THREE COMMON MISTAKES PEOPLE MAKE AT CASINOS
As gambling comes under scrutiny by mathematicians, human psychology pushes us to make the same errors
Many people think of gambling as a frivolous entertainment at best, or a corrupting sin at worst. But throughout history, there have been mathematicians and scientists who have seen the games you’d confront in a Las Vegas casino a very different way — as a playground for ideas where they can test notions of how the world works.
That’s the premise of a new book, The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling.
In the book, mathematician Adam Kucharski traces the long, tangled relationship of betting and science, from the origins of probability theory over a dice game to the kind of sophisticated counting techniques that have won MIT graduates millions in Vegas.
In an interview, Kucharski said he has always been obsessed with the puzzles of casino games. But when he was a PhD student, he started getting recruited by betting hedge funds, which were earning big profits for their investors by putting wagers on such events as the outcomes of soccer games.
That piqued his interest and triggered a deep dive into the interconnected history of science, math and gambling.
You have so many stories in the book of these amazing successes, where mathematicians and statisticians triumph over casinos and games. What was one of the most lucrative strategies in history you found?
One of the stories I really liked was about students at MIT, who started thinking about lotteries as part of a math project in 2005. Generally, you’d expect to lose money in lotteries, because that’s how they work. But as they expanded their analysis, they found a lottery that had been introduced fairly recently in Massachusetts called Cash WinFall that had this specific property. If the jackpot reached a certain limit and nobody won it, the prizes would roll down, meaning they would go to people who matched fewer numbers.
In these weeks where you had this rolldown feature being triggered, it could be quite profitable. The MIT students realized that if you bought enough tickets in the right combinations of numbers, you could pretty much guarantee a profit.
Firstly, it’s a great story because it starts with this innocuous college project and then grows into something where they incorporate a company to do this systematically. A number of syndicates also were getting involved as well, because essentially this had become the most lucrative lottery in the United States.
But then there was one week when the MIT group actually bought up enough tickets to trigger the roll-down. They realized that if they bought enough tickets to raise the jackpot to $2 million, they could force the lottery to roll down immediately, while the other syndicates were waiting for it to occur two or three weeks later.
What has science learned from gambling?
My day job is in public health, looking at disease outbreaks. Many of the methods we use originated with games and gambling. All the concepts around probability, how we measure the chance of an event, were only developed in the 16th century with people studying dice games. The concepts of statistical theory and testing a hypothesis were also inspired by dice games and roulette just over 100 years ago.
Games also gave rise to some more modern computational techniques. In the late 1940s, a mathematician was looking at a form of solitaire and wanting to know how the cards might fall. He wasn’t a big fan of pen-and-paper calculations, so he decided to lay it out and see what happened. He realized that if you have these complicated probability questions, you can simulate lots of random outcomes, and then you get a sense of what patterns you might see. Today, we call that the Monte Carlo method, and we use it to simulate the outcome of things like epidemics.
What have you learned about the mistakes that people often make when trying to predict the outcome of games? For example, in the section in the book on horse racing, you mention that people often gamble too much on underdogs. Are there other common errors?
There’s a number of biases we fall into. One is the “favourite-long-shot bias.” In horse racing, if you look at the horses that are in the back of the pack, they have higher odds than their performance suggests they should. In other words, people overestimate the chance of long shots winning.
That feature also pops up in other sports, and even in how we predict weather or severe political events. People tend to focus on things that are surprising and overestimate the chances of unlikely events.
Another is known as the Monte Carlo fallacy. This originated in roulette, where when the same colour comes up multiple times, people tend to start piling money on the other colour. They think that if black has come up a lot, then red must be due. Of course, it isn’t, because the result is still completely random, but there’s this psychological bias dragging us one way.
A third psychological quirk which pops up a lot in games is what’s known as gambler’s ruin. This is the tendency where if people win at a game, they increase the amount of money they’re risking. But often when people lose, they don’t decrease the amount that they’re risking. Mathematically, this will always lead you to bankruptcy. This is why bankroll management is incredibly important, because you need to resist this temptation and adjust the amount you’re risking depending on where you are in the game.
Your book talks about this fascinating intersection between the financial industry and gambling. How is the line between the two being blurred?
There’s a few ways that the distinction between betting and investment seems to be changing. One is the emergence of betting syndicates that are acting more like hedge funds. Historically, many betting syndicates have been very private, made up of a few individuals with their own bankroll or a few investors. But now some of these syndicates are targeting external investors and openly recruiting PhD students and other mathematically minded people.
There are a few things that overlap between the industries: One is whether you class something as betting or an investment. Spread betting, for instance, where you bet on the amount of change in a particular stock, is classed as gambling in the U.K. But in Australia, it’s deemed an investment and you pay capital gains on any money you make. And in the U.S., it’s gambling and entirely banned. The ability to make consistent profits on what seems like gambling is challenging the idea of what we define as a financial asset.
MIT students realized that if you bought enough tickets in the right combinations of numbers, you could pretty much guarantee a profit