Ed Thorp

Posted : admin On 10.03.2021

Here I summarise the investment lessons imparted by Ed Thorp in his book “A man for all markets1. My first three sections cover his views on investing, risk and market inefficiencies. My last two sections describe the hedge fund strategies Dr Thorp employed as well as his views on hedge funds in general. I discussed his life lessons in an earlier post.

Thorp is the author of the bestseller Beat the Dealer, which transformed the game of blackjack. His subsequent book, Beat the Market, co-authored with Sheen T. Kassouf, influenced securities markets around the globe. Thorp is an American mathematics professor, hedge fund manager, and blackjack player. To beat roulette, he and the father of information theory, Claude Shannon, invented the.


Before he embarked on a career in the financial markets, Dr Thorp did a tremendous amount of reading, including, for example, “Security Analysis” by Graham and Dodd. He recounts that, in general, a lot of what he read was nonsense and he was “surprised and encouraged by how little was known by so many.”

He describes two crucial mistakes he made with his first ever share purchase. Firstly he did not understand the company whose stock he bought, as his decision was based on a newspaper story. He concludes that ”most stock picking stories, advice, and recommendations are completely worthless”.

Secondly, by refusing to sell after a large decline in its share price, he anchored himself to his buying price. He believes that anchoring “bedevils” most investors. Instead, they should consider the economic fundamentals of the investment as well as the opportunity cost of holding it.

Next, he examined “charting” or the technical analysis of stocks and commodities, but after months of investigating data and predictions, he concluded that there is no value in it. People see patterns in things and offer explanations when there are none. Similarly, market participants and the financial media forever interpret insignificant price moves, as they are unable to distinguish between statistical noise and unusual events.

Even though he achieved spectacular success in the markets, Dr Thorp believes superior stock picking ability is rare. He recommends indexing for most investors, as the return to the average active investor equals that of the index minus fees. Also, the majority of mutual funds do not beat the index.

Unless you have a big enough edge, he also advocates using a buy-and-hold strategy. At least you are not handing out some of your wealth to high-frequency traders. He agrees with Paul Krugman that high-frequency trading serves no useful purpose and the resources consumed create no social good. (I discussed frequent batch auctions as a possible solution to curtailing high-frequency trading in an earlier post.)

Risk versus investment return

Understanding and dealing correctly with the trade-off between risk and return is a fundamental, but poorly understood, challenge faced by all gamblers and investors.“ – Ed Thorp

Similar to some other successful investors, such as Charlie Munger2, Dr Thorp believes most people do not understand the probability calculations required in investing, as well as gambling and everyday life. A proper balance should be maintained between risks and return by not betting too much and by not leaving too much money on the table. According to him, this is where Long Term Capital Management (LTCM) got it wrong in 1998.

He used the Kelly Criterion to determine his bet sizes as it is theoretically rigorous. However, he only placed bets at emotionally comfortable levels, which enabled him to invest or gamble with “calm and discipline”. Dr Thorp suggests that in practice one should implement half the Kelly Criterion’s bet sizes to avoid wild swings in a portfolio’s value. Also, the Kelly system requires exact probabilities, and when these are unknown, one should use conservative estimates.

After a geared investment in silver went wrong, he realised that he did not fully appreciate the riskiness of trading on margin. Gearing should be set at a level where you can tolerate the worst possible outcome.

He rejects the concept of “value at risk” which measures the capital required for the worst 5% of expected outcomes, as “these extreme events are where ruin is to be found”. The formal methodology of stress testing is also inadequate as it only simulates the effects of the significant adverse events of the past.

Dr Thorp believes that market participants are not prepared for Black Swan events and mentions as examples, LTCM in 1998 and the US insurance company, AIG, during the 2007 financial crisis. He is of the opinion that the 1987 stock market crash was caused by portfolio insurance investment strategies. The market dropped by 23% in one day, which is, as measured by the Dow Jones Industrial Average, the worst in its history.

He used a more comprehensive approach by analysing tail risk and by considering extreme questions such as what is the effect of a 25% market fall on his portfolio in one day.

Inefficient markets

We did not ask: ‘Is the market efficient, but rather, in what ways and to what extent is the market inefficient? And how can we exploit this?’ “ – Ed Thorp.

As explained by Dr Thorp, the efficient markets hypothesis can never be logically proven, rather one can only argue to what extent it succeeds in describing reality. He provides many counter-examples including his own track record as well as that of Warren Buffett.

Mispricing of options, warrants, convertible bonds and statistical arbitrage are market inefficiencies Dr Thorp profited from in his hedge funds. Apart from these he also exploited the discounts and premiums to net asset values in closed-end funds.

As a specific example of a market inefficiency, he discusses the 60% fall of Emulex’s share price within 15 minutes on 25 August 2002, in response to a hoax. Even after it was uncovered as fake news, the stock was still 11.4% down eleven days later. Thus, the market does not accurately reflect all available information.

A second example Dr Thorp discusses is the spinoff of PalmPilot from the company 3Com. The market grossly mispriced PalmPilot shares despite this being highlighted in the press at the time. Shareholders in PalmPilot should have sold their stake to buy 3Com which would have given them an even bigger stake in PalmPilot during the subsequent spin off, as well as an additional holding in 3Com.

Dr Thorp also reckons that the efficient market theory is falsified by the many investors who are easily duped, and often so for decades, such as, for example, the investors in Bernard Madoff’s hedge fund. Hence, investors do not rationally incorporate all relevant information into their investment decisions.

Dr Thorp’s version of the efficient market hypothesis is:

  1. Some information is instantly available to a minority who listens at the right time and place.
  2. Each person is financially rational only in a limited way.
  3. Participants typically only have some of the information available to determine a fair price. For each situation, both the time to process and the ability to analyse, vary.
  4. Reaction to news is not instantaneous and is often spread out over hours, days or months.

Hedge fund strategies

Dr Thorp is the father of quantitative market neutral hedge funds. Legalizing casino gambling in texas. The hedging of mispriced securities with optionality was a major source of profit during his career. This included options, warrants, convertible bonds and convertible preference shares.

Later on, he also employed statistical arbitrage after examining a multitude of indicators such as earnings yields, dividend yields, price-to-book ratios, momentum, short interest, earnings surprises and trading by company insiders. Their system was based on a combination of these indicators and was successful, but dependent on market circumstances.

He also developed a successful trading system, which they called “most-up-most-down” (MUD). This involved buying the stocks that had fallen the most (the bottom 10%) and selling short those that rose the most (the top 10%) during the previous two weeks.


Statistical arbitrage systems need to be continually improved upon as other participants discover the anomalies. Furthermore, in Dr Thorp’s words: “Every stock market system with an edge is necessarily limited in the amount of money that it can use and still produce an extra return.”

Later on, with the help of Gerry Bamberger, they reduced the volatility of their statistical arbitrage returns considerably by implementing not only positions that are market neutral, but also sector neutral. This reminds me of “Rule 20” in David Dremans book ”Contrarian Investment Strategies: The Next Generation3. Mr Dreman’s rule requires a long only investor to buy, say, the 20% least expensive stocks within each major industry. The investor is then short the more expensive 80% of stocks within each sector, relative to the market index. However, unlike Dr Thorp’s strategy, which is relatively short term, Mr Dreman suggests implementing his strategy for a five year period.

Dr Thorp lowered the volatility or risk of their arbitrage portfolio even further by making it neutral to factors such as inflation and the oil price. However, the tradeoff of from this risk reduction is also a decrease in returns as fewer portfolios satisfy all the conditions.

His fund also profited from the mispricing caused by spin-offs, such as the PalmPilot example discussed above.

Arguments against hedge funds

Despite being a remarkably successful hedge fund manager and also running a hedge fund-of-funds within his partnership, Dr Thorp is very critical of the industry.

In his view, picking good hedge funds is just as difficult as picking winning stocks, because, similar to companies, hedge funds are little businesses.

He highlights the following issues:

  1. Hedge fund industry returns are subject to survivorship bias as performance reporting is voluntary and poor performing funds refrain from submitting data.
  2. Overall, hedge fund investors receive poor returns, as the aggregate performance fees they pay are very high relative to the aggregate value-add delivered. This is so because the combined value add includes the value destruction from poor performing funds.
  3. Hedge fund managers often follow a “heads we win, tails you lose” strategy. Often managers close down an underperforming hedge fund, just to set up a new fund with a clean slate.
  4. Sometimes track records are build up in small closed funds by using IPO’s or cherry picking. Only those with good track records are then made publicly available, even though it is highly unlikely that the initial performance would be repeated.
  5. Dr Thorp also refers to some unethical behaviour within the industry, such as, for example, managers who cherry pick investments for personal accounts ahead of their hedge funds. He also reckons that the improper charging of fees to partnerships is sometimes an issue.

So, Dr Thorp believes that the most important thing to check before investing in a hedge fund is the honesty, ethics, and character of its operators.

For my summary of Dr Thorp’s philosophy of life go to this post. For my review of his book “A man for all markets” see here.

If you are interested in another take on Dr Thorp’s investment advice, refer to Tren Griffin’s 25iq post “A Dozen Lessons on Investing from Ed Thorp”.

1Thorp, Edward O. (2017). A Man for All Markets. One World Publications.
2Griffen, Tren (2015). A Dozen Things I’ve Learned from Charlie Munger about Risk. 25iq.com. (Available here).
3Dreman, David (1998). Contrarian Investment Strategies: The Next Generation. Simon & Schuster.

Advantage gambling has a long history beyond the realms of sports betting. The value bettor of today is the blackjack card counter of yesterday. Indeed, if you set your mind on beating a game of chance, you will see opportunities where nobody else assumed they existed. If you come up with your original idea you have a good chance of making a fortune. The stories of those who did inspire anyone who has set the goal of beating the betting markets. Today I would like to tell you the fascinating story of the men who cracked the roulette – Ed Thorp.

If you a regular follower of this blog, you have already read my article on Bill Benter and his horse racing model. In fact, Bill Benter was inspired by Ed Thorp’s book on blackjack card counting to become a professional gambler. In a sense, Ed Thorp has started a lineage of the sport’s betting greatest. So we could say this article is about where it all began. Let’s see.

Ed Thorp: The life of an advantage gambler

Ed Thorp was born in a low-middle class family. Due to his mathematical talent, he managed to start a promising academic career. After getting his physics degree, Thorp was admitted to a PhD in mathematics from UCLA (University of California, Los Angeles), which he graduated in 1958. Reportedly, this is where his academic interest in gambling started to grow. After his graduation, Thorp has worked as a professor in MIT, New Mexico State University and University of California, Irvine.

From mathematics to Blackjack

In the meantime, Thorp developed his theories in games of chance further. Even though Thorp was pursuing an academic career, he was not afraid to apply his theories in practice. His most notable research (and the one that would later on grant him a widespread recognition) was in the field of blackjack. Thorp developed a winning card-counting scheme and in association with pro-gambler and notable undeground figure Manny Kimmel, made his first profits in Vegas casinos.

Ed Thorpe Beat The Market

Ed Thorp’s 10 Count System

The card counting system of Ed Thorp took advantage of the fact that casinos were not reshuffling the deck before it was dealt to the end. Observing the cards leaving the deck, the relatively simple system calculated the chances to be dealt a good card from what is left.

Ed Thorp Gallery

Ed Thorp managed to prove that the system worked in practice as well as in theory. His discovery prompted him to write the best selling book Beat the Dealer, which laid down his system in detail. This was the first blackjack card-counting system made available to the general public. The book educated the first generation of smart punters, that would use their newly learned system to try and beat the casino, among which was the very William Benter.

Unfortunately the system in itself is insufficient to beat the casino nowadays. Today, casinos shuffle cards way before the end of the deck. However, it has been the basis for some more sophisticated blackjack card-counting systems to follow. Thorp’s contribution to the field of blackjack earned him a place in the Blackjack Hall of Fame

Stepping it up – association with Claude Shannon

Ed Thorp was starting to feel the taste of success, but his biggest hit was yet to come. Directing his effort away from shady illegal bookmakers and towards some of the brightest minds he encountered in his tenure as a mathematics professor, Thorp started working with Claude Shannon to find new edges on the gambling market.

Who is Claude Shannon

Claude Shannon was an early associate of John Kelly (yes, that Kelly) in Bell Labs. The two have worked together in the field of game theory and were well aware of each others work. This would lead to Shannon being among the first to recognize the potential of the Kelly criterion and apply it successfully to gambling and investing.

Shannon became famous for his research in the field of combined application of electricity and algebra to solve numerical problems, which earned him the nickname “the father of information theory”. It is safe to say that Shannon laid the foundation for the discovery of the modern computer.

And what else would the father of information theory do in his spare time, than find ways to crack the roulette.

Ed Thorp and Claude Shannon’s joint venture: Cracking the Roulette

It was known at the time that it is impossible to beat a balanced roulette. In its most popular format, the roulette has 36 red and black sections. Those are offering a 1/36 chance to pay you 36 times your stake, for an expected value of zero each. Then comes the green 0, which doesn’t win you anything and represents the house edge (and negative expected value for the gambler from the game) of 1/37 or around 2.7%. Pretty simple and very random game known to be EV- is what the roulette was at the time.

But was it really that random?

The question Throp and Shannon asked themselves was, is the roulette really random? After careful observation they have noticed some patterns of behaviour from the dealers, who were rolling the wheel.

In order for a casino to maximize its profit, the roulette must roll as many times as possible. This puts pressure on the dealer to run the wheel as quickly as he can. A good dealer would therefore be one that can learn to do the turns as seamlessly and automatically as possible. It is a skill that is acquired in time and the experienced dealers in Vegas casinos seemed to have it.

However, what this learned automation leads to, was that a dealer would (unknowingly to himself) tend to roll the wheel exactly a certain amount of times every time he rolls. A novice dealer would make, say, 27 to 31 rolls of the wheel. An experienced one, on the other hand would stay between 28 ¾ and 29 ¼.

The edge this discovery could yield was massive. Restricting the possible number of outcomes by half could enormously increase the EV of the gambler. He only needed to identify in which area of the wheel the ball was expected to land. To find this out was a difficult problem. But not so much for Thorp and Shannon.

The first wearable computer

Chances are you already have seen one of these:

The iWatch is the Apple model of a smartwatch, a.k.a. a wearable computer. Those things are quite popular nowadays. Their uses include measuring your heart rate while doing sports, checking the weather or making a phone call. But they were actually invented for gambling by, you guessed it, Ed Thorp and Claude Shannon. In other words, none of those fancy gadgets that millions of people are wearing today wouldn’t have existed, if not for those two smart men spending months sitting and thinking of ways to make some money on the roulette in Vegas. Remember that for the next time someone tells you gambling is immoral or a zero-sum game.

The two have tested the prototype of the first wearable computer in Shannon’s home basement in 1961. After the tests were successful, they have put it to good use in a number of casinos. The computer was counting the revolutions of the wheel and transferred the results via an electrical signal. It then transformed the signal into a sound played into the player’s ear, in what was an early form of a micro earpiece. Granted, the whole thing was a bit bulky and nothing that you can sell in an iStore nowadays. But it did the work, allowing its wearer to place a roulette wager with an estimated 44% edge over the house.

A money-printing machine?

The edge was indeed massive and there was enough unassuming casinos around there willing to take the action. This is not to say the scheme didn’t have its weak spots. For example, the connection to the earpiece was causing a lot of trouble. Therefore, it had to be fixed live every now and then, as Thorp recalls. Nevertheless, partly as a result of Thorp and Shannon’s invention, the state of Nevada banned the use of wearable devices in casinos later in 1985.

Today, the wearable computer is part of the exhibition of the MIT Museum in Cambridge, Mass.

What came next?

It quickly became apparent that for a mind of the caliber of Thorp, sharp gambling is too small of a playing field. Thorp applied his earned capital and mathematical insights in the financial market, which has since earned him hundreds of millions of dollars. However, he will always have a special place in hearts and minds of the gambling community due to his contributions to the field. Thorp’s work inspired the first generation of smart gamblers, who would employ mathematical and statistical models and use the assistance of electronic devices to win in games of chance.

From there on, the computer model of Bill Benter that beat the racetrack was only a matter of time and, of course, finding the right man for the job. Until today, when all sorts of sophisticated algorithms are being applied en masse to predict the outcome of a sporting event and beat the betting market. It was a fascinating development, that opened great opportunities in front of mathematically gifted people, but also continuously narrowed the playing field for everyone else. We shall see what the future brings in that regard.

Ed Thorp on the web

Ed Thorp Beat The Dealer

If you would like to dive deeper into Throp’s life story you can check his biography. It lays out the details around his discoveries and includes many interesting anecdotes. Furthermore, on Mr. Thorp’s website, you can find, among other things, a lot of great free articles on the topics of finance and gambling written by him, where you can learn a thing or two about his methods.

Finally, The Investor’s Podcast has done an interview with Ed Thorp, where you could hear the man speak:

As is obvious from the name of the podcast, the episode revolves more around finance. I find it an interesting piece nevertheless.


This was my report on the fascinating story of Ed Thorp and his gambling success. Being perhaps the first prominent advantage gambler, Ed Thorp contributed tremendously to the fields of blackjack, roulette and games of chance in general. Furthermore, he was ready to share chunks of his knowledge along the way by writing bestselling books and regularly appearing in the public via interviews or his own writings. In that way, he paved the way for many future betting legends such as Bill Benter, Zeljko Ranogajec, Tony Bloom and others.

Ed Thorp Beat The Market

The road to success is long and hard, but I hope Ed Thorp’s story gave you some inspiration to continue on your betting journey and perhaps a few ideas to work on. Next in line I have a few articles in mind about live betting, the progress of my LoL model and some interesting betting tools. If you subscribe to my Twitter channel and my newsletter on the upper-right corner of your screen, you will make sure not to miss any of these. I hope you enjoyed the article and see you around!

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