JACKSON, Tenn. – Oct. 17, 2002 – As the debate wages on for and against the possibility of bringing a lottery into the state of Tennessee, we continue to hear the many arguments from both sides of the political and religious spectrums. If you think about it, though, the lottery is essentially very much mathematical, and therefore mathematics has much to say about the lottery. Even more interesting, every talk that discussed the lottery that I have ever heard at a mathematics conference has been anti-lottery. Why? The numbers just don’t add up.
One of the topics you might encounter in an introductory college statistics course is that of expected value. Without getting into a math lesson, the general idea of this concept is that it gives a measure of what one would expect to gain or lose, on average, from some situation governed by random processes. For instance, consider a slot machine that has a payback rate of 95% - then the expected value to the person playing the slot machine is -5 cents per dollar bet. The more you bet, the more you would expect to lose. If you bet $1000 using this machine, you would expect to lose $50. Of course, you could come out ahead, but on average you would lose 5% of the total amount that you bet. Casinos and state lotteries use the expected value concept to determine the net proceeds they can expect from a given level of betting.
Many people actually play gambling games, including the lottery, with the expectation that they will win, or come out ahead. This simply does not reflect mathematical reality, since every such game has a negative expected value. It's no wonder that a few years ago the plenary speaker at a meeting of the Southeastern Section of the Mathematical Association of America called the lottery "a tax on the mathematically ignorant." To make matters even worse, many people bet more and more money hoping it will give them a better chance. Again, the math shows that the more money you bet, the more money you can expect to lose.
Another line you may have heard is that state lotteries are not as bad as casinos. From a mathematical point-of-view, however, lotteries are actually much worse. The expected value of most traditional casino games is in the range of -3 cents to -5 cents per dollar bet. Most state lotteries have an expected value of around -50 cents to -60 cents per dollar bet. In other words, you would expect to lose money more than ten times as fast with the lottery as with a slot machine or blackjack in a casino.
Let's switch gears for a moment and look at the probability of winning a large prize, such as the Powerball, the most popular of the big-prize multi-state lotteries. The probability of winning the Powerball on one ticket is less than 1 in 80,000,000. According to one of the most popular college statistics textbooks on the market, you are more likely to be struck by lightning twice than you are to win the Powerball on one ticket! Of course, that's why many people buy more tickets – but remember, the more tickets you buy, the larger your expected loss! Will someone win the Powerball? Sure. But it won't be you!
Now let's look at the lottery as a potential revenue source for the state. From where does the revenue come? Statistical studies have shown that the revenue typically comes from the poor. More than 6% of the income of the poor is taken in by the lottery, while maybe 1% of the income of the middle class, and next to nothing from the wealthy, is brought in. If any state legislator dared propose an income tax with those characteristics, he would be lynched.
So why does the lottery enjoy so much support, and why does it prey so heavily on the poor? I believe it is due, in large part, to the false hopes of financial gain that are fueled by mathematical ignorance. I'll end as did a mathematician in a talk to a national honor society convention: when it comes to playing (or voting for) the lottery, "stupid is as stupid does."
Bryan Dawson is chair of the Department of Mathematics and Computer Science at Union University in Jackson, TN. Contact him c/o Union University, 1050 Union University Dr., Jackson, TN 38305 or firstname.lastname@example.org.
Written by Bryan Dawson, chair of the Department of Mathematics and Computer Science
Sara B. Horn,