Investor Masterclass
Edward O. Thorp
The Mathematician Who Beat the Dealer
Quick Answer
What do Edward O. Thorp’s ideas teach investors?
Thorp connects a measured edge with position size and risk control. Kelly sizing aims to maximize long-run logarithmic growth under specific assumptions; uncertain odds and large drawdowns limit its use in investing. Smaller positions and hedges can reduce some risks, but cannot guarantee survival or profit. He has pointed most people toward index funds.
Start Here: The Short Version
Difficulty: Intermediate
Big idea: Thorp connects evidence of an edge with cautious sizing. Estimation errors, costs and losing streaks can still cause severe losses.
Use this lesson to understand the investor’s core idea first. Then use the examples, vocabulary, and application prompts to turn the idea into a practical investing rule.
Edward O. Thorp showed that blackjack could be beaten by counting cards. He then applied the same thinking to warrants, convertible bonds and hedge funds. This page explains his three core tools: measuring an edge, sizing positions with the Kelly criterion, and hedging. It also explains why beginners should size far more cautiously than any formula suggests.
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1962
Year Beat the Dealer was published
Random House; UC Irvine Libraries says it sold over one million copies
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1969
Year he and Jay Regan launched the fund later named Princeton Newport Partners
A hedged fund built on convertible bonds and warrants; it closed at the end of 1988
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About 20%
Yearly growth Thorp reported for that fund and its successors
November 1969 to May 1998, by his own 2006 account; he did not say whether fees were deducted
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Figures as of September 2026.
Lesson ideas on this page are teaching lines written by our editors from Edward O. Thorp’s published work and public interviews; they are not direct quotes. Figures reflect publicly reported records.
Key Takeaways
- An edge is a measured advantage; if you cannot measure it, assume it is zero.
- The Kelly criterion sizes each bet by the size of your edge.
- Betting above Kelly adds risk without adding growth; about twice Kelly erases growth.
- Careful professionals bet a fraction of Kelly because edge estimates may be too high.
- Hedging lets you earn a price gap instead of betting on market direction.
- Check whether reported returns are even possible, as Thorp did with Madoff in 1991.
- Thorp has said most people should use index funds unless they can show something better.
From Blackjack to Princeton Newport
Edward O. Thorp was born in Chicago in 1932. He earned a physics degree from UCLA in 1953, a master’s degree in 1955 and a PhD in mathematics in 1958. From 1959 to 1961 he taught at MIT.
At MIT he used an IBM 704 computer to work out blackjack odds. In January 1961 he presented his strategy to the American Mathematical Society and published it in the Proceedings of the National Academy of Sciences. He also began working with Claude Shannon, who introduced him in 1960 to J. L. Kelly Jr.’s paper on bet sizing. Together they built a wearable computer to predict roulette and tried it in Las Vegas in 1961.
Thorp taught at New Mexico State University until 1965. He then joined the University of California, Irvine as a founding member of its mathematics faculty. Beat the Dealer, published in 1962, became a bestseller. Casinos responded by changing blackjack rules and barring him, according to his publisher. At Irvine he worked with economist Sheen Kassouf on warrants, which led to Beat the Market in 1967.
In 1967 Thorp began managing hedged portfolios for clients. By his own account, in late 1967 he arrived at the option pricing formula later published by Fischer Black and Myron Scholes. He used it to trade warrants. In 1969 he and stockbroker Jay Regan launched Convertible Hedge Associates, renamed Princeton Newport Partners in 1974. He stayed at Irvine until 1982, the last five years as a professor of mathematics and finance.
Career Milestones
1961 | Presents his blackjack strategy and tests a wearable roulette computer with Claude Shannon. |
1962 | Publishes Beat the Dealer with Random House. |
1967 | Publishes Beat the Market with Sheen Kassouf and begins managing hedged portfolios. |
1969 | Launches Convertible Hedge Associates, later Princeton Newport Partners, with Jay Regan. |
1988 | Princeton Newport Partners closes at the end of the year. |
2017 | Publishes his memoir, A Man for All Markets, with a foreword by Nassim Nicholas Taleb. |
Three Influences
Claude Shannon Shannon, the MIT mathematician known as the father of information theory, worked with Thorp in 1960 and 1961. Together they built a small wearable computer that timed a roulette ball, and they tried it in Las Vegas. Shannon also introduced Thorp to J. L. Kelly Jr.’s paper on bet sizing. That idea shaped how Thorp later sized his bets and his fund’s positions.
J. L. Kelly Jr.’s 1956 paper Kelly, who had worked with Shannon at Bell Labs, published a 1956 paper on sizing repeated bets. His rule aims to make capital grow as fast as possible over the long run. Thorp learned of it from Shannon in 1960, soon after working out his card counting theory. He used it for blackjack bets and later to allocate capital in his partnership.
Sheen Kassouf and the warrant market Kassouf was an economist among UC Irvine’s founding faculty. In 1965 and 1966 he and Thorp built models for warrants, securities that let the holder buy a company’s stock at a set price. Their book, Beat the Market, followed in 1967. Thorp has said he was looking for low risk relative to return, and hedging warrants against stock fit that search.
Thorp’s path shows that an edge starts as a measurement: prove the odds first, then commit money only as fast as the evidence allows.
The lesson in one line
Princeton Newport and the Market Neutral Hedge
Thorp and Jay Regan launched Convertible Hedge Associates in 1969 and renamed it Princeton Newport Partners in 1974. Thorp’s office in Newport Beach, California, did the research and generated trades. The East Coast side ran the business and the trading desk. Thorp describes it as the first market neutral derivatives hedge fund, aiming to profit from mispricing rather than market direction.
Its core trade was the convertible hedge. The fund held convertible bonds and sold short the same companies’ stock, in ratios that made small price moves roughly cancel out. It also hedged warrants. Around the turn of 1980 its researchers found that stocks tended to reverse short term moves, which became the basis of statistical arbitrage. By Thorp’s account, the partnership made about $250 million for its partners, half or more from convertibles.
In a 2006 paper, Thorp wrote that the partnership and its successors compounded at about 20% a year from November 1969 to May 1998. He noted roughly zero correlation with the stock market. That paragraph does not specify the fee basis. The following index comparison uses different dates and does not match risk or fee treatment, so it is not a like-for-like performance assessment. For context, the S&P 500 returned 13.4% a year including dividends over the calendar years 1970 to 1998, our calculation from the Damodaran data behind our S&P 500 Return Calculator. The partnership closed at the end of 1988; the federal case involving people at the firm is covered under Notable Decisions. Thorp later ran Ridgeline Partners from 1994 to 2002.
The Framework
Thorp’s approach rests on a small number of principles. These four do most of the work.
Measure the edge before you bet
Thorp did not trust a hunch about blackjack. He computed the odds, published them, then tested them in casinos with small bets first. His market work followed the same pattern. A model said what a warrant or convertible should cost, and the gap between model and market was the opportunity. For a beginner the lesson is blunt: if you cannot write down your edge and test it, treat it as zero.
Size by the edge, then cut it
Kelly sizing maximizes long-run expected logarithmic growth in a specified repeated-bet model with known probabilities and payoffs. Betting above the model’s optimum reduces that growth and increases risk. The often-cited half-Kelly growth and drawdown figures come from simplified models, not universal stock-market rules. Under uncertain estimates, fractional sizing reduces exposure but does not remove the risk of substantial losses.
Hedge the risks you are not paid to take
Thorp’s funds tried to earn the gap between a security’s price and its model value rather than guess the market’s direction. Pairing a convertible bond or warrant with an offsetting stock position left the fund exposed mainly to that gap. By his account, returns had little link to the stock market. Hedges still cost money, need regular adjustment, and can fail when related prices stop moving together.
Check whether the numbers are possible
In 1991 Thorp compared a money manager’s reported option trades with the volume the market actually recorded. He concluded the trades could not have happened. The manager was Bernard Madoff, who was arrested in 2008. The principle reaches well beyond fraud. Before trusting any result, including your own backtest, ask whether the trades, prices and volumes behind it could really have existed.
The Thorp Vocabulary
A small set of terms runs through Thorp’s work. Learn these six and the rest of this page is easier to follow.
Edge
Your expected profit per dollar risked, averaged over many bets. A positive edge means you expect to gain over time, though any single bet can lose. Thorp’s card counting found the moments when the remaining cards favored the player, and he bet more at those moments.
Kelly criterion
A rule from J. L. Kelly Jr.’s 1956 paper for sizing repeated bets to maximize long run growth. For a simple bet, a shortcut on Thorp’s website, which he credits to William Poundstone, is to stake a share of your bankroll equal to your edge divided by the odds. It assumes you know your edge accurately, which investors rarely do.
Fractional Kelly
Betting a fraction of a model’s Kelly amount. In Thorp’s idealized continuous model with zero risk-free rate, half Kelly retains three quarters of the optimum growth rate. In that model, the probability of ever falling below half of initial capital is 1 in 2 at full Kelly and 1 in 8 at half Kelly. These are model results, not real portfolio forecasts or peak-to-trough drawdown probabilities.
Warrant
A security issued by a company that gives its owner the right to buy the company’s stock at a set price. Its value rises and falls with the stock. Beat the Market showed how to estimate what a warrant should be worth and how to hedge it against the stock.
Convertible arbitrage
Holding a convertible bond, which can be exchanged for stock, while selling short the same company’s stock. The ratio is set so small price moves roughly cancel out, leaving the bond’s mispricing as the target. Thorp wrote that half or more of Princeton Newport’s profits came from convertibles.
Statistical arbitrage
Trading many small long and short stock positions based on a statistical pattern rather than a view on any one company. Thorp’s team built its version on a finding, made around the turn of 1980, that stocks tended to reverse short term price moves. Patterns like this can weaken over time.
Notable Decisions
These six moments show the approach in practice, including the setbacks as well as the successes.
The wearable roulette computer, 1961
With Claude Shannon, Thorp built a computer the size of a cigarette pack, with 12 transistors, to time the roulette ball. Toe switches fed it data, and tones in an earpiece gave the prediction. UC Irvine describes it as the first wearable computer. In Las Vegas it produced small wins at dime stakes, but earpiece parts broke often, which limited its use. A real edge still has to survive real conditions.
Card counting and Beat the Dealer, 1962
Thorp first took his system to the casinos in 1961 with a $10,000 bankroll. By his account, he won $11,000 in 20 hours of full scale betting. His 1962 book spread the method to ordinary players and sold over one million copies. Casinos responded by changing rules and barring him. Thorp says card counting still works but is harder, because good rules are scarcer and casinos detect counters.
Warrant hedging and an option formula, 1967
Beat the Market, written with Sheen Kassouf, showed how to value warrants and hedge them against their stock. By Thorp’s account, he arrived at an option pricing formula in late 1967. Fischer Black and Myron Scholes published that formula in 1973. Thorp used it to trade warrants from late 1967 on, and he has said it gave him an advantage few other traders had.
Statistical arbitrage, 1980
Around the turn of 1980, Thorp’s team found that stocks tended to reverse short term price moves. They built a strategy of many small long and short positions on that pattern and ran it until Princeton Newport closed. Thorp has said it began to weaken in 1987. By his 2003 account, a later version compounded at 20% a year net to investors from August 1992 to October 2002.
The end of Princeton Newport, 1988
Princeton Newport closed at the end of 1988 after nearly two decades of hedged trading. In a federal case in New York, five people associated with the firm were convicted, including cofounder Jay Regan. A Drexel Burnham Lambert trader was also convicted. Counts included tax fraud and racketeering. In 1991 an appeals court upheld the conspiracy convictions. It vacated most other counts, including tax fraud and racketeering, and sent them back to the trial court. Thorp was not among the defendants in that appeal.
Madoff’s impossible trades, 1991
A pension fund client asked Thorp to review its holdings, including an investment with Bernard Madoff. That investment had reported about 20% a year in the 1980s. According to Forbes, Madoff claimed 123 Procter & Gamble call options on a day when only 20 traded. Option volumes in other stocks were also too thin. Thorp advised the client to pull out; Forbes noted he did not take the finding to regulators.
30 Simple Investor Lessons
This section turns Edward O. Thorp’s best known ideas into simple teaching lines. Each line is a lesson summary written by our editors, not a direct quote. Check the evidence and limits before applying a teaching line.
Quote safety note: Treat these as educational principles, not verbatim quotes. For Edward O. Thorp’s exact words, go to the primary sources listed at the end of this page.
Find an Edge You Can Measure
Lesson idea
An advantage you cannot measure is only a hope.
Means. Thorp computed blackjack odds on an MIT computer and published his method before risking serious money on it.
Apply. For any strategy you follow, write the specific reason it should beat an index fund and the number that would prove it.
Lesson idea
Most edges are small, so they only show up across many repetitions.
Means. Card counting helps only in some situations, so its benefit appears over many hands rather than a few.
Apply. Before judging any strategy, count how many separate decisions its results rest on, and treat small samples with caution.
Lesson idea
Whether a market can be beaten depends on the market and on the person trying.
Means. Thorp has said efficiency depends on both the market and what its participants know and can do.
Apply. List the information or skill you have that most buyers of a stock lack; if the list is empty, assume no edge.
Lesson idea
An edge that becomes widely known tends to shrink.
Means. After Beat the Dealer, casinos changed rules and learned to spot counters; Thorp’s statistical arbitrage pattern began weakening in 1987.
Apply. Note when you first read about a popular strategy, then check how its results held up after it became well known.
Lesson idea
Start small and let the evidence decide how fast you grow.
Means. On his first casino trip Thorp bet $1 to $10 a hand for eight hours, then raised stakes in stages.
Apply. Test any new approach with virtual money in the StockEducation simulator, and increase size only if your written results support it.
Position Sizing and the Kelly Criterion
Lesson idea
How much you bet can matter as much as what you bet on.
Means. Two people with the same edge can end up far apart if one of them bets too much.
Apply. Next to each position in your simulator portfolio, write why it is that size as well as why you own it.
Lesson idea
The Kelly idea ties the size of a bet to the size of the edge.
Means. For an even money bet, Kelly stakes your chance of winning minus your chance of losing, as a share of your bankroll.
Apply. Take a made up coin that lands heads 55% of the time at even money, and confirm its Kelly bet is 10%.
Lesson idea
A small edge, sized sensibly, can compound into a large gain.
Means. For a specified path of 55 wins and 45 losses, staking 10% of remaining capital at each even-money bet turns $10,000 into $16,501: 10,000 × 1.1^55 × 0.9^45. This is an illustrative path, not expected wealth or a promised outcome. It assumes independent bets with known 55% win probability and no costs.
Apply. In a spreadsheet, simulate 100 bets on the made up coin several times and note how widely the final results vary.
Lesson idea
Betting more than Kelly adds risk and eventually removes growth.
Means. On the same specified 55-win, 45-loss path, staking 20% of remaining capital ends at $9,863: 10,000 × 1.2^55 × 0.8^45. Doubling the optimal fraction in this particular model reduces long-run growth. The threshold differs with other payoffs and probabilities.
Apply. Write down the largest share of your portfolio you have put in one idea, and ask whether its edge justified that size.
Lesson idea
No measured edge means the Kelly bet is zero.
Means. If your chance of winning is no better than your chance of losing, the formula says not to bet at all.
Apply. Before sizing any active position, write your estimated edge and its evidence; if you cannot, keep the idea to virtual money.
Why Professionals Bet Less Than Kelly
Lesson idea
Half the bet can keep most of the growth.
Means. On that same 55-win, 45-loss path, staking 5% of remaining capital ends at $14,554: 10,000 × 1.05^55 × 0.95^45. Ten consecutive losses would reduce the starting $10,000 to $5,987 at 5%, or $3,487 at 10%. Fractional sizing still allows deep losses.
Apply. Compare that with roughly $16,500 at 10%, and write down whether the extra gain is worth the bigger swings to you.
Lesson idea
Deep drawdowns are the hidden price of full Kelly.
Means. In Thorp’s idealized continuous model with zero risk-free rate, the probability of ever falling below half of initial capital is 1 in 2 at full Kelly and 1 in 8 at half. These figures concern initial capital, not a later peak, and are not real stock-market probabilities.
Apply. Write the largest drop you could sit through without quitting, then compare it with the maximum drawdown in your simulator results.
Lesson idea
Your estimate of your own edge is probably too optimistic.
Means. Thorp advises assuming your true edge is below your estimate and betting less, since overbetting an uncertain edge can turn growth negative.
Apply. Take the return you expect from an idea, cut it in half, and check whether the idea still looks worth the risk.
Lesson idea
Markets differ from a coin toss, so any Kelly number is a rough guide at best.
Means. The formula assumes known odds and repeated independent bets, while stocks bring uncertain odds, related moves and occasional extreme days.
Apply. List three ways a real stock differs from the made up coin, and note how each argues for a smaller position.
Lesson idea
Beginners should size far below what any formula suggests.
Means. A new investor has no track record to measure an edge against, so small single positions are the cautious reading of Kelly.
Apply. Set a maximum size for any one position, write it atop your plan, and practice keeping to it with the simulator’s virtual $1,000,000.
Hedging and Market Neutral Thinking
Lesson idea
A hedge lets you bet on a price gap instead of the market’s direction.
Means. Thorp’s funds paired convertible bonds or warrants with offsetting stock positions, so profits depended mainly on mispricing.
Apply. For any hedge you read about, write down which risk it removes and which risk it keeps.
Lesson idea
Returns that do not depend on the market can be as valuable as high returns.
Means. Thorp reported about 20% a year from 1969 to 1998 for his partnership and its successors, with roughly zero market correlation.
Apply. Check your simulator portfolio’s results next to the S&P 500 and note whether its swings mostly follow the index.
Lesson idea
Every hedge has a cost and a way to fail.
Means. Hedges need upkeep, pay trading costs, and can break down when related prices stop moving together.
Apply. In a paper-only example, describe two offsetting positions, their holding costs, and a situation in which both could lose. Do not assume the simulator supports the required instruments or hedge.
Lesson idea
Know what an option or warrant should be worth before you trade it.
Means. Thorp traded warrants with a pricing model from late 1967, years before Black and Scholes published their formula in 1973.
Apply. Look up one listed option and write down what drives its value: stock price, strike price and time left before expiry.
Lesson idea
Carry only the risks you are being paid to carry.
Means. Thorp kept exposure to the mispricing he had measured and hedged away the rest, including the market’s overall direction.
Apply. Run a stock you follow through the Stock Risk Analyzer and note which listed risk drivers you actually intend to bear.
Test Claims and Spot the Impossible
Lesson idea
Check that reported trades could actually have happened.
Means. According to Forbes, Madoff claimed more Procter & Gamble option trades on one day than the whole market recorded.
Apply. When a fund or adviser describes a strategy, ask which markets it trades and whether independent records of those trades exist.
Lesson idea
Returns that look too good deserve extra scrutiny.
Means. Forbes says the Madoff investment’s reported 20% a year in the 1980s was what first made Thorp suspicious.
Apply. Use the CAGR Calculator to turn a manager’s claimed start and end values into a yearly rate, then compare it with an index.
Lesson idea
Ask for the documents, then read them.
Means. Thorp’s review began with the records of the trades themselves rather than a summary of the results.
Apply. For any investment held through a manager, write down who holds the assets and where you would find an independent statement.
Lesson idea
A result without a working mechanism is a warning sign.
Means. Madoff’s reported returns needed option trades on a scale the market could not supply, so his claimed method could not explain them.
Apply. For any strategy pitch, write one sentence on how the money is made, and treat it as unproven if you cannot; our How to Spot an Investment Scam lesson lists the other warning signs.
Lesson idea
Apply the same skepticism to your own results.
Means. A backtest or lucky streak can look like skill, which is why Thorp tested ideas with small stakes before scaling up.
Apply. Keep your own dated notes. Review the evidence monthly, and distinguish an explained outcome from one that may reflect luck.
Discipline, Survival and Index Funds
Lesson idea
Put your method in writing so others can check it.
Means. Thorp presented his blackjack analysis to mathematicians and in a scientific journal before writing a popular book.
Apply. Write your investing rules on one page and ask a friend to find the weakest assumption.
Lesson idea
Anyone claiming to beat the index has to prove it first.
Means. Thorp has said people should use index funds unless an alternative is shown to be better, and that active shortfalls roughly match fees.
Apply. Compare the yearly fee of any active fund you hold with a broad index fund’s fee in our Investment Fee Calculator, and write the extra return needed.
Lesson idea
Survival comes before growth.
Means. Thorp showed that consistently betting too much eventually leads to ruin, however good the edge.
Apply. Write down the one loss that would force you to stop investing, and make sure no single position could cause it.
Lesson idea
Keep a record so you can separate skill from luck.
Means. Thorp’s career rested on records: computed odds, tested hands, and model prices compared with market prices.
Apply. In your own notes, write the evidence behind a hypothetical position and reread it a week later. Record what would challenge the idea.
Lesson idea
Treat a model as a guide rather than a guarantee.
Means. Even with a pricing model in hand, Thorp hedged his positions and sized them with the Kelly approach.
Apply. For each calculator or model result you rely on, note one assumption that could be wrong and what you would do then.
Final Reflections
Edward O. Thorp’s lasting lesson is that risk is managed before a bet is placed rather than after. At the blackjack table and in his funds, he first measured an edge. He connected position size to an estimated edge and used hedges to reduce selected exposures. Kelly gave that discipline a model, while fractional Kelly reduced exposure to estimation errors. Neither guarantees survival or removes all risks.
His record also carries warnings. Edges shrink once others find them, models rest on assumptions, and even a successful fund can end for reasons outside its strategy. For most beginners, the takeaway is modest. Without a measured, tested edge, Kelly logic points to small positions, and Thorp himself has pointed most people toward index funds. His habit of checking whether numbers are even possible serves every investor. Practice these habits with virtual money before risking real money.
Five Commitments for the Disciplined Investor
- Measure and write down my edge before risking real money.
- Size every position so that a losing streak cannot end my investing.
- Bet less than any formula suggests while my skill is unproven.
- Know which risks each position carries and which ones I am paid to take.
- Check whether a reported result is actually possible before trusting it.
Sources Used for This Lesson
Editorial verification note. Investor quotations are risky because many popular lines online are paraphrased, shortened, or misattributed. To avoid that risk, this lesson presents teaching lines and investor lessons written by our editors, not verbatim quotes. The sources below allow readers to check the historical claims and mathematical assumptions. Model results and attributed historical figures should not be treated as promises of future performance.
Before using any line in ads, social posts, printed material, or legal or compliance sensitive pages, verify the exact wording against the primary sources below.
- Edward O. Thorp, A Perspective on Quantitative Finance: Models for Beating the Market (Quantitative Finance Review, 2003)
- Edward O. Thorp, The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market (Handbook of Asset and Liability Management, Vol. 1, Elsevier, 2006)
- Putting the Cards on the Table: A Talk with Edward O. Thorp, PhD (Margaret M. Towle, The Journal of Investment Consulting, Vol. 12, No. 1, 2011)
- Edward O. Thorp: FAQ
- UC Irvine Libraries, Finding the Edge: The Work and Insights of Edward O. Thorp, A Winning Hand
- UC Irvine Libraries, Finding the Edge: A Spin of the Wheel
- UC Irvine Libraries, Finding the Edge: Higher Mathematics at UCI
- UC Irvine Libraries, Finding the Edge: A Career in Quantitative Finance
- Online Archive of California: Guide to the Edward O. Thorp papers, 1946 to 2023 (UC Irvine Special Collections)
- Forbes: The Card Sharp Who Cottoned Onto Madoff’s Fraud In 1991 (Robert Lenzner, April 6, 2010)
- United States v. Regan, 937 F.2d 823 (2d Cir. 1991), via OpenJurist
- Penguin Random House: A Man for All Markets by Edward O. Thorp
This lesson is for general financial education only. It does not provide personal financial advice, stock recommendations, or a guarantee of investment results.
