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Game Theory: A Regulator, a Mathematician, and a Psychologist Walk Into a Casino...


Some notes from the 15th International Conference on Gaming and Risk Taking, now on in Las Vegas -- where else?

I am writing from Las Vegas, where I have come to attend the 15th International Conference on Gaming and Risk Taking. It is an academic conference, but an unusual one. Most of the ones I attend are annual meetings for narrow disciplines, centered around making contacts and getting jobs rather than advancing knowledge. They're pretty boring.

This one is different. Held about every three years, it brings together people who would never meet under other circumstances: regulators, casino executives, mathematicians, economists, psychologists -- most of whom study problem gambling, historians, advantage gamblers (people like blackjack card counters and quantitative sports bettors who enjoy a positive edge in games that are supposed to favor the house), and people who think advantage gamblers are criminals. Founder and long-time organizer Bill Eadington - who sadly died this year - described the idea:
Started in 1974 as the National Conference on Gambling and Risk-Taking, the conference began as a gathering of academics in a variety of disciplines from around the United States who were interested in the impact of gambling from several points of view, ranging from analyses of mathematical questions about gambling, to the fundamentals of pathological gambling, to understanding business dimensions of gaming enterprises, to broader inquiries into the impact of gambling on society.

The name changed to "International" with the seventh conference, and this year the word "Gaming" replaced "Gambling." The first change was a recognition of a shift that had already occurred. The second change is inaccurate, as only a minority of participants are focused on "gaming" (commercial casino games); most are interested in gambling in all of its forms.

One of the things I learned in middle age is that the things that define your life are not always the choices you make for that purpose. A lot of the important things just happen, and only afterwards come into focus. I have been going to the conferences for all of my adult life. Each one was a week taken out of whatever I was doing at the time, and each one led me to important new contacts and ideas. Also at each one, I reconnect with people on different life paths, many of whom cannot be found; they have to find you. For most of the conferences, I was an anonymous lurker, perhaps presenting a minor paper or session, but mostly going to listen, meet, and learn. At the last one, however, I was honored to give the keynote address, proof that if you hang around long anything long enough, you collect awards.

This year, I'm presenting two papers. One is co-authored with Nick Maughan and Raphael DiGuisto and involves an analysis of millions of financial bets placed at an Internet site (the company that generously provided the data is a large, publicly-listed entity that wished to remain anonymous). The data can be used to address many fascinating issues.

One is that a significant minority of bettors consistently beat the financial markets, winning up to several hundreds of thousands of dollars. This is statistically much stronger evidence than the usual studies of professional money managers. With a professional manager, you have to make assumptions about what the manager is trying to do - absolute returns, risk-adjusted returns, returns over benchmark, tax-adjusted returns, whatever. The manager has lots of constraints and costs that affect decisions. And it takes decades of data over hundreds of managers to get much statistical significance, but you cannot assume everything else stays constant over this period.

With the Internet gamblers, we have thousands of binary bets over periods from five minutes to a few days. We know they're trying to win money, nothing else, with no relevant constraints or costs. We have complete data on every trade, and every potential trade. For most of them, the gambling is tax-free -- either by law, or because they are ignoring the law.

However, the most interesting finding to me (so far, anyway; there's a lot of analysis left to do with these data) is the losing bettors. As is usually the case, we find that people bet more when they are wrong than when they are right. This is the basic insight that gave birth to the field of financial risk management. When people decide how much to risk by judgment, even the most experienced risk-takers generally do a worse than random job. That is, they would be better off risking the same amount each time than varying bet amounts by how good a gamble they think something is. This has been documented in just about every kind of risk-taking. A risk manager at a minimum can keep the bet sizes even, and with some work, can reverse the process so the more the risk-taker wants to bet, the less he or she is allowed to bet. The final goal is to come to an understanding of what the edge is, so the risk-taker can bet the optimal amount each time.

What impressed me is that the losing bettors - the large majority, of course - are not betting randomly. If they were, they would lose the house edge (about 3%, depending on the bet). In fact, they lose more than the house edge, because they bet more when they're wrong than when they are right. So in some sense, they know to make money; they just act in the opposite way. My co-authors and I were able to show that if you could intercept the bets and change the amounts -- or in some cases, the direction -- based on the previous records of the bettor, you could make money from everyone's bets, even after paying the house edge. It's easy with winners, of course; you could pass the bets through unchanged. With the biggest losers, you can just reverse the bet. But you can do much better than those simple rules.

I have another paper, a solo effort, on the history and future of research on financial bubbles. There are a lot of other great presentations (or at least ones that look great based on the presenter and the abstract). I expect to meet some old and new friends, some of whom seem to live permanently undercover, as if part of a self-developed witness protection program.

There are also a lot of changes going on in the gambling industry and some fascinating developments in the neuropsychology of gambling. It will be strange to have a conference without Bill Eadington, one of the few people respected by all subcultures of gambling researchers, but things change and life goes on.

These days, I have a great time in Las Vegas. Mostly things away from the Strip like the Gamblers Book Club and some of the genuine Old West stuff and some of the genuine new ethnic stuff; but also some of the touristy stuff on Las Vegas Boulevard. For most of my life until 2000 or so, I avoided Las Vegas unless I needed to go there for a big poker game. I never liked casinos, and casinos didn't care for poker players. But both Las Vegas and I have changed, and we now fit together pretty well, at least for visits.

I'll do a post or two on some of the more interesting presentations I see, and maybe inspire a few of you to attend the 16th International Conference.
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