Sunday, May 23, 2010


Recently Mega Millions has joined Powerball in my state. It was a big move and there was lots of press to get people started buying tickets. After all, there are not that many multistate lotteries. And that is where you win the big money. You can always expect both lotteries to be in the tens of millions of dollars, and tickets are only a dollar. This is in comparison to many state lottery tickets, which also cost a dollar, but do not have gigantic payouts. Now of course, the payouts are in proportion to the odds of winning, with your simple pick four using numbers zero to nine with odds of winning of 1:10,000, to powerball, where you have six numbers and the odds are 1:195,249,054.

It is easy to see why people get so excited about the lottery when the payout reaches $100 million. Who does not want to win $100 million? And if you watch the lottery payouts over time, when there is no winner for several weeks, the payout climbs and climbs. You will also notice that once it approaches $100 million, it also begins to rise rapidly. The curve of payout over time is exponential. What does this tell us? It tells us that people are more interested in playing the lottery as the payout increases. What that also tells us is how people perceive the odds of winning the lottery as well as risk.

So the average lottery player believes that it is only worth spending one dollar on a lottery ticket if the payout is close to $100 million. There are variations, of course, such as players that buy more than one ticket and more tickets as the payout increases. Or players that only jump in once the payout reaches a certain level and jump in with more than one ticket. But there is an inherent misunderstanding about odds that also causes the payout to rise exponentially.

The classic example was the flipping of a coin. If you flipped a coin four times and it came up heads four times, many people were apt to believe the odds of a fifth head were either better or worse than even odds, depending on their incorrect reasoning. The example has been used so often over time that almost everyone understands that the odds of a fifth head is fifty percent. But is not that everyone necessarily understands the odds, but that they understand the gist or catch in the question. In the beginning many people misinterpreted the question as asking what the odds are of getting five heads in a row. This is a slightly more complex odds problem that, given the state of America’s mathematics comprehension, is difficult for many to solve. And so they make a best guess founded on personal bias.

In the case of lotteries there is a misperception of odds that occurs as the payout rises. There are two odds in play with any lottery. The first are the odds of you as a player personally winning the lottery. These odds are fixed unless the rules of the game changes, and everyone understands that because they have learned from the classic example above. The second are the odds that someone, anyone, wins the lottery. These odds change and improve as the number of players increases. So as the payout increases, the number of players increases, and the likelihood that someone will win the lottery increases. This is why you rarely see payouts over $300 million. The problem is that many people confuse the two odds.

While it is true that buying more tickets improves your chances of winning, it does not improve them to the same odds of anyone winning, since there are many more people playing with many more tickets than you are proportionately buying. Thus people believe their odds are better than mathematically calculated. This misperception can be corrected by imagining that you are the only player for the lottery. It removes the confounding odds of anyone winning and allows you to see your true odds. Not that you should not play the lottery, since many states use lottery sales to fund state programs, but it will save you a little disappointment when you do not win. Variations on this theme can be applied to the stock market and real estate, but that is another post.