The Man Who Beat the Casino and Stock Exchange: Ed Thorp

We recently covered a podcast with Crazy Mike Thorp, in which he jokingly regretted that his father was not the famous Ed Thorpe.

Edward O. Thorp is a renowned mathematician and hedge fund manager who was the first to realize that players can gain a mathematical advantage in certain games against the casino. A couple of years ago, Ed, now 93, reminisced on Tim Ferriss's podcast about the highlights of his career—winning at blackjack and roulette, innovative trading ideas, and uncovering the largest Ponzi scheme in history.

— Could you speak a little about your upbringing and your formal education?

I was born in Chicago during the presidency of Herbert Hoover — that’s president number 31 — so I’ve seen sixteen presidents in my lifetime. I moved out to California with my parents during World War II and basically grew up here. I went through junior high and high school in California, then attended UC Berkeley and UCLA, where I earned a bachelor’s and a master’s degree in physics.

In the middle of my Ph.D. work in physics, I realized I needed more mathematics, so I began taking math courses. Eventually, I saw that I could graduate more quickly in mathematics than in physics, so I switched fields and earned my Ph.D. in math instead.

After that, I taught at UCLA, MIT, New Mexico State University, and finally the University of California, Irvine.

— How did gambling, or applying mathematics to gambling, enter the picture for you?

"I’m a curious person, and you could say it happened purely by chance. When I was teaching at UCLA, I became interested in the idea of beating blackjack. Someone told me about an article that explained how to play almost even with the house.

During Christmas vacation in 1958, just after I had finished my Ph.D., my wife and I went to Las Vegas. I had never gambled before because I knew the odds were against the player and most people lost. But I decided to try it and bet $10, playing for about 40 minutes.

I had an interesting experience. For the first 20 minutes, I used a small card that told me what plays to make. People around me thought I was a fool who knew nothing about the game — and they were right that I didn’t — but the card made me much smarter than the other players. I made some unusual plays that caught their attention.

At one point, I drew a seven-card 21, which is extremely rare. Most casinos paid a bonus for that, though this particular one didn’t. They thought I was trying for that hand, and when I pulled it off, they were amazed.

That experience made me realize that the other players didn’t know much about the game at all. So I went back and carefully reread the statistics article, and from my mathematics background, I saw how I could actually devise a system to beat the game.

And around that time, I moved from UCLA to MIT, where I had access to the big computers they had in 1959 — enormous IBM 704 machines the size of refrigerators that served 30 New England universities.

I taught myself how to program and began running simulations. As I worked through my ideas, I saw that I had a winning system. It was just a matter of finishing all the calculations, so I did.

Once I was confident the system worked, I wanted to publish it quickly. I knew from experience in mathematics that if I didn’t, someone else might claim credit. That had already happened to me twice before, and I didn’t want it to happen again.

I started looking for someone who could help me get the work published quickly. It turned out that on the MIT campus there was a man I knew nothing about named Claude Shannon. He was an Institute Professor and a member of the National Academy of Sciences. If he approved my work, he could get it published in the Proceedings of the National Academy of Sciences in just a couple of months."

"I sought him out. The secretary at MIT’s math department told me it was pointless — that he didn’t see people and was very private — and even if I managed to see him, I’d only get five minutes.

But I persisted and finally met him for lunch. We spoke for about five minutes, and after our conversation, he said, “Well, it looks like you’ve got all the main ideas here. Yes, I’ll put this through. But we’ll have to change the title.”

My original title was A Winning Strategy for Blackjack. Shannon changed it to something more restrained, like A Favorable Strategy for 21. He didn’t want the National Academy to think it was just a gambling paper, and a softer title sounded more appropriate.

The paper was submitted — and it caused a sensation. I had also submitted an abstract to the American Mathematical Society meeting in Washington, D.C., where I planned to present. At first, they rejected it, saying, “This is just another fool with a system that doesn’t work. We know you can’t beat gambling games.”

But on the abstract committee was someone I knew well from UCLA, a number theorist named John Selfridge. He became quite well known in number theory, and he said, "Well, if Thorp says it's true, it probably is, so you should accept this abstract." So I went there and I presented. I thought there'd be about 50 mathematicians in the audience, but instead there were 300 people. It was jammed, and a lot of people were very oddly looking — they had pinky rings on, sunglasses, and Hawaiian shirts in the middle of winter.

After I finished, they lunged for my little handout. I brought 50 handouts, thinking that was all I would need, and I basically tossed them out and left as quickly as I could."

"Then I was picked up by a fellow named Tom Wolfe, who became a famous American novelist. He was a young reporter then and wrote a piece for AP that went across the country. It got massive press, and that led to me writing a book and telling everybody how to do it.

After a couple of years — between the time I wrote the book and when I told people how to do it by publishing — I went out and played blackjack myself and proved the system worked. I figured there was no point in writing a book unless I knew it really worked. I knew it worked in theory, but what if you actually tried to do it? A lot of things seem to work in theory, but when you get down and actually put something to the test, you find out there are all kinds of things you didn't think of.

It turned out, in this case, it worked very well. We made $11,000 in one weekend with a test, which is about that with a zero on the end in today's money. This was in about 20 hours of serious play. So I had lunch money at MIT for a very long time thereafter."

— In 20 hours of serious play, do you recall roughly what the bankroll was, or the starting capital?

"Yeah, it was $10,000. That was the starting amount."

— Rewinding a bit to your earlier story — when you were first sitting at that blackjack table, if I heard you correctly, you said you had a little card. Could you describe what was on the card?

"Yeah, it was a set of rules for hitting and standing, doubling down, and pair splitting. It was the best way to play with a higher degree of approximation — the best way to play against a full deck or what was left of a randomly shuffled deck if you didn't know anything more about the cards that had been used up.

My contribution, after I understood this, was to figure out what would happen when some of the cards were missing from the deck, because the cards that are used up are not a representative sample of the cards in the deck — they can vary quite radically. For example, you might use all the aces early, and that would be bad for the player, or you might use none of them until late in the game, and that would be quite good for the player."

Ed. – In other interviews, Thorp said he made a decent amount of money playing blackjack, but it didn't pan out as a long-term career. Casinos quickly realized something was wrong with his game, and Ed was immediately blacklisted. Thorp resorted to various tricks, even wearing a fake beard and other disguises. But in those days, casinos were closely tied to criminal activity and resorted to highly questionable methods. Once, Thorp's drink was drugged during a game, and another time, his car's brakes were damaged. At some point, he realized it was time to quit blackjack.

— And with Claude Shannon — the person who doesn’t meet anyone — you said you were able to get five minutes at lunch. Why were you able to get time with Claude, or why do you think he was willing to spend time with you?

"It turns out that he was willing to spend five minutes, I think probably just to get rid of me. But after that, he kept asking me questions, and it became 15 minutes. Then he approved the paper I wanted to submit, and he said, 'What else are you working on?'

So I said, 'Well, there’s another project, which I actually started before blackjack and which got me interested in gambling — a way of beating roulette.' Claude Shannon, it turns out, was probably the king of gadgeteers. He built many ingenious machines over the course of his life. He built robots that would run mazes, machines that would play chess — he just loved all that sort of thing.

He had a house full of gadgets and equipment — hundreds of thousands of dollars' worth in 1958–59 money. So when he heard about roulette and I explained my ideas to him, he got very excited. We continued to talk, and this five-minute meeting became half an hour, then an hour. Then we adjourned to the cafeteria at MIT to grab a bite, and we went on for another couple of hours.

We decided we would join together and make an all-out effort to build a machine that would allow us to predict the outcome of a roulette game."

In the case of roulette, what we did was build a small computer that had about 11 transistors — 11 or 12, I don't remember which, because we had two versions, and I forget whether we ended up with the 11- or 12-transistor version. The computer is now at the MIT Museum in Cambridge and has been on exhibit in various parts of the world at one time or another.

Over about a nine- or ten-month period, we worked in Shannon's basement almost full-time and built this wearable computer. It turned out to be the first wearable computer, according to the MIT Media Lab. One person would wear the computer and enter push-button information about the position and velocity of the ball and the rotating wheel in the center. Then the computer would instantly — and I do mean instantly — tell you where to bet.

The other person would sit at the roulette table, apparently not connected with the observer who was busy inputting the roulette information. That person would hear a series of musical tones, and when the tones stopped, the last tone in the octave would tell them which section of the wheel to bet on. We divided the wheel into eight sections with a little bit of overlap, and the person who bet — which happened to be me — was able to quickly put down money on five neighboring numbers on the wheel.

We had a massive edge of 44%.

( Ed. – Although the device proved its effectiveness in practice, it never found long-term use. The main problem was the earpiece, whose cord kept breaking. In 1961, Thorp moved to another university, and his partnership with Shannon ended permanently .)

– For those who can’t see the video, you look like you’re in your 60s, and I am beyond excited to hop right into that.

"I kind of wandered into health and fitness by accident initially, just like I wandered into blackjack and roulette. I’m curious and always looking for things to understand, and I like the idea of self-improvement too. So, I was walking behind the student co-op one night when I was about 20 and heard a bunch of clanking. I looked down into the basement, and there were some fairly burly guys down there pumping iron. I walked in and said, 'This is a waste of time. This is ridiculous.'

One of them said to me, 'I’ll bet you a milkshake that if you work out with us for a year — just one hour an evening, three evenings a week — you’ll double your strength in a set of exercises that we describe.'

I said, 'I don’t believe it. Let’s try it.'

So I went down, and the four exercises were: the squat with a barbell on a rack, the military overhead press, the bench press, and… deadlift? No, it wasn’t deadlift. It was something else — I forget the fourth one at the moment, but I’ll think of it. Clean and jerk maybe? Who knows. Or bent row — yeah, it was something along those lines. But it was a compound exercise like the others.

There was a fourth exercise. Anyhow, what happened was I — I wouldn’t say I was a 98-pound weakling, but maybe a 150-pound weakling — and at the end of a year, I could military press 185, which was at least double what I started with. I could bench press 375. I could do 15 reps at 325, and I could squat with 375. I could do sets, and I forget what the other one was — wish I could remember it.

In any case, I was astounded that all this came to pass, so it made me pay attention to strength, at least. Some time went by, and I did a little swimming because I got interested in scuba diving.

Then, one day in my 30s, I was jogging along the beach with my brother-in-law. He said, 'Let’s go for a little jog.' I went about a quarter mile and was gasping. I was 35 then, I remember, and I said, 'This is awful. I’m in terrible shape. I have to do something about this.'

They had a book on aerobics by somebody named Ken Cooper, who had a lab down in Texas and started, in large part, the aerobics revolution that swept the country."

"I’ve evolved. I try to listen to my body, so I do what I enjoy. The rule I started to follow was: some is better than none, and more — up to a point — is better than less. There’s no excuse. If you tell yourself, 'I’m not going to do this because I can’t do the whole program,' that’s a big mistake. Just start doing it, and I find that if you start and get used to it, you find more and more things that you kind of like and can build on. Then you just keep getting better at it.

I was probably in my best shape at around 55 to 65 because of all this."

— What does your strength training look like now, or over the last few decades?

"As I get older, it declines. I get weaker, and it gets a little harder to do things. I feel a little more tired, and I can’t do as many reps or sets. So I have a mix of things I do now.

I’ll do squats — usually now just bodyweight — and I’ll do goblet squats or lunges with a lot of emphasis on one leg, then shift and do a lot of weight on the other leg. I do pull-ups. The best I’ve done recently, which is not very much, is four underhand pull-ups and two overhand pull-ups. I used to be able, 10 years ago, to do a dozen of each.

What else… I do a lot of back exercises regularly on the mat, and that’s very helpful for keeping my back in shape and keeping my core in pretty good condition."

— How did finance or investing enter the scene for you?

"Well, the way I got into finance and investing was that I made money at blackjack and from book royalties. So for the first time in my life, I had any spare money. Before that, as an academic, my wife and I were living month to month with no surplus, and then kids were coming, and that made it even tougher.

Once I had some money from both gambling and book royalties, I wanted to figure out what to do with it. Investing made good sense to me — I would put some capital aside and let it grow.

I started out by making a lot of foolish beginner mistakes, which cost me. Then I decided to sit down and re-figure this thing out, so I began to study investing in my spare time. I spent the summer of 1964 — which was, I guess, the third year I was at New Mexico State — just reading all summer in a big bookstore in Beverly Hills, reading all the investment books and newspapers they had.

Then I started again in the summer of ’65, reading whatever I could find. I happened to get a little book on warrants — common stock purchase warrants — which were the forerunner to what people call call options now.

When I saw that, a light came on, and I realized I could mathematize this. I could figure out how to value these things, and if I did that, I’d probably be ahead of the crowd who didn’t know how to do these things. I’d probably have an edge.

By chance, I came to UC Irvine when it opened in the fall of 1965, and I was telling one of the deans there about this idea that I had and was working on. He said, "Oh, we have someone else who does that," and it turned out to be Sheen Kassouf. So the two of us connected, and Sheen Kassouf had actually been doing it in practice. He had already made an elementary model for trying to judge warrants.

We decided to write a book together and work out more of the details in theory, and that became the book Beat the Market. That launched both of us into separate businesses. I began to do what are called warrant hedges. Basically, you buy a cheap warrant and short the common stock against it — that’s one way. Or you short an overpriced warrant and buy the common stock against it to hedge the risk, because they tend to move together.

In the case of the overpriced warrant, as it collapses toward zero or toward its conversion value, you capture an excess return. What I found was that you could make a steady 25% a year with practically no risk doing this. I was doing it for myself, and then word spread around the UCI campus and people wanted to sign up.

So I signed up the Dean of the Graduate Division, the secretary to the chancellor, some people in the math department, and so forth. I was managing a whole collection of little accounts for people, and they were making 25% a year. They kept telling everybody about it.

The Dean of the Graduate Division happened to be an investor with a firm owned by Warren Buffett. Warren Buffett was, at that point, shutting down his partnership because everything was overpriced — back in 1968, prices were crazy. The dean wanted to know where to move his money, so he introduced me to Warren Buffett to check me out and see if I might be a good place to put it."

"Warren and I got along fine, and apparently I passed the test, because the dean gave me his money to invest. I got to know Warren Buffett, and I was sorry to see that he was going out of business because I thought — as I told my wife then — “This is going to be the richest man in the world.” We’ll come back to that a little later; I think you’ll find the follow-up to that quite interesting.

Anyhow, I got the idea of forming a hedge fund from Warren Buffett, who was just closing down his hedge fund. So I went into business managing accounts and then merged the accounts into a hedge fund — a private limited partnership. That ran for about 20 years and used ideas that I kept generating — mathematical finance ideas — to stay ahead of other investors and make excess returns.

In 20 years, we only had three down months, and those down months were less than 1%. Basically, we just printed money every month. It made just under 20% annualized during that time. I’m very risk-averse, as you’ll find as we continue to talk, and this fund ran with extremely low risk but had a very high return. That was my entrée into investing."

— There were two other people who, I believe, read Beat the Market or were influenced by it: Fischer Black and Myron Scholes. Could you perhaps fill in the dots there? Because Nassim Taleb refers to the Black-Scholes model with a different name. Could you fill in the gaps for people who are listening?"

"I actually figured out what this model was back in the middle of 1967, and I decided that I would just use it for myself. Later, I kept it quiet for my own investors. The idea was basically to make a lot of money out of it for everybody, and it was fun for me just to develop it and apply it to various things.

Fischer Black and Myron Scholes read Beat the Market, which was the launching pad for me in finding this model, and it was also a launching pad for them. They saw how to improve the ideas in Beat the Market, and they made a mathematical finance model that valued warrants and options very accurately. It was based on a set of assumptions that are fairly narrow but pretty good.

I thought I was the only one who had this model. So when the Chicago Board Options Exchange opened in 1973, I thought I’d have the field to myself. But unfortunately, Fischer Black and Myron Scholes published the idea — and they did a better job of the model than I did because they had very tight mathematics behind their derivation.

I had to make a couple of assumptions to get to the same point, but they were reasonable assumptions, which turned out to stand up in practice and in theory later on. In any case, they published the model, and I thought, “Oh, I have this hedge fund I’ve been running for a few years. It’s been doing well. We’re going to make a lot of money in options.” But now Scholes and Black have told everybody what the secret is.

People didn’t catch on right away, though. When the Chicago Board Options Exchange opened for business in April 1973, the only people on the floor were my traders — and they were busy mopping up. It was like having machine guns against bows and arrows."

— What investing skills are applicable in life?

"Well, let’s take risk as a good example. You learn about investment risk and how you want to avoid very great risks or minimize them, because great investment risks can take you out of the game altogether.

You might have a situation where you multiply your money by 10 times, but you might also lose it all. Some things that are very highly volatile — like buying cryptocurrency — are in this category, where you may have the chance of a very large gain but also the chance of a very large loss. And if you lose most of your capital, it’s very hard to climb back out.

For instance, if you lose 90% of your capital, you’ve got to multiply what’s left by 10 in order to get back to even, which means you have to make 900% to offset that 90% loss. That’s not going to be easy to do. It takes a long time. So you want to avoid really bad outcomes."

I applied that, for example, to COVID. I thought about what to do and how to deal with it. At my age, the stats that came over in early 2020 showed that people 85 and up were dying at the rate of 18% — if they were male — of those who got it. And even now, the death rate is very high for those who get it. If they’re unvaccinated, it’s probably pretty close to that. If they’re vaccinated, it’s maybe a fraction of that.

I consider that a risk that can take me out of the game with a fairly high probability. So I decided I was going to avoid getting COVID if I possibly could. I was going to mask up, avoid crowds, and think about what the risks of various activities I do are — then decide whether they’re worth it.

I did my own analysis of COVID and its risks and tried to be very careful from then on. I think it’s paid off, and it’s paid off for my family too. I’ve passed this information on to people around me."