How to Win a Lottery

To play the Texas lottery, you pay $1 to pick six numbers between 1 and 54. If no one wins one of the three weekly drawings, the jackpot rolls over to the next week.

The Chance of Winning the Lottery

Guaranteed

During 2023, a business called Rook TX, bought somewhere near 25 million lottery tickets–enough to cover almost every number combination. While it cost them close to $26 million, they won Lotto Texas and took home $57,804,000 before taxes. Using a courier service app, Rook TX purchased the tickets online from (what appears to be) its home state of New Jersey.

Like the Texas group, In 1730 or so, the French philosopher Voltaire earned enough from the lottery to support his less lucrative life as a philosopher. At the time, hoping to encourage bond sales, France connected lottery tickets to bond purchases. Collaborating with 12 other people, Voltaire (and a mathematician) figured out that they could accumulate many of the cheapest bonds to acquire the number of lottery tickets they needed to win. At half a million livre, Voltaire’s jackpot money funded further investments that made him independently wealthy

Responding to the Rook TX maneuver (and a second similar winner), the Texas Lottery Commission banned courier services. I guess they wanted to give everyone an equal chance of winning.

Not Guaranteed

The chance of you and I winning the Texas lottery is 1 in 25,827,165. For the larger lotteries like Powerball, it is tinier–closer to 1 in 292 million. The Wall Street Journal visualized the odds:

Our Bottom Line: Probability Neglect

Defying the law of demand where a higher price reduces the quantity we are willing and able to buy, Mega Millions will soon raise the price of a lottery ticket to $5. Predicting the extra revenue will create additional billion dollar prizes, they expect a spike in sales. The Mega Million people say that sales skyrocket when the lottery tops a billion dollars.

Also, Mega Millions says they probably will improve the odds, moving them down to 1 in 299 million.

When a behavioral economist hears 1 in 299 million, she might say that lotteries display probability neglect. Yes, ticket buyers know they have an infinitesimal chance of winning. But, somewhat irrationally, we ignore the probability because it makes us feel so much better. It is also possible that we have more of a personal response kicking in. When a terrorist event becomes more vivid, for example, we imagine more of a probability that it will happen. With the lottery, some of us daydream life as a billionaire.

My sources and more: Thanks to Slate Money for alerting me to the Texas Lottery story. Then, as the home of Rook TX, a local NJ newspaper had the Texas lottery story as did the Lottery Commission, this Texas TV station, and the NY Times. Meanwhile, our Mega Millions update came from WSJ and  USA Today. Also, this econlife post had some other stories as did WSJ. But if you read just one other article, do look at the Voltaire story in the Smithsonian Magazine.

Please note that several of today’s sections were in past econlife posts.