At $540 Million, Is Lotto Still A Tax On People Who Don't Get Math?
This week's fight at the Hemingways has been about whether to buy a Megamillions ticket. My view is that Lotto is a tax on people who don't understand statistics. His view is, and I quote, "Come on! It's over $500 million! I had an uncle who won the lottery once."
It will not surprise you that my background is in math and his is in wishful thinking. (I kid because I love. And also because he is literally right about everything ... except this.)
I come from a long line of fighting about gambling. See, my dad is a pastor and really sees no moral value in gambling. My mom views it like others might view any other entertainment expense. You might spend $100 a year on going to movies. When she's in Vegas, she plays a roll of quarters on the slots and stops when she runs out of money or time.
But I'm curious if we reach a point where the risk of reward makes the purchase of a ticket more reasonable. Scientific American says "No Matter How Huge, Mega Millions Jackpot Will Always Be a Bad Bet."
The prize is so high it exceeds the number of possible number combinations on a ticket, which is about 176 million. (In other words, the chance that any particular ticket is a winner is about 176 million to one.) The math seems to imply that a $1 ticket has an expected value of $500 million divided by 176 million, or nearly $3. Yet a closer look at the math reveals that the Mega Millions jackpot is a bad bet no matter how large the prize. ...
Certainly, the threat of having to split is there, but does that really make it a bad bet—especially when the jackpot is so very high? According to the mathematicians, yes. As the number of tickets sold goes up, the chance that more than one person will share in the jackpot does as well, according to a well-known mathematical function called a binomial distribution. When Emory University mathematicians Skip Garibaldi and Aaron Abrams worked through the equations, they found that lotteries are generally a terrible bet—Mega Millions and Powerball particularly so. (I encourage you to take a look at their paper “Finding good bets in the lottery, and why you shouldn’t take them,” which was published in the American Mathematical Monthly in 2010.)
Even in the case of the current drawing, which offers a jackpot so large that Garibaldi and Abrams show how it should only occur on average every 22 years, the number of tickets that go out is correspondingly large. “I ran the numbers last night,” Garibaldi told me over the phone. “You can tell by the amount they estimate the jackpot to be what they estimate the ticket sales to be.” Based on the current jackpot, an estimated 380 million tickets have been sold this week. The estimated return on an investment of this week’s Mega Millions drawing? Negative 19 percent, per his calculations.
I wonder if there's a simply way to figure out when the estimated return on investment is not negative. Either way, considering the economic situation of our family and our country, I think our "win the lotto" retirement plan might be the best bet we have.