Playing the lottery is not necessarily irrational


in Economics, Geek stuff, Psychology

People sometimes describe lotteries as a tax on those who are bad at math. The tickets are worth less than their face value, given the size of the payout and your odds of winning.

That is all true enough. At the same time, it bears remembering that we each get to live a single very finite life. Used well, the winnings from a lottery could improve that one and only life a lot – particularly if the money is used to advance a particular cause that is important to you, rather than used hedonistically.

Losing the cost of a bunch of lottery tickets is irrational if your aim is to maximize how much money you are likely to have in your life. At the same time, betting on a long shot can be rational in the sense that there is a large amount of upside that you have no hope whatsoever of capturing if you do not play.

Expressed another way, the problem with lotteries is that you basically pay $5 for a one-in-a-million shot of winning $1,000,000. The ticket is overpriced and the money is probably wasted. At the same time, there is probably no other way in which you are going to get $1,000,000. At least playing the lottery gives you some chance, however infinitesimal.

The logic is similar to that of buying insurance against your house burning down. If you had a huge number of houses, you would be better off not paying premiums and just dealing with the cost of fires yourself. Because you only have one house, however, you overpay on premiums in order to avoid a catastrophic outcome.

All that said, and as I have argued before, I don’t think lotteries and casinos should be allowed to advertise. It is better for the state to keep gambling legal and regulated, rather than allowing it to become one more racket for organized crime along with drugs and prostitution. At the same time, neither the state nor private companies should be permitted to take advantage of the weak understanding of probability in the general public through advertising a profoundly false promise that winning is likely. Casinos also should not be allowed to serve alcohol.

To sum up, winning the lottery is an extreme long shot, but when you only have a single chance to try something it can be a rational strategy to accept a set risk (the near certainty that the money spent on a ticket is wasted) in exchange for a chance at a large benefit.

{ 6 comments… read them below or add one }

. September 21, 2011 at 10:18 am
Matt September 21, 2011 at 12:22 pm

There are cases when the ticket isn’t worth less than face value. For instance, the odds of winning lotto 6/49 are “49 choose 6” which is 1 in 13,983,816. The cost to play said lottery is $2. Therefore, if the lottery is $28 million dollars (which is certainly not unheard of) your ticket is worth approximately face value. Of course, the possibility of multiple winners confuses the math, but my point is that the ticket isn’t necessarily worth less than face value.

In fact, I’ve heard of at least one case where someone attempted to buy every combination due to the fact the payout was significantly higher than the cost of each ticket. I believe this was in Pennsylvania, but I’m having difficulty finding a source to back me up.

Alex September 21, 2011 at 5:02 pm

“Used well, the winnings from a lottery could improve that one and only life a lot – particularly if the money is used to advance a particular cause that is important to you, rather than used hedonistically.”

If you were to win 10,000,000 in a lottery, how would you spend the money?

Milan September 21, 2011 at 7:48 pm

Fund innovative climate change advocacy projects, maybe. Take people who have good ideas for ways to drive action on climate change and provide them with moderate amounts of funding to help develop those projects – grants ranging from a few thousand to a few tens of thousands of dollars.

coyote September 22, 2011 at 7:09 am

Worded another way: five bucks for a little hope and some moments of pleasant dreaming is not necessarily a bad price…

oleh September 28, 2011 at 4:20 am

Limited lottery spending does allow someone moments of pleasant dreaming. But I wonder how effective is it for one person to win $10,000,000.

What if the lotteries multiply that chance of realizing on that pleasant dream by multipying the number of big winners by having a maximum reward. For example winning $100,000 will make a substantial difference to practically everyone. If the now “$10,000,000” winner was replaced with 100 “$100,000” winners, the chance of the pleasant dream being realized in a significant fashion is multiplied by 100.

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