as a smaller state.

The Mathematics of Lottery: Odds, Combinations, Systems

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By applying these data, one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind

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Spreading the Fortune: The Distribution of Lottery Prizes across Countries

It has been 15 years since Cook and Clotfelter described the scale economies associated with state-run lotto games in an American Economic Review article entitled “The Peculiar Scale Economies of Lotto.” U.S. states with larger populations are identified as having the ability to offer games with larger jackpots to attract higher sales per capita. The current paper extends this analysis to all current U.S. state and multi-state lotto-style lottery games as well as to a sample of international lotto games for comparative purposes. The development of the two major U.S. multi-state games over time is also examined to illustrate that changes in the structure of those games can be explained by an application of the scale economies concept offered by Cook and Clotfelter.lotto, lottery, public finance, gambling

Iowa Lottery Action, June 19-July 9, 2006, Vol. 13, no. 12

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