Fellow economist Susan Woodward sent me this anecdote about Ronald Coase and gambling that I thought worth sharing. It led me to remember my own interesting story about gambling and one famous economist.
Bob Hall [her husband] and I were talking about the 1987 Coase conference at Yale, which I attended but Bob did not.
I was a major buddy of John Peterman (then the director of the Federal Trade Commission’s Bureau of Economics) who was a favorite student of Coase, and so I was seated by Coase at the dinner. We talked about what I was working on (at the Council of Economic Advisers) and I answered, “National lotteries.” I opposed them because I thought the government should lean against all gambling. (I was raised Protestant.)
“No, no,” said Coase. His mother had had a very hard life, but she had bought a state lottery ticket every week, and spent the weekend fantasizing about what she would do if she won. It made her life much better! The utility gain, he stated, is highest from a low probability but high payoff lottery. Even if the odds are poor, state lotteries are good because they are honest. That changed my view.
Susan’s story reminded me of my own story. My mentor at Fortune magazine when I started writing frequently for Fortune in 1984 was Dan Seligman, the book review editor. [I’ve written about Dan’s mentoring here and here.] He also had a regular column called “Keeping Up.” Besides being a great writer, Dan had a great sense of humor and a solid understanding of economics.
One more thing about Dan is that he loved gambling. So when people criticized gambling and, even worse, pushed to ban it, Dan didn’t like that.
MIT Nobel Prize winner Paul Samuelson had written a negative statement about gambling. Samuelson stated, just as many economists and others maintain, that gambling is zero sum; what one side gains is exactly what the other side loses. But, as I said, Dan understood economics. He understood that if you observe people doing anything, they must like it. If they keep doing it, that’s further evidence that they like it. The fancy term economists use is “revealed preference.” Their actions reveal their preferences.
In essence, what people leave out when they say that gambling is zero-sum is the pleasure people get from gambling. Not everyone gets that pleasure and those who don’t tend not to gamble.
In his column, Seligman could have used the argument I just made. But he found a cleverer way of responding to Paul Samuelson. People who knew much about Samuelson knew that he loved playing tennis. Dan was one of those people. So he turned Samuelson’s anti-gambling argument against him. In tennis, argued Dan, when one side wins, the other side loses. So tennis is zero-sum. Should we then be critical of tennis and maybe even ban it?
You might respond that people enjoy tennis. Exactly.
READER COMMENTS
Mactoul
Jan 17 2025 at 10:27pm
People buy lottery in order to win. So, net payout being negative implies lottery being an irrational activity. That playing lottery is conducive to fantasies is neither here or there. Plenty of activities could induce fantasies.
Gambling may be enjoyable in itself but tennis certainly is. People don’t play tennis in order to win.
Jon Murphy
Jan 18 2025 at 7:11am
It is precisely here and there. People do indeed engage in activities because it is pleasurable.
David Henderson
Jan 18 2025 at 10:12am
Jon,
Exactly.
If Mactoul were consistent in rejecting zero-sum games that give people pleasure, he would have to oppose tennis.
Jon Murphy
Jan 18 2025 at 10:39am
Agreed. And note that he is imposing his view on people (“People buy lottery in order to win”).
Jose Pablo
Jan 19 2025 at 8:33pm
I very much doubt that the “utility from fantasizing” fully explains why it makes “rational” sense (still understood as “utility-maximizing behavior”) to buy lottery tickets.
There is also, very likely, as Mactoul, points out a lot of “irrationality” involved, which probably doesn’t happen when playing tennis (at least if there is no money involved).
Kahneman and Tversky in “Prospect theory: An analysis of decision under risk“, analyze some of the “irrational” biases at work. People overweight low probability events (buying lottery tickets and sweating in your plane seat while taking off). If you ask lottery buyers they sure are going to overstate their odds.
But, in any case, you should be very careful (more than Mactoul seems to be) with these “definitions” of irrationality. Very likely the same biases at play here have helped us (humans) to survive.
Economics is at its best when limited to the positive analysis of what people do, instead of the (frequently arrogant) normative positions that result in the endless effort of trying to teach people how to “properly be people”.
Maybe, in the realm of economics, “rational” should mean “as humans do“.
johnson85
Jan 23 2025 at 3:58pm
I don’t buy lottery tickets very often, but I do occasionally, and I am pretty much only buying it for the fantasy. I mean, I have enough hope of winning that I check the numbers after they are announced, but I don’t really buy them to win, as I wouldn’t spend the money on that. Similarly, my elementary age son bought a sailboat magazine. He didn’t buy it because he wanted to buy one of the sailboats being reviewed. He just wanted to fantasize about buying them.
With the number of people that have gambling addictions, I can understand the argument for prohibiting gambling even if I disagree with it. But you can’t just ignore the main utility and say there’s no reason to gamble (or buy a sailboat magazine if you can’t afford a sailboat).
steve
Jan 17 2025 at 11:31pm
Should you really consider gambling at a casino zero-sum? The odds are set in favor of the house. If they think you are counting cards they boot you. The sports betting pools we always had at work were zero sum.
Steve
robc
Jan 18 2025 at 9:13am
Its zero sum including the house in the sum.
David Henderson
Jan 18 2025 at 10:13am
Exactly.
john hare
Jan 18 2025 at 4:10am
When the Powerball is over $200M, I will spend $2 on a ticket. (average perhaps $100 a year) I’m buying the ability to fantasize for a day. On the other side, I’m going to the trade show in Vegas next week and expect to lose $10. Primarily to say that I did it. Stupid yes, but I’m getting a different utility.
Alan Goldhammer
Jan 18 2025 at 9:29am
When the Powerball is over $200M, I will spend $2 on a ticket. (average perhaps $100 a year) I’m buying the ability to fantasize for a day.
LOL! My threshold is higher. I buy a ticket when it is over $500M for fantasy.
john hare
Jan 19 2025 at 3:26am
Makes sense to me. I’ve had people criticize my method as even $10M would change my life. To me, odds of 200,000,000 to 1 discourage going for $10M. Not that it is rational behavior going for the $200M as that is the calculated annuity with the cash payout after taxes being about 1/3 of that. $100 or so a year for a fantasy is acceptable to be while $1,000 a year is not.
Jon Murphy
Jan 18 2025 at 7:15am
That’s the way with me, especially with roulette. I love watching that little white ball spin round and round. The click-clack as it settles into space. For the briefest of moments, all the infinite branches of possibility are laid open. The thrill of the unknown. The possibility of victory. The possibility of defeat. It’s so much fun.
Alan Goldhammer
Jan 18 2025 at 9:37am
Though not an economist, Edward Thorp wrote the best treatise on gambling: “Beat the Dealer” for Blackjack. He later became a very successful hedge fund manager, investing for a number of his UC Irvine faculty colleagues. My gambling story is somewhat simple. I spend the summer of 1970 honing my card counting skills so that I could implement Thorp’s strategy when I stopped off in Las Vegas on my way to Indiana for grad school. I had a loss limit of $50 and a win limit of $500. It took me only about 2 hours to hit the win limit and I walked away from the table to cash in the winnings.
It’s much harder to implement a strategy these days as they use mulitple decks of cards and re-shuffle constantly. Casinos are always on the look out for card counters as well.
David Seltzer
Jan 18 2025 at 11:22am
Alan: good story about Ed. He was an investor in an early hedge fund I managed in Chicago. He believed, in spite of EMH, there were inefficiencies in various markets that could be exploited. We had long conversations about this. When our fund tried to implement his strategies, we seldom succeeded. Efficient markets, markets with full information, quickly eliminate “free lunches.” I liked Ed he was a smart guy.
David Seltzer
Jan 18 2025 at 11:14am
I was a market-maker on the CBOE. A number of traders went to Las Vegas to gamble. I was invited but declined. I didn’t see the utility in paying a dollar for a bet that paid ninety cents. When they returned they were unanimous in saying they had FUN!!!. One of the traders was awarded a grand suite, limo service and dining in the casino’s finest eatery. He was treated well was because he lost a lot at the tables. The monetary loss was the price of fun for him.
Billy Kaubashine
Jan 19 2025 at 3:51pm
The lottery bundles millions of after-tax dollars into new bundles that are large enough to be taxed once again at the highest rate.
Diabolical genius!
Jose Pablo
Jan 19 2025 at 5:24pm
The lottery is a wonderful way of raising revenue for the government.
In 2022 around $50b were collected by the Federal and State governments (32.5 b through the sale of tickets less costs and payouts + around 17 b through taxes on prices)
Collecting revenue while making people enjoy it. That’s genius!
The government should try this more often!
Amateur tennis, on the other hand, raises no revenue for the government. Shameful sport!
TMC
Jan 19 2025 at 5:58pm
I get how the lottery might be worth it for the players. It’s a small cost for having fun. It does NOT follow that the government should be involved.
David Henderson
Jan 19 2025 at 6:05pm
I agree.
Knut P. Heen
Jan 20 2025 at 10:12am
Zero-sum in money does not have to be zero-sum in utility. Fire insurance is also zero-sum in money. The defense of fire insurance is decreasing marginal utility which translates to risk-aversion in a stochastic world (losing $100 is worse than winning $100).
You need a strange utility function to explain gambling as a utility improving activity. I think indivisible goods can produce such a utility function along the lines pointed out by Coase. The point is that a lottery ticket is cheap like a cup of coffee, but gives a huge payout with a small probability. Imagine that you dream about a particular property you cannot afford by working and saving. Giving up some cups of coffee and hope you are lucky, does not come off as irrational as some may argue. The counter-argument that you can save the coffee and rent the property for an hour or two instead does not appeal to me.
Jose Pablo
Jan 20 2025 at 9:41pm
Giving up some cups of coffee and hope you are lucky, does not come off as irrational as some may argue.
It does if you are grossly overstimating your probabilities of winning (as lottery players do).
But you can also say that they extract utility from the overstimation of their probabilities of winning (which they certainly do).
The problem with the utility concept (as used by Coase in this case) is that it explains too much.
Knut P. Heen
Jan 21 2025 at 12:09pm
The St.Petersburg-paradox proves that people do not overestimate the probability of winning. The expected value of participation is infinite and most people are only willing to pay a few dollars to participate. That is why the solution to the paradox has to be some form of risk-aversion.
Herb
Jan 21 2025 at 12:26am
I have several friends who like to play the “scratchers” here in CA. I kid them that I appreciate them paying additional taxes. They realize they lose money over time, but they enjoy the occasional winnings.
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