Edward Thorp

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
by William Poundstone
Published 18 Sep 2006

Zwillman’s death left Manny Kimmel holding a portfolio of businesses, some legitimate and some not, some owned by Kimmel and others apparently in partnership with Zwillman’s estate and/or still other murky entities. Kimmel had an idea for parlaying this wealth. It was going to be the biggest gamble of his life. It involved the stock market. Edward Thorp ONE FRIEND DESCRIBED Edward Oakley Thorp as “the most precise man I have ever met.” This zeal for measurement was evident from earliest youth. It has been claimed that mathematical talent is, ironically, linked with a child being slow to speak. Ed Thorp was born in Chicago on August 14, 1932, and did not utter his first words until he was nearly three. The Thorp family was at a Montgomery Ward department store when a group of people stepped out of an elevator.

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“Claude Shannon’s Cryptography Research During World War II and the Mathematical Theory of Communication.” Roll, Richard (1988). “R2.” Journal of Finance 43:541–66. ———, and Robert J. Shiller (1992). “Comments: Symposium on Volatility in U.S. and Japanese Stock Markets.” Journal of Applied Corporate Finance 5:25–29. Rotando, Louis M., and Edward O. Thorp (1992). “The Kelly Criterion and the Stock Market.” American Mathematical Monthly, Dec. 1992, 922–31. Rubinstein, Mark (1975). “The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets.” UC Berkeley Research Program in Finance, Working Paper No. 34. ———(1987).

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He sent part of this unpublished material regarding Kimmel to Ed Thorp, who forwarded it to me. Zwillman biography: See Stuart 1985. Chose number with fewest bets: Stuart 1985, 29. Story about Kaplus shooting: Stuart 1985, 42. 40 percent of imported liquor: Stuart 1985, 53. Kimmel won parking lot in crap game: Bruck 1994, 29. Kimmel mortgaged parking lots: Bruck 1994, 32, which quotes Eddie Hand on this. Taught himself calculus, trigonometry, probability: This is from Peter Ruchman’s interview with Jack Newton, some of which was published in Ruchman 2000. Ed Thorp believes that Kimmel had little understanding of math.

Concentrated Investing
by Allen C. Benello
Published 7 Dec 2016

For most investors that tiny fissure wasn’t worth the time or effort. For Edward O. Thorp, whose bread‐and‐butter was convertible arbitrage, this was a rare opportunity. To make it worthwhile he would need to drive a bus through that tiny crack. He would need to lay down $662.5 million dollars to collect just $2.5 million. How could he justify risking such a titanic sum for such a minuscule payoff? Thorp had a secret. He employed a little-known formula for optimal position sizing—the mysteriously named Kelly Criterion. However he plugged the details of the trade into Kelly’s formula, the answer was unavoidable: Bet the farm. Claude Shannon and Ed Thorp While working as a post‐doctoral researcher at the Massachusetts Institute of Technology (MIT) in November 1960, Thorp submitted an abstract for a talk to the annual meeting of the American Mathematical Society.

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Notes 1. Ken Kurson, “What a Card!,” Worth, September 1999. 2. Edward O. Thorp, “The Legacy of Beat the Dealer,” Wilmott.com, September 24, 2002. 3. Ibid. 4. Ibid. 5. Howard Gardner, The Mind’s New Science: A History of the Cognitive Revolution (New York: Basic Books, 1987. 6. William Poundstone, Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (New York: Hill and Wang, 2006). 88 Concentrated Investing 7. 8. 9. 10. http://home.williampoundstone.net/Kelly.htm. Ibid. Ibid. Edward O. Thorp, “The Legacy of Beat the Dealer,” Wilmott.com, September 24, 2002.

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Charles Munger, “A Lesson on Elementary, Worldly Wisdom as it Relates to Investment Management and Business,” transcript of talk to University of Southern California Business School, 1994, https://web.archive.org/web/20060208032616/ http://ycombinator.com/munger.html. 31. Leonard C. MacLean, Edward O. Thorp, and William T. Ziemba, “The Kelly Capital Growth Investment Criterion: Theory and Practice,” Singapore: World Scientific Publishing Company, 2011. 32. Ibid. 33. Ibid. 34. Leonard MacLean, Edward O. Thorp, and William T. Ziemba, “Good and Bad Properties of the Kelly Criterion,” Unpublished, January 1, 2010. 35. John Maynard Keynes, The General Theory of Employment, Interest and Money (London: Palgrave Macmillan, 1936). 36.

The Quants
by Scott Patterson
Published 2 Feb 2010

Indeed, many of the most important breakthroughs in quant history derived from this obscure, puckish mathematician, one of the first to learn how to use pure math to make money—first at the blackjack tables of Las Vegas and then in the global casino known as Wall Street. Without Thorp’s example, future financial titans such as Griffin, Muller, Asness, and Weinstein might never have converged on the St. Regis Hotel that night in March 2006. Edward Oakley Thorp was always a bit of a troublemaker. The son of an army officer who’d fought on the Western Front in World War I, he was born in Chicago on August 14, 1932. He showed early signs of math prowess, such as mentally calculating the number of seconds in a year, by the time he was seven. His family eventually moved to Lomita, California, near Los Angeles, and Thorp turned to classic whiz kid mischief.

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That night at the St. Regis: Several details of the poker event were gleaned from MFA News 2, 1 (Spring 2006). In 1990, hedge funds held $39 billion: Based on data from Hedge Fund Research, a Chicago research group. 2 THE GODFATHER: ED THORP Just past 5:00 A.M.: I conducted numerous interviews with Ed Thorp and exchanged many emails. Many details about Ed Thorp’s blackjack career, including a description of his foray into blackjack in 1961, were found in his colorful book Beat the Dealer: A Winning Strategy for the Game of Twenty-One (Vintage, 1962). Other details were found in the excellent Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, by William Poundstone (Hill and Wang, 2005).

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I confirmed details I used from this book with Thorp. The strategy was from a ten-page article: “Getting a Hand: They Wrote the First Blackjack Book but Never Cashed In,” by Joseph P. Kahn, Boston Globe, February 20, 2008. He’d kept his roulette strategy largely secret: “The Invention of the First Wearable Computer,” by Edward O. Thorp (http://graphics.cs.columbia.edu/courses/mobwear/resources/thorp-iswc98.pdf.) Science-fiction writer Arthur C. Clarke: Voice Across the Sea, by Arthur C. Clarke (HarperCollins, 1975). 3 BEAT THE MARKET On a typical day of desert sun: Much like the blackjack chapter, many details of this chapter derive from interviews with Thorp, Fortune’s Formula, and Thorp’s second book, Beat the Market: A Scientific Stock Market System.

A Man for All Markets
by Edward O. Thorp
Published 15 Nov 2016

Copyright © 2017 by Edward O. Thorp All rights reserved. Published in the United States by Random House, an imprint and division of Penguin Random House LLC, New York. RANDOM HOUSE and the HOUSE colophon are registered trademarks of Penguin Random House LLC. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Names: Thorp, Edward O., author. Title: A man for all markets : from Las Vegas to Wall Street, how I beat the dealer and the market / Edward O. Thorp. Description: New York : Random House, [2017] | Includes index. Identifiers: LCCN 2016026545| ISBN 9781400067961 | ebook ISBN 9780812998740 Subjects: LCSH: Thorp, Edward O. | Investment advisors—United States—Biography. | Mathematicians—United States—Biography. | Gambling systems. | Investments. | Finance—Mathematical models.

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considerable controversy In addition to Poundstone’s history, mathematically trained readers can study some of the burgeoning modern developments in The Kelly Capital Growth Investment Criterion: Theory and Practice, editors Leonard C. MacLean, Edward O. Thorp, and William T. Ziemba, World Scientific, 2010. As he told The Wall Street Journal “Old Pros Size Up the Game,” by Scott Patterson, Wall Street Journal, March 22, 2008, page A9. Gross left PIMCO in 2014 and went to Janus to manage money. out in Wilmott magazine See “Understanding the Kelly Criterion,” by Edward O. Thorp, Wilmott, May 2008, pp. 57–59, and http://undergroundvalue.blogspot.com/​2008/​02/​notes-from-buffett-meeting-2152008_23.html. Computer simulations The simulations were done by mathematician Art Quaife.

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“The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market.” Handbook of Asset and Liability Management, Volume 1, Zenios, Stavros Andrea, and W. T. Ziemba, Editors. Amsterdam: Elsevier, 2006. Wong, Stanford. Professional Blackjack. La Jolla, CA: Pi Yee, 1994. BY EDWARD O. THORP A Man for All Markets Beat the Dealer Beat the Market Elementary Probability The Mathematics of Gambling ABOUT THE AUTHOR EDWARD O. THORP is the author of the bestseller Beat the Dealer: A Winning Strategy for the Game of Twenty-One (Random House 1962, 1966). It presented the first scientific system ever devised for a major casino gambling game and revolutionized the game of blackjack.

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
by Justin Fox
Published 29 May 2009

The phrase “self-fulfilling prophecy” was coined by sociologist Robert K. Merton.19 Merton also wrote about the vagaries of scientific credit and naming, mainly the fact that the right people often don’t get credit for major discoveries. There was some of that at work with the options formula. Edward O. Thorp, a math professor at the University of California–Irvine, had figured out the mechanics of it back in 1968. But he hadn’t devised a proof of the formula—other than that when he used it, he made money. Plus, he kept it to himself. In scientific terms he didn’t really deserve credit. Some have since argued that Bachelier’s was the true breakthrough on options pricing, and everything else mere embroidery on his theme.

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One of them, neurologist Ralph Waldo Gerard, was dean of the graduate school at the brand-new Irvine campus of the University of California. UC–Irvine was also home to a math professor interested in money management, thereby entwining his remarkable story with that of Buffett. In 1959, as an instructor at MIT, Edward O. Thorp had figured out how to beat the house at blackjack by counting cards. Crucial to his success was an IBM 704 in an MIT basement, which he used to analyze the changing probabilities as cards were removed from the deck. After presenting his findings at the January 1961 meeting of the American Mathematical Association, Thorp was profiled in several newspapers and swamped with mail from would-be gambling partners.

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Author of sharp critiques of efficient market finance in the 1980s and early 1990s who went on to be Secretary of Treasury in the Clinton administration and top economic adviser to President Barack Obama. Richard Thaler University of Rochester product who became Daniel Kahneman and Amos Tversky’s first student among economists. Went on to be a founding father of behavioral economics and an influential professor at Chicago’s Business School. Edward Thorp Math professor at UC–Irvine who, after figuring out how to beat the house at blackjack and writing a bestselling book about it, figured out the formula for pricing options before Fischer Black and Myron Scholes did and became a pioneer of computer driven, black-box hedge fund management. Jack Treynor As a consultant at Arthur D.

The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall
Published 2 Jan 2013

The firm hobbled along for another year, but the legal proceedings had ruined its reputation. In 1989, Princeton-Newport Partners closed. Over the course of twenty years, it had average returns of 19% (over 15% after fees) — an unprecedented performance. After Princeton-Newport closed, Thorp took some time off before regrouping to form Edward O. Thorp Associates, his own money management firm. Though he has long since given up managing other people’s money professionally, he still runs the fund today using his own capital. Meanwhile, hundreds of quant hedge funds have opened (and closed), trying to reproduce Princeton-Newport’s success. As the Wall Street Journal put it in 1974, Thorp had ushered in a “switch in money management” to quantitative, computer-driven methods.

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Try a Little Luck and a Firm Full of Ph.D.s.” Institutional Investor, November 1. Mackay, Charles. 1841. Extraordinary Popular Delusions and the Madness of Crowds. London: Richard Bentley. MacKenzie, Donald. 2006. An Engine, Not a Camera. Cambridge, MA: MIT Press. MacLean, Leonard C., Edward O. Thorp, and William T. Ziemba. 2011. The Kelly Capital Growth Investment Criterion. Singapore: World Scientific Publishing. Maddy, Penelope. 1997. Naturalism in Mathematics. New York: Oxford University Press. — — — . 2001. “Naturalism: Friends and Foes.” Philosophical Perspectives 15: 37–67

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I am also grateful to the people who agreed to be interviewed for the book, and who helped me make contact with the book’s subjects and their families. Thank you to Doyne Farmer, Pia Malaney, Sally McClenaghan, Joe Murphy, Holly Osborne, Peter Osborne, Lee Smolin, Didier Sornette, Clay Struve, Ed Thorp, and Eric Weinstein. Pia Malaney, Holly Osborne, Melita Osborne, Peter Osborne, Didier Sornette, Ed Thorp, and Eric Weinstein deserve special thanks for reading early drafts of the chapters to which they contributed and offering useful comments for accuracy. Some friends and colleagues, in addition to providing valuable insights along the way, also read earlier drafts and offered comments.

A Mind at Play: How Claude Shannon Invented the Information Age
by Jimmy Soni and Rob Goodman
Published 17 Jul 2017

“LIVERSIDGE: When The Mathematical Theory”: “Profile of Claude Shannon—Interview by Anthony Liversidge,” in Claude Elwood Shannon: Collected Papers, xxvii. “the occasional liberties taken”: Shannon, “Mathematical Theory,” 50. “When Shannon’s paper appeared”: Solomon W. Golomb, “Claude Elwood Shannon,” Notices of the AMS 49, no. 1 (2001): 9. “Distinguished and accomplished as Doob was”: Edward O. Thorp, personal communication, April 8, 2017. “It turned out that everything he claimed”: Sergio Verdú, “Fireside Chat on the Life of Claude Shannon,” www.youtube.com/watch?v=YEt9P2kp9BE. Chapter 19: Wiener “the American John Von Neumann”: Nasar, A Beautiful Mind, 135. “I had full liberty . . .

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“I even did some work”: “Profile of Claude Shannon—Interview by Anthony Liversidge,” in Claude Elwood Shannon: Collected Papers, xxiv–xxv. “used common sense”: Peggy Shannon, interviewed by the authors, December 9, 2015. “I make my money”: Price, “Claude E. Shannon: An Interview.” “Inside information”: Poundstone, Fortune’s Formula, 21. Chapter 28: A Gadgeteer’s Paradise “The secretary warned me,” etc.: Edward O. Thorp, “The Invention of the First Wearable Computer,” Proceedings of the 2nd IEEE International Symposium on Wearable Computers, October 1998, 4–8. “The division of labor”: Thorp, personal communication, March 24, 2017. Chapter 29: Peculiar Motions “Do you mind”: Lewbel, “A Personal Tribute to Claude Shannon.”

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Johnson presented Claude Shannon with the National Medal of Science in honor of his “brilliant contributions to the mathematical theories of communications and information processing.” 37 Shannon’s early MIT lectures on information theory attracted packed houses, but none drew a bigger crowd than his talk on the stock market, which he delivered to an overflowing crowd in the university’s largest lecture hall. 38 In Massachusetts, Professor Shannon grew a beard and took up jogging. He also fully indulged his tinkering habit: many of his best-known creations were devised in an extensive home workshop. 39 What was arguably world’s first wearable computer was developed by Shannon and Edward Thorp to calculate roulette odds. After several successful test runs at Las Vegas casinos, they abandoned the project out of fear of provoking a run-in with the Mafia. 40 Assembled from Shannon’s erector set and modeled on W. C. Fields, this robot could bounce-juggle three balls. The balls rebounded off a tom-tom drum, and the robot moved its paddle arms in a rocking motion, “each side making a catch when it rocks down and a toss when it rocks up.” 41 Shannon was both a skilled juggler himself and the author of the first serious paper on the mathematics of juggling.

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution
by Gregory Zuckerman
Published 5 Nov 2019

Douglas Bauer, “Prince of the Pit,” New York Times, April 25, 1976, https://www.nytimes.com/1976/04/25/archives/prince-of-the-pit-richard-dennis-knows-how-to-keep-his-head-at-the.html. 6. Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance (Hoboken, NJ: John Wiley & Sons, 2004). 7. Edward O. Thorp, A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market (New York: Random House, 2017). 8. Scott Patterson, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (New York: Crown Business, 2010). 9. Patterson, The Quants. 10.

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Simons and his colleagues weren’t alone in suggesting that stock prices are set by a complex process with many inputs, including some that are hard or even impossible to pin down and not necessarily related to traditional, fundamental factors. Around that time, Harry Markowitz, the University of Chicago Nobel laureate and father of modern portfolio theory, was searching for anomalies in securities prices, as was mathematician Edward Thorp. Thorp would attempt an early form of computerized trading, gaining a head start on Simons. (Stay tuned for more, dear reader.) Simons was part of this vanguard. He and his colleagues were arguing that it wasn’t important to understand all the underlying levers of the market’s machine, but to find a mathematical system that matched them well enough to generate consistent profits, a view that would inform Simons’s approach to trading years later.

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Ignoring the trading model, Ax had presciently purchased Eurodollar futures, which soared as stocks plummeted, helping Axcom offset other losses. Word was beginning to get out that Simons had math wizards attempting a new strategy, and a few individuals showed interest in investing in Axcom, including Edward Thorp, the pioneering quantitative trader. Thorp made an appointment to meet Simons in New York but canceled it after doing some due diligence. It wasn’t Simons’s strategies that most concerned him. “I learned Simons was a chain-smoker and going to their offices was like walking into a giant ashtray,” said Thorp, who had moved to Newport Beach, California.

The Dhandho Investor: The Low-Risk Value Method to High Returns
by Mohnish Pabrai
Published 17 May 2009

Chapter 10 1 William Poundstone, Fortune’s Formula: The Untold Story of the Unscientific Betting System (New York: Hill and Wang, 2005). 2 Michael Mauboussin, “Mauboussin on Strategy: Size Matters,” Legg Mason Capital Management, February 1, 2006, www.leggmason.com/funds/knowledge/mauboussin/Mauboussin_on_Strategy_020106.pdf. 3 Peter D. Kaufman, ed., Poor Charlie’s Almanack (Virginia Beach, VA: Donning Company Publishers, 2005), p. 184. 4 Edward O. Thorp, Beat the Dealer: A Winning Strategy for the Game of Twenty-One (New York: Vintage, 1966). 5 See note 4. 6 See note 1. 7 Chris Leither, Ludvig von Mises, Meet Benjamin Graham: Value Investing from an Austrian Point of View, Austrian Economics and Financial Markets Conference, Venetian Hotel Resort Casino, Las Vegas, NV, February 18-19, 2005; posted on the web at http://mises.org/journals/scholar/Leithner.pdf (accessed November 18, 2006). 8 Warren Buffett, Letters to Partners of the Buffett Partnerships, 1956-1970, 1963, 1964 letters. 9 Roger E.

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For a detailed treatise on how to calculate the Kelly bet size for such bets, go to www.cisiova.com/betsize.asp. This web site not only gives the general case Kelly Formula, but the author has generously programmed the formula for use by anyone at no charge. The intersted reader may also wish to read Edward Thorp’s paper, “The Kelly Criterion in Blackjack, Sports Betting and the Stock Market.” For the first example, the answer is 89.4 percent of your $10,000 bankroll or $8,940. Papa Patel had likely never heard of the Kelly Formula. In Chapter 1, we noted that when Papa Patel invested $5,000 in his first motel, he pretty much bet it all on this investment.

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They are always fixating on trying to figure out when the odds are with them and raising their bets accordingly. As blackjack is played today in casinos, the overall odds are soundly with the house and playing blackjack at a casino is a losing proposition. (I have to admit that this hasn’t stopped me yet.) But it wasn’t always a losing proposition. In the 1960s, an MIT math professor, Ed Thorp, used MIT’s computers to run a variety of calculations and came up with optimized blackjack play. Thorp named the optimal play of cards Basic Strategy. He wrote the best-selling book, Beat the Dealer.4 It is, even today, regarded as a classic work, and blackjack players the world over rely on Basic Strategy to optimize their card play.

Beat the Market
by Edward Thorp
Published 15 Oct 1967

Other books by EDWARD O. THORP Elementary Probability Beat the Dealer Other books by SHEEN T. KASSOUF Evaluation of Convertible Securities A Theory and an Econometric Model for Common Stock Purchase Warrants BEAT THE MARKET A scientific Stock Market System Random House New York BEAT THE MARKET A Scientific Stock Market System Edward O. Thorp, Ph.D. Professor of Mathematics University of California at Irvine Sheen T. Kassouf, Ph.D. Assistant Professor of Economics University of California at Irvine 987 © Copyright, 1967, by E. O. Thorp and S. T. Kassouf All rights reserved under International and Pan-American Copyright Conventions.

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Service of Italy, 101 United Industrial, 29, 72-73 United States Finance Corp., 156 Univac, 65-66, 68 Universal American, 29, 69, 72-73 76, 79, 86-88, 105, 119, 132, 196 Universal American 1962 warrant, actual profits in, 93fn potential hedge investment in, 197 short sales never banned, 139fn Universal Pictures warrants, 18 University of California, Irvine, 49 University of Chicago, Center for Research in Security Prices, 9 Up-tick, 92 defined, 36 Uris Building, 29 Volatile price movements, 134-137 Volatility, 42, 118 compared, 119 defined, 117 estimated, 118-119 Walgreen Co., 101 Wall Street Journal, 26, 53, 71, 104, 109, 128, 162, 166 Warrant axis, 21 Warrant hedge, 43fn Warrant prices, effect of common on, 18-22 effect of short position on, 129 prediction of, 201, 204 sources of, 107fn Warrant terms, sources for, 107fn Warrants, 15 adjusted, 24-26 attached to bond, 98 best, 77, 79 Canadian, 103, 106, 107, 200-203 choosing warrant situations, 88-89 definition, 15 effect of dilution, 110-111 effect of dividend, 110-111 effect of past price history, 111 exercise price, 16 expiration date, 16 extension of conversion privilege, 137-138 gain from short sales, 37 latent, 145 not traded on NYSE, 71 over-the-counter, 103, 106-107, 201 perpetual, 16 premium, 28 profits from shorting, 37 regional, 103 short selling, 36-39 tables of, 29, 202-203 tax advantage in issuing, 98 terms of, 72 why issued, 16 Warrant-stock diagram, applied, 73-77 construction of, 18-22 “corner,” 151 explained, 18ff zero-profit lines in, 47-49 Western Decalta, 203 Weston (George) Ltd., 107 Where Are the Customers’ Yachts?, 161 White Oil Company, 99 Writer, option, 164 definition, 162 Yield, current, 144 to maturity, 144 Xerox 4s of ‘84, 156-158 Zero-profit line, 80 explained, 47 how to draw, 48, 81 with reverse hedge, 124 Yearly range, 119 ABOUT THE AUTHORS EDWARD O. THORP is the author of the best-seller Beat the Dealer: A Winning Strategy for the Game of TwentyOne, published by Random House in 1962 and in revised form in 1966. It presented the first scientific winning system ever devised for a major casino gambling game. He has also written Elementary Probability (1966) and numerous mathematical papers on probability, game theory, and functional analysis.

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Library of Congress Catalog Card Number: 67:22624 Manufactured in the United States of America Designed by Betty Anderson Contents INTRODUCTION 3 Chapter 1 A SYSTEM IS BORN 7 First venture into the market. The market calls: boardrooms and chartists. The “circus”. Fundamentals: the “better” they are, the faster they fall. Textron and Molybdenum. The moment of discovery. Steady profits in bust and boom. 2 WARRANTS: OPTIONS ON THE FUTURE 15 Rediscovery of the system: Ed Thorp under a tree. What is a warrant? Get rich quick? The warrant-stock diagram. The two basic rules relating warrant prices to stock prices. Adjusted warrants and adjusted exercise price. Reading the financial pages. Checking the two rules. The warrant-stock law: predictability in the stock market. 3 SHORT SELLING: PROFITS IN BAD TIMES 33 Short selling.

Red-Blooded Risk: The Secret History of Wall Street
by Aaron Brown and Eric Kim
Published 10 Oct 2011

Brandon Adams, Gustavo Bamberger, Bill Benter, John Bogle, Rick Bookstaber, Reuven Brenner, Eugene Christiansen, Emanuel Derman, Art Duquette, Dylan Evans, Doyne Farmer, Justin Fox, Kenneth French, Lisa Goldberg, James Grosjean, Ian Hacking, Michael Heneberry, Carey Hobbs, Craig Howe, James McManus, Michael Maubossin, Nick Maughan, Perry Mehrling, Robert Merton, Joe Nocera, John O’Brien, Deborah Pastor, Scott Patterson, William Poundstone, Kevin Rosema, Myron Scholes, James Stoner, Nassim Taleb, Edward Thorp, Whitney Tilson, James Ward, Paul Wilmott, and Bruce Zastera were particularly helpful. The title comes from my daughter, Aviva Pastor. Tiffany Charbonier, Bill Falloon, Stacey Fischkelta, Meg Freeborn, Sharon Polese, and other folks at John Wiley & Sons provided essential feedback and support.

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The second reason to discuss exponentials goes back to the 1956 discovery by physicist John Kelly that exponentials trump risk. If you can organize your risk taking to get the optimal level of exponential growth, you end up better off than you can possibly be using any other strategy. Mathematician and hedge fund innovator Edward Thorp named the strategy “fortune’s formula.” In a sense you conquer risk since your outcome is guaranteed to be better than that of someone who avoids risk. It’s not risk if you can’t lose. Kelly’s result was theoretical, and we do not know how to conquer risk completely. But his work has led to sophisticated practical techniques for harnessing the power of exponentials to exploit risk.

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Other rocket scientists had been floor traders or other kinds of risk takers. What we had in common were quantitative training, a similar view of the world, similar aspirations, and at least several years of experience supporting ourselves with independent risk-taking activities. We also had in common a few books, first among which were Edward Thorp’s Beat the Dealer (Random House, 1962) and Beat the Market (Random House, 1967), the latter written with Sheen Kassouf. Ed was the mathematics professor who analyzed and popularized blackjack card counting, and also beat the house at other casino games. In the mid-1960s he turned to investing and invented or perfected an extraordinary number of what are now the standard hedge fund strategies.

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling
by Adam Kucharski
Published 23 Feb 2016

(Source: Kahn, “Legendary Blackjack Analysts Alive.”) 37It was meant to be a relaxing holiday: Thorp, Edward. Beat the Dealer (New York: Random House, 1962). 38Thorp gradually turned the research: Kahn, “Legendary Blackjack Analysts Alive.” 38He saw it more as an academic obligation: Towle, Margaret. “Interview with Edward O. Thorp.” Journal of Investment Consulting 12, no. 1 (2011): 5–14. 39“It showed that nothing was invulnerable”: Author interview with Bill Benter, July 2013. 39Switching his university campus in Cleveland: Yafa, Stephen. “In the Cards.” The Rotarian, November 2011. 39The decision was to prove extremely lucrative: Ibid. 39his firm was commissioned by the Australian government: Dougherty, Tim.

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As a result, gamblers can—in theory—avoid falling into Poincaré’s second degree of ignorance by measuring the initial path of the roulette ball. They just need to work out what measurements to take. THE RITZ WASN’T THE first time a story of roulette-tracking technology emerged. Eight years after Hibbs and Walford had exploited that biased wheel in Reno, Edward Thorp sat in a common room at the University of California, Los Angeles, discussing get-rich-quick schemes with his fellow students. It was a glorious Sunday afternoon, and the group was debating how to beat roulette. When one of the others said that casino wheels were generally flawless, something clicked in Thorp’s mind.

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It wasn’t a particularly effective deterrent. After reading the sign, only one thought came to mind: card counting works. It was the late 1970s, and casinos had spent the previous decade or so clamping down on a tactic they saw as cheating. Much of the blame—or perhaps credit—for the casinos’ losses goes to Edward Thorp. In 1962, Thorp published Beat the Dealer, which described a winning strategy for blackjack. Although Thorp has been called the father of card counting, the idea for a perfect blackjack strategy was actually born in a military barracks. Ten years before Thorp released his book, Private Roger Baldwin had been playing cards with fellow soldiers at the Aberdeen Proving Ground in Maryland.

Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors
by Wesley R. Gray and Tobias E. Carlisle
Published 29 Nov 2012

Then we test the research to find the best metrics for uncovering value: the cheapest price, the highest quality, and those stocks signaling that they are likely to quickly close the gap between price and value. Finally, we combine those metrics into a single method for finding high-performance value investment opportunities. NOTES 1. Benjamin Graham and David Dodd, Security Analysis: The Classic 1934 Edition (McGraw-Hill, 1996). 2. Edward O. Thorp, “A Mathematician on Wall Street: Bridge with Buffett.” Wilmott Magazine, November 2005, pp. 34–36, www.wilmott.com/pdfs/110329_thorp.pdf. 3. Jonathan Davis, “Buffett on Bridge,” www.buffettcup.com/BuffettonBridge/tabid/69/language/en-GB/Default.aspx. 4. Ibid. 5. Thorp. 6. William Poundstone, Fortune's Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street (New York: Hill and Wang, 2005). 7.

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William Poundstone, Fortune's Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street (New York: Hill and Wang, 2005). 7. Scott Patterson, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (New York: Crown Business, 2010). 8. Poundstone, p. 148. 9. Poundstone, p. 320. 10. Warren Buffett, “Shareholder Letter,” Berkshire Hathaway, Inc. Annual Report, 1992. 11. Edward O. Thorp and Sheen T. Kassouf, Beat the Market: A Scientific Stock Market System (Random House, 1967). 12. Warren Buffett, “Shareholder Letter,” Berkshire Hathaway, Inc. Annual Report, 1987. 13. Thorp and Kassouf, 1967. 14. Thorp, 2005. 15. Warren Buffett, “Shareholder Letter,” Berkshire Hathaway, Inc.

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We study the best way to combine the research we've considered into a cohesive strategy, and then back-test the resulting quantitative value model. CHAPTER 1 The Paradox of Dumb Money “As they say in poker, ‘If you've been in the game 30 minutes and you don't know who the patsy is, you're the patsy.'” —Warren Buffett (1987) In the summer of 1968, Ed Thorp, a young math professor at the University of California, Irvine (UCI), and author of Beat the Market: A Scientific Stock Market System (1967), accepted an invitation to spend the afternoon playing bridge with Warren Buffett, the not-yet-famous “value” investor. Ralph Waldo Gerard hosted the game.

Skin in the Game: Hidden Asymmetries in Daily Life
by Nassim Nicholas Taleb
Published 20 Feb 2018

IRE Transactions on Information Theory 2(3): 185–189. Lamont, Michèle, 2009. The Dignity of Working Men: Morality and the Boundaries of Race, Class, and Immigration. Cambridge, Mass.: Harvard University Press. Lazaridis, Iosif, et al., 2017. “Genetic Origins of the Minoans and Mycenaeans.” Nature 548, no. 7666: 214–218. MacLean, Leonard C., Edward O. Thorp, and William T. Ziemba, 2011. The Kelly Capital Growth Investment Criterion: Theory and Practice, vol. 3. World Scientific. Mandelbrot, Benoit, 1982. The Fractal Geometry of Nature. Freeman and Co. ———, 1997. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. New York: Springer-Verlag.

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For, in the quarter millennia since an initial formulation of decision making under uncertainty by the mathematician Jacob Bernoulli, one that has since become standard, almost all people involved in the field have made the severe mistake of missing the effect of the difference between ensemble and time.fn1 Everyone? Not quite: every economist maybe, but not everyone: the applied mathematicians Claude Shannon and Ed Thorp, and the physicist J. L. Kelly of the Kelly Criterion got it right. They also got it in a very simple way. The father of insurance mathematics, the Swedish applied mathematician Harald Cramér, also got the point. And, more than two decades ago, practitioners such as Mark Spitznagel and myself built our entire business careers around it.

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Unless one is a genius, that is, has the clarity of mind to see through the mud, or has a sufficiently profound command of probability theory to cut through the nonsense. Now, certifiably, Murray Gell-Mann is a genius (and, likely, Peters). Gell-Mann discovered the subatomic particles he himself called quarks (which got him the Nobel). Peters said that when he presented the idea to Gell-Mann, “he got it instantly.” Claude Shannon, Ed Thorp, J. L. Kelly, and Harald Cramér are, no doubt, geniuses—I can personally vouch for Thorp, who has an unmistakable clarity of mind combined with a depth of thinking that juts out in conversation. These people could get it without skin in the game. But economists, psychologists, and decision theorists have no geniuses among them (unless one counts the polymath Herb Simon, who did some psychology on the side), and odds are they never will.

Wonderland: How Play Made the Modern World
by Steven Johnson
Published 15 Nov 2016

,” Creative Computing, August 1981, www.wheels.org/spacewar/creative/SpacewarOrigin.html. “The game of Spacewar!”: Stewart Brand, “Spacewar!,” Rolling Stone, December 7, 1972, www.wheels.org/spacewar/stone/rolling_stone.html. “Using data from the American Ephemeris”: Graetz, “The Origin of Spacewar!” “mechanically well made”: Edward O. Thorp, “Wearable Computers,” Digest of Papers, Second International Symposium on. 1998. “It had perhaps a hundred thousand”: Ibid. “As we worked and during”: Ibid. “The computer’s techniques”: Ken Jennings, “My Puny Human Brain,” Slate, Newsweek Interactive Co. LLC, February 2012. Chapter 6.

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Seconds later, he was gone. The mysterious stranger at the roulette table was not, contrary to appearances, a criminal or a mafioso; he was not even, technically speaking, cheating at the game—although years later his secret technique would be banned by the casinos. He was, instead, a computer scientist from MIT named Edward Thorp, who had come to Vegas not to break the bank but rather to test a brand-new device: the very first wearable computer ever designed. Thorp had an accomplice at the roulette table, standing unobserved at the other end, pretending not to know his partner. He would have been unrecognizable to the average casino patron, but he was in fact one of the most important minds of the postwar era: Claude Shannon, the father of information theory and one of the key participants in the invention of digital computers.

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“high-rent” product development, 220 Minecraft, 201 networks of the early 1990s, 170 PDP-1, 215–16 for purposes of non-scientific pursuits, 219–20 Claude Shannon, 221–26, 223 software, development of, 215–19 Spacewar! 216–20, 218 “Spacewar: Fanatic Life and Symbolic Death Among the Computer Bums,” 219–20 Edward Thorp, 221–27 Turing Test, 227 Type 20 Precision CRT, 215–16, 218 Watson, 228–30 wearable computers, 221, 225–26 Conflagration of Moscow, The, 164–66 Conroy, David, 241 Constantine the African, 134 Cooperstown, New York, 199–200 Copland, Aaron, 97 Cortés, Hernan, 213 cotton appealing texture of, 26–28 British East India Company, 28 “Calico Madams,” 28 chintz and calico, vivid colors of, 26–27, 27 described by John Mandeville, 26 economic fears regarding the import of, 28–29 European desire for, 29–31 importing from India, 26, 28 inventions to aid in the production of fabric, 29, 30 slavery to produce, 34–36 Cox, James, 14 criminology physiological causes vs. environmental causes, 47–48 Cristofori, Bartolomeo, 88 cultural diversity in modern times, 274–76 Darrow, Charles, 198–99 Darwin, Charles, 269–70 Das Kapital (Marx), 153–54 De Coitu (Constantine the African), 134 Defoe, Daniel, 24, 28 Dell, Michael, 216 demand for cotton fabrics, 29–31, 34–36 “desire of Novelties,” 30–31 for experiencing the world through exotic spices, 137–38 for new experiences and surprises, 61 for rubber, 214 democratizing force of fashion, 38–40 department stores as alternatives to chapels and cathedrals, 43–44 Au Bonheur des Dames (Zola), 43–44 Le Bon Marché, 41–46, 45 commercial profitability of wandering shoppers, 41–44 credit, extending, 44 “department-store disease,” 47 haggling, elimination of, 44 influence of Aristide Boucicaut, 40, 41–42, 48–49 origins of, 41 sensory overload and disorientation, 41–42 shoplifting, 46–49 De Smet, Pieter, 137 Devil’s Milk, The (Tully), 214 Devlin, Keith, 208–209 Diamond, Jared, 141, 143 dice astragali, 205–206, 208–209 and probability, 206–207, 209 to speed up the game of chess, 203 standardized design of, 209 Dickens, Charles, 163 Digital Revolution artistic origins of the, 83 Spacewar!

The Predators' Ball: The Inside Story of Drexel Burnham and the Rise of the JunkBond Raiders
by Connie Bruck
Published 1 Jun 1989

Finally, from the line of questioning at this deposition, it appears that Columbia Savings, First Executive, and the Princeton-Newport Limited Partnership (controlled by James Regan and Edward Thorp, Milken’s partners in Belvedere Securities, the Chicago brokerage firm in which he had the majority interest) may have done well, along with Milken, on the Caesars World exchange. Milken was asked whether he had had any conversation about the Caesars World bonds with Tom Spiegel, Fred Carr, James Regan or Edward Thorp between the time of his Caesars meeting and the announcement of the exchange offer about two weeks later. Milken testified that he had not.

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Belvedere was somewhat unusual among Milken’s investment partnerships in that it had people participating in it who were not members of Drexel. At the outset, Belvedere Securities had among its general partners two money managers whom Milken had done business with since the early seventies, James Regan and Edward Thorp. Regan and Thorp controlled a number of entities, including an arbitrage fund, Princeton-Newport Partners, and Oakley-Sutton Management. Three other general partners of Belvedere had all been previously associated with a Regan-Thorp group. The sixth general partner, which contributed 75–100 percent of the firm’s capital, was Milow Corporation (seemingly standing for Michael-Lowell).

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If true, this would have given Atlantic Capital added motivations (beyond the high yield of the bonds) for being probably the single largest subscriber to the junk bonds in the 1985 takeovers; it would have had a powerful interest in the deals’ going through, since it was a shareholder in the target company, and it would also be repaying the favors of Drexel’s tips. As the investigation continued, the government would become interested in another satellite group with which Milken had done business, the Regan-Thorp entities. James Regan and Edward Thorp and their associates had been Milken’s partners at least since the Treasuries-stripping days of Dorchester Government Securities and Belvedere Securities, and they had been a focus of SEC interest in the 1985 investigation into the trading of Caesars World securities. In December 1987, federal agents would raid and confiscate more than sixty boxes of documents and business records going back to January 1984 from three firms which operated from the same address in Princeton, New Jersey—Princeton-Newport Arbitrage Partners, Englewood Partners and the Oakley-Sutton Management Corporation.

Market Wizards: Interviews With Top Traders
by Jack D. Schwager
Published 7 Feb 2012

The term is often used to describe losses resulting from the application of a trend-following system to a choppy or trendless market. In such markets, trend-following systems will tend to generate buy signals just before downside price reversals and sell signals just before upside price reversals. EXCERPT Edward Thorp The Innovator Read an excerpt from Jack D. Schwager’s latest book in the Market Wizards series . . . Edward O. Thorp, a PhD mathematician and near PhD physicist, came to the markets via gambling, but not gambling in the conventional sense. Normally, casino games of chance have a negative edge for the player, and the longer one plays, the greater the chance of financial ruin.

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.: Buying Value and Selling Hysteria Mark Weinstein: High-Percentage Trader Part IV: The View from the Floor Brian Gelber: Broker Turned Trader Tom Baldwin: The Fearless Pit Trader Tony Saliba: “One-Lot” Triumphs Part V: The Psychology of Trading Dr. Van K. Tharp: The Psychology of Trading The Trade: A Personal Experience Postscript: Dreams and Trading Final Word What I Believe 22 Years Later Appendix 1: Program Trading and Portfolio Insurance Appendix 2: Options—Understanding the Basics Glossary Excerpt: Edward Thorp Additional Praise for Market Wizards “Market Wizards is one of the most fascinating books ever written about Wall Street. A few of the ‘Wizards’ are my friends—and Jack Schwager has nailed their modus operandi on the head.” —Martin W. Zweig, Ph.D., Editor, The Zweig Forecast “It is difficult enough to develop a method that works.

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I had asked you about how you made the transition from casino games to markets. After my successful casino games—I also developed a system for beating Wheel of Fortune—I got to thinking about games in general and thought, the biggest game in the world is Wall Street. Why don’t I look at and learn about that? Visit www.wiley.com/go/jackschwager to learn more about Edward Thorp, Jamie Mai, Michael Platt, Joel Greenblatt, Colm O’Shea, and others, and to find out more about Jack Schwager’s latest work. 1 Thorp recalls the specifics of the stock parking charge as follows: I was told that a trader at Drexel (Bruce Newberg, one of those charged in the PNP case) had a $25 million capital line from Drexel, which he fully used.

The Missing Billionaires: A Guide to Better Financial Decisions
by Victor Haghani and James White
Published 27 Aug 2023

We hope that by showing you the value of an optimal approach to this experiment, you'll be better equipped to follow a similar approach to risk‐taking with your life‐savings over the long term, where it really matters. Connecting the Dots This [coin‐flip experiment] is a great experiment for many reasons. It ought to become part of the basic education of anyone interested in finance or gambling. —Edward O. Thorp While we did expect to observe some poorly conceived betting strategies from our subjects, we were surprised by the fact that so many players went bust betting on such a favorable opportunity. Before this experiment, we did not appreciate just how ill‐equipped so many people are to appreciate or take advantage of a simple advantageous opportunity in the presence of uncertainty.

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The prolific writer and financial impresario Frank Fabozzi was the first to publish our work in his anthologies and in the academic journals for which he has served as editor. Our understanding has been shaped by many deep thinkers and writers in finance who have generously shared their insights through academic articles, lectures, and books, including John Campbell, Robert Shiller, John Cochrane, Phil Tetlock, Ed Thorp, Cliff Asness, and Howard Marks. We thank our coauthors of previous articles, which provide the foundation of several chapters of the book, including Rich Dewey, Vlad Ragulin, Larry Hilibrand, Jeff Rosenbluth, and Andy Morton. There are many people at Wiley who helped make this book a reality, and we thank them all, but in particular we must sing the praises of our publisher, Bill Falloon, whose wisdom, good nature, and patience are responsible for this book coming to life.

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For instance, gamblers proficient at card‐counting in casino six‐deck blackjack games have about a 51% chance of winning each hand when the deck evolves in their favor. Correct bet‐sizing is critical to success and has been written about extensively by a number of professional gamblers. One of the most well‐known and prolific of these is Ed Thorp, a mathematics professor, professional gambler, and hedge fund manager who in 1962 penned Beat the Dealer: A Winning Strategy for the Game of Twenty‐one. A good rule of thumb for people with a normal amount of risk‐aversion is that if you are offered a gamble that is independent from existing risks you bear, and the downside represents less than 0.1% of your wealth, you should accept it if it has a positive expected value, because the edge you need to accept such a gamble is so small.

More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded)
by Michael J. Mauboussin
Published 1 Jan 2006

Rogers is confusing frequency with how much money is made on average. 5 Brent Schlender, “The Bill and Warren Show,” Fortune, July 20, 1998. 6 Charlie Munger, “A Lesson on Elementary, Worldly Wisdom As It Relates to Investment Management and Business” Outstanding Investor Digest, May 5, 1995, 50. 7 Warren Buffett, speech given at the Berkshire Hathaway Annual Meeting, 1989. 8 Alfred Rappaport and Michael J. Mauboussin, Expectations Investing (Boston, Mass.: Harvard Business School Press, 2001), 105-8. 9 Steven Crist, “Crist on Value,” in Andrew Beyer et al., Bet with the Best: All New Strategies From America’s Leading Handicappers (New York: Daily Racing Form Press, 2001), 63-64. 10 Edward O. Thorp, Beat the Dealer (New York: Vintage Books, 1966), 56-57. 4. Sound Theory for the Attribute Weary 1 See Mitchel Resnick, Turtles, Termites, and Traffic Jams (Cambridge, Mass.: MIT Press, 1994), 50-52. Also see, Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities, and Software (New York: Scribner, 2001), 12-13. 2 Professor Burton Malkiel: “It’s like giving up a belief in Santa Claus.

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Or do you find horses you ‘like’ and hope for the best on price? Most honest players admit they follow the latter path.” Replace the word “handicapping” with “investing” and “horses” with “stocks,” and Crist could be talking about the stock market. Yet another domain where expected-value thinking is pertinent is blackjack, as Ed Thorp’s best-selling book, Beat the Dealer, shows. In blackjack, the payoffs are set, and the player’s principal task is to assess the probability of drawing a favorable hand. Thorp showed how to count cards in order to identify when the probabilities of a winning hand tilt in a player’s favor. When the odds favor the player, the ideal strategy is to increase the bet (effectively increasing the payout).

Alpha Trader
by Brent Donnelly
Published 11 May 2021

Also, math is fun. COUNTERINTUITIVE MATH FACTS Education has made all the difference for me. It builds software for your brain. Mathematics taught me to reason logically and understand numbers, tables, charts, and calculations. Even more valuable, I learned at an early age to teach myself. EDWARD O. THORP, A Man for All Markets One of the most fun parts of math is that even though it is 100% objective and rational, it can still surprise us and it can sometimes feel a little bit like magic. Part of acquiring a higher-level and rational understanding of math and probability is to simply understand that math, statistics, and probability are not always 100% intuitive.

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But overall, the multi-factor fundamental approach with a technical filter is a strong, logical approach to trading. CHAPTER 11 YOU FEELING LUCKY, PUNK? Data collection, risk management and variance Most of what I have learned from gambling is also true for investing. People mostly don’t understand risk, reward and uncertainty. Their investment results would be better if they did. EDWARD O. THORP, A Man for All Markets In this chapter, we will discuss risk management. If you are new to trading, this chapter will help you build and implement a robust risk management framework. If you are an experienced professional, I hope you will extract a few nuggets of wisdom and alternative viewpoints and use these observations to make incremental improvements to your current framework.

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New Canaan, Connecticut 2021 APPENDIX A FURTHER READING BOOKS Trading classics Market Wizards (series), Jack Schwager (1989) Reminiscences of a Stock Operator, Edwin Lefèvre (1923) Luck vs. skill, process vs. outcome The Success Equation, Michael Mauboussin (2012) Thinking in Bets, Annie Duke (2018) Be disciplined Willpower, Baumeister and Tierney (2012) The Science of Self-Discipline, Peter Hollins (2017) The Disciplined Trader, Mark Douglas (1990) Behavioral finance bibles Thinking, Fast and Slow, Daniel Kahneman (2011) Irrational Exuberance, Robert Shiller (2000) Get organized The Seven Habits of Highly Effective People, Stephen Covey (1988) The Checklist Manifesto, Atul Gawande (2009) The Power of Habit, Charles Duhigg (2012) Be self-aware The Power of Now, Eckhart Tolle (1997) Breath, James Nestor (2020) The Hour Between Dog and Wolf, John Coates (2012) Get quantitative Fortune’s Formula, William Poundstone (2005) Superforecasting, Dan Gardner and Philip Tetlock (2015) Fooled by Randomness, Nassim Taleb (2001) Fooled by Technical Analysis, Michael Harris (2015) A Man for All Markets, Edward Thorp (2017) Risk, Dan Gardner (2008) How to Lie with Statistics, Darrell Huff (1954) BLOGS, PODCASTS AND NEWSLETTERS Aspen Trading daily and intraday trading newsletter, Dave Floyd Epsilon Theory website, podcast and newsletter, Ben Hunt and Rusty Guynn Exante blog on Substack, Jens Nordvig et al.

Trend Following: How Great Traders Make Millions in Up or Down Markets
by Michael W. Covel
Published 19 Mar 2007

Commencement address given before the graduating class of 1989, University of Georgia, June 17, 1989. 5. Gibbons Burke, Managing Your Money. Active Trader (July 2000). 6. Mark Rzepczynski, Portfolio Diversification: Investors Just Don’t Seem to Have Enough. JWH Journal. 7. Jack Reerink, The Power of Leverage. Futures, Vol. 24, No. 4 (April 1995). 8. Edward O. Thorp, The Mathematics of Gambling. Hollywood, CA, 1984. 9. Larry Harris, Trading and Exchanges: Market Microstructure for Practitioners. New York: Oxford University Press, 2003. 10. Going Once, Going Twice. Discover (August 2002), 23. 11. Jim Little, Sol Waksman, A Perspective on Risk. Barclay Managed Futures Report. 12.

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I am also indebted to the following authors whose works continue to be treasure troves of information and insight: Morton Baratz, Peter Bernstein, Clayton Christensen, Jim Collins, Jay Forrester, Tom Friedman, Gerd Gigerenzer, Daniel Goleman, Stephen Jay Gould, Alan Greenberg, Larry Harris, Robert Koppel, Edwin Lefevere, Michael Lewis, Jesse Livermore, Roger Lowenstein, Acknowledgments Ludwig von Mises, Lois Peltz, Ayn Rand, Jack Schwager, Denise Shekerjian, Robert Shiller, Van Tharp, Edward Thorp, Peter Todd, Brenda Ueland, and Dickson Watts. This book could only have come to fruition with the editorial guidance of Jim Boyd at FT Press, as well as the able assistance and attention to detail of Dennis Higbee. I also want to thank Donna Cullen-Dolce, Lisa Iarkowski, Stephen Crane, John Pierce, and Lucy Petermark.

Dealers of Lightning
by Michael A. Hiltzik
Published 27 Apr 2000

The uncompromising give-and-take of Taylor’s ARPA contractor meetings lent itself to reproduction at PARC in the form of “Dealer.” The name derived from the book Beat the Dealer, by Edward O. Thorp, an MIT math professor who had developed a surefire system for winning at blackjack—“beating the dealer”—by counting the high-and low-value cards dealt out in hands. (This truly effective system would make the unassuming Ed Thorp the godfather of professional blackjack card-counting.) Taylor was not much of a blackjack buff. What interested him about Beat the Dealer was its compelling metaphor of a doughty individual fielding the challenge of a group of trained and determined adversaries.

Alex's Adventures in Numberland
by Alex Bellos
Published 3 Apr 2011

A coin flip is random because we don’t know how it will land, but flipped coins obey Newtonian laws of motion. If we knew exactly the speed and angle of the flip, the density of the air and any other relevant physical data, we would be able to calculate exactly the face on which it would land. In the mid 1950s a young mathematician named Ed Thorp began to ponder what set of information would be required to predict where a ball would land in roulette. Thorp was helped in his endeavour by Claude Shannon, his colleague at the Massachusetts Institute of Technology. He couldn’t have wished for a better co-conspirator. Shannon was a prolific inventor with a garage full of electronic and mechanical gadgets.

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In 1956 an article was published in an obscure statistics journal that claimed to have devised a playing strategy that gave the house an advantage of just 0.62 percent. After reading the article, Thorp learned the strategy and tested it during a vacation trip to Vegas. He discovered that he lost his money much slower than the other players. He decided he would begin to think deeply about blackjack, a decision that would change his life. Ed Thorp is now 75 but I suspect he doesn’t look that different from how he looked half a century ago. Slim, with a long neck and concise features, he has a clean-cut college-boy haircut, unpretentious glasses, and a calm, upright posture. After returning from Vegas, Thorp reread the journal article. ‘I saw right away, within a couple of minutes, how you could almost certainly beat this game by keeping track of the cards that were played,’ he remembered.

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He sold all his possessions, including his clothes, and in a Las Vegas casino bet the total amount – $135,300 – on red. Had he lost, he would have at least become a C-list TV celebrity, as the bet was being filmed for a TV reality show. But the ball landed on red 7, and he came home with $270,600. At blackjack, Ed Thorp was presented with a different issue. His card-counting system meant that he could tell at certain points during the game whether he had an advantage over the dealer. Thorp asked himself: what is the best betting strategy when the odds are in your favour? Imagine there is a bet where the chance of winning is 55 percent and the chance of losing 45 percent.

Reset: How to Restart Your Life and Get F.U. Money: The Unconventional Early Retirement Plan for Midlife Careerists Who Want to Be Happy
by David Sawyer
Published 17 Aug 2018

It’s risky and not what even investing geniuses such as Warren Buffett would tell you to do. 2. Don’t trust the experts Unless they’re gods like Ed Thorp. Empirical studies find that if you want to make money out of the stock market, do not listen to stock market analysts[341]. As Jim Collins writes in The Simple Path to Wealth: “what the media wants from these commentators is drama. Nobody is going to sit glued to their TV while some rational person talks about long-term investing[342].” Investor and author of Beat the Dealer, Ed Thorp, agrees: “Most stock-picking stories, advice and recommendations are completely worthless[343].” 3.

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Good if it goes up, good if it goes down It’s easy looking at the long-term when times are good. But what about when you’re mired in the daily 2% hits to your life savings that are commonplace when the market gets the jitters? I’ve spoken to scores of people and observed thousands putting these principles into practice, but it’s the thoughts of leaders such as Ed Thorp and Warren Buffett that keep me grounded. Said Thorp: “People say, ‘Gee, what if your Berkshire [Hathaway B, Warren Buffett’s investment vehicle] goes down?’ I say, ‘Oh, that’s good because now I can buy more’” They say, ‘But what if it goes up?’ I say, ‘Well, that’s good too because I feel good because I feel suddenly richer.’

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[341] do not listen to stock market analysts: “Don’t listen to analysts if you want to make money on the stock market...” 10 Jan. 2018, toreset.me/341. [342] “while some rational person talks about long-term investing”: “The Simple Path to Wealth: Your road map to financial... – Amazon UK.” toreset.me/342, p. 78. [343] “completely worthless”: “A Dozen Lessons on Investing from Ed Thorp – 25iq.” 22 Jul. 2017, toreset.me/343. [344] “the magic of compound interest”: “Tony Robbins on stock market corrections: Get used to them...” 8 Feb. 2018, toreset.me/344a. And if you want to buy Tony Robbins’s handy book MONEY Master the Game: 7 Simple Steps to Financial Freedom you can find it here: toreset.me/344b

Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took Vegas for Millions
by Ben Mezrich
Published 2 Dec 2002

But he knew about BS from a television special he had seen on cable: a framework of proper plays based on what the dealer was showing, developed first—in a flawed but thorough form—by four army engineers who played tens of thousands of hands and published their results in the September 1956 edition of the Journal of the American Statistical Association. BS was then thoroughly reworked in the early sixties by a UCAL and visiting MIT math professor named Edward Thorp, then tweaked numerous times over the years by experts with access to IBM computers. Kevin had never bothered to study basic strategy because he gambled only occasionally—and he wasn’t really sure how much of a difference it made, anyway. Was skill really that much of a factor in blackjack? Didn’t it all boil down to a matter of luck? 

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“I’ve done a bit of reading on the subject.” “Good, good. So you must have heard of the hi-lo method of counting, right?” Kevin nodded again. His memory wasn’t photographic like some other MIT kids he knew, but he retained things fairly well. He knew that the hi-lo method dated back to 1962 and the publication of Edward Thorp’s groundbreaking best-seller Beat the Dealer. In the book, Thorp outlined a simple counting method that allowed players to keep rough track of the number of high cards left in an unplayed shoe. Instead of counting individual cards, players simply kept track of a single number, the running count.

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Again, blackjack is the only popular casino game where what you see affects what you are going to see. This fact, and this fact alone, makes blackjack beatable. It’s just a matter of figuring out how best to take advantage of the game’s continuous probability. To this end, in 1963, MIT professor Edward Thorp did simulations on the relative effect that each card has on the player’s chances of winning. What he found was that when many low cards remained in the deck (sevens and below), the odds were in the dealer’s favor. Contrarily, when there were many high cards remaining (nines, tens, face cards, and aces), the odds shifted to the player.

The Joys of Compounding: The Passionate Pursuit of Lifelong Learning, Revised and Updated
by Gautam Baid
Published 1 Jun 2020

Yet we live in a world that starkly resembles option number 3. Welcome to the World of Extremistan Extreme events are where ruin is found. It’s also true that these extreme changes in securities prices may be much greater than you would expect from the Gaussian or normal statistics commonly used. —Edward Thorp The devil is in the residuals, as all of us have discovered to our sorrow. —Howard Marks According to Nassim Nicholas Taleb, the world could be divided into the safe and comfortable Mediocristan and the unsafe and seemingly improbable Extremistan. In Mediocristan, nothing is scalable; everything is constrained by boundary conditions, time, the limits of biological variation, and the limits of hourly compensation.

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They bet big when they have the odds. And the rest of the time, they don’t [emphasis added]. It’s just that simple.7 But how can investors determine the optimal size of the individual bet? The Kelly criterion gives us the answer. The Kelly Criterion Formulated by John L. Kelly and popularized by the practical success of Ed Thorp, the Kelly criterion is a formula used to determine the optimal bet size for a given set of probabilities and payoffs. Although the formula can be stated in several ways, the following expanded version appeared in Thorp’s interview in the book Hedge Fund Market Wizards: where: F = Kelly criterion fraction of capital to bet, PW = probability of winning the bet, PL = probability of losing the bet, $W = dollars won if bet is won, and $L = dollars lost if bet is lost.8 If an individual knows the odds and payouts of a given bet with precision, the Kelly criterion bet size will maximize capital over the long run.

The Bond King: How One Man Made a Market, Built an Empire, and Lost It All
by Mary Childs
Published 15 Mar 2022

But for much of his senior year, he was stuck in a hospital bed with a collapsed lung and in need of multiple skin grafts. In his boredom, he picked up a book he’d bought after spring break the year before, when he’d lost fifty dollars at blackjack that he didn’t have to lose. He was skeptical that Ed Thorp’s Beat the Dealer: A Winning Strategy for the Game of Twenty-One could work, but he was stuck. He read the whole thing. When he finished reading it, he got a deck of cards and started testing Thorp’s strategy in his hospital bed. “I had to prove it, because I didn’t believe it,” Gross recalls. “I had nothing to do, so I proved it.”

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He was never surprised or unnerved when this happened; a hum of anxiety told him it was about to happen at every moment. Casinos hated card counters. This moment was always so close at hand that, whenever a casino actually kicked him out, it was almost a relief. He’d feel oddly proud. Because it showed that his plan was working, that he was succeeding in following Ed Thorp’s path. Counting cards isn’t illegal, but a casino aims for volume, to exploit its slight statistical edge over its customers’ hands. If a customer ruins the randomness of the game, it ruins the model. Casinos can deny anyone service, and they don’t like when a player exploits a slim mathematical advantage; that’s their game.

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But breaks bungled his rhythm, so he stopped taking them: he stood longer and longer, and got comfortable with sixteen-hour days. After that summer, Gross went off to Vietnam, serving in the navy, and when he got back in 1969, he put the ten thousand dollars he’d generated in Vegas toward business school. In 1967, Ed Thorp published another book, Beat the Market: A Scientific Stock Market System, about arbitraging convertible bonds and stocks and warrants. When Gross got to business school, he picked the book up. The topic happened to line up with what they were teaching in his program at UCLA, its professors on the cutting edge of warrants and options.

Quantitative Trading: How to Build Your Own Algorithmic Trading Business
by Ernie Chan
Published 17 Nov 2008

My contention is that it is much more logical and sensible for someone to become a profitable $100,000 trader before xi P1: JYS fm JWBK321-Chan xii September 24, 2008 13:43 Printer: Yet to come PREFACE becoming a profitable $100 million trader. This can be shown to be true on many fronts. Many legendary quantitative hedge fund managers such as Dr. Edward Thorp of the former Princeton-Newport Partners (Poundstone, 2005) and Dr. Jim Simons of Renaissance Technologies Corp. (Lux, 2000) started their careers trading their own money. They did not begin as portfolio managers for investment banks and hedge funds before starting their own fund management business.

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A OPTIMAL CAPITAL ALLOCATION AND LEVERAGE Suppose you plan to trade several strategies, each with their own expected returns and standard deviations. How should you allocate capital among them in an optimal way? Furthermore, what should be the overall leverage (ratio of the size of your portfolio to your 95 P1: JYS c06 JWBK321-Chan September 24, 2008 13:57 96 Printer: Yet to come QUANTITATIVE TRADING account equity)? Dr. Edward Thorp, whom I mentioned in the preface, has written an excellent expository article on this subject in one of his papers (Thorp, 1997), and I shall follow his discussion closely in this chapter. (Dr. Thorp’s discussion is centered on a portfolio of securities, and mine is constructed around a portfolio of strategies.

A Hacker's Mind: How the Powerful Bend Society's Rules, and How to Bend Them Back
by Bruce Schneier
Published 7 Feb 2023

Las Vegas: How physicists used science to beat the odds at roulette,” Forbes, https://www.forbes.com/sites/startswithabang/2017/05/23/how-physicists-used-science-to-beat-the-odds-at-roulette. 36Nevada banned the use of devices: Don Melanson (18 Sep 2013), “Gaming the system: Edward Thorp and the wearable computer that beat Vegas,” Engadget, https://www.engadget.com/2013-09-18-edward-thorp-father-of-wearable-computing.html. 36Casinos have responded: Grant Uline (1 Oct 2016), “Card counting and the casino’s reaction,” Gaming Law Review and Economics, https://www.liebertpub.com/doi/10.1089/glre.2016.2088. 37Laws were passed banning: David W.

Python for Algorithmic Trading: From Idea to Cloud Deployment
by Yves Hilpisch
Published 8 Dec 2020

Capital Management A central question in algorithmic trading is how much capital to deploy to a given algorithmic trading strategy given the total available capital. The answer to this question depends on the main goal one is trying to achieve by algorithmic trading. Most individuals and financial institutions will agree that the maximization of long-term wealth is a good candidate objective. This is what Edward Thorp had in mind when he derived the Kelly criterion to investing, as described in Rotando and Thorp (1992). Simply speaking, the Kelly criterion allows for an explicit calculation of the fraction of the available capital a trader should deploy to a strategy, given its statistical return characteristics.

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On the other hand, having RESTful APIs for algorithmic trading available, such as the one from Oanda, simplifies the automation task considerably since the core part boils down mainly to making use of the capabilities of the Python wrapper package tpqoa for tick data retrieval and order placement. Around this core, elements to mitigate operational and technical risks should be added as far as appropriate and possible. References and Further Resources Papers cited in this chapter: Rotando, Louis, and Edward Thorp. 1992. “The Kelly Criterion and the Stock Market.” The American Mathematical Monthly 99 (10): 922-931. Hung, Jane. 2010. “Betting with the Kelly Criterion.” http://bit.ly/betting_with_kelly. Python Script This section contains Python scripts used in this chapter. Automated Trading Strategy The following Python script contains the code for the automated deployment of the ML-based trading strategy, as discussed and backtested in this chapter: # # Automated ML-Based Trading Strategy for Oanda # Online Algorithm, Logging, Monitoring # # Python for Algorithmic Trading # (c) Dr.

Fed Up!: Success, Excess and Crisis Through the Eyes of a Hedge Fund Macro Trader
by Colin Lancaster
Published 3 May 2021

You need to learn how to scale and how to build a great business and great teams. Selecting team members, managing them, getting the right mix of skill sets and technical abilities. All of this means less time trading and more time managing. Many of the early hedge fund guys found their inspiration to go into this business in a guy named Ed Thorp. He wrote a couple of famous books. My first boss gave me one of them early in my career, and it got me hooked. Ed wrote Beat the Dealer, which was the first book to prove mathematically that blackjack could be beaten by card counting, and Beat the Market, which outlined many of the early arbitrage strategies.

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Helms was famous for his 1984 photograph celebrating the Detroit Tigers World Series championship. His story illustrates many of the challenges the city was already going through in the 1980s, deadspin.com/the-slow-sad-death-of-a-riots-symbol-5812647. 21 VBT is Value Balance Training. See vbthub.com. 22 www.25iq.com/2017/07/22/a-dozen-lessons-on-investing-from-ed-thorp 23 Ibid. 24 PDCF: primary dealer credit facility MMLF: money market mutual fund liquidity facility CPFF: commercial paper funding facility MSBLP: Main Street Business Lending program PMCCF: primary market corporate credit facility SMCCF: secondary market corporate credit facility TALF 3: term asset-backed securities loan Part 3: The Aftermath Chapter 7 QE Dreaming April 2020 4/1/20—Fed loosens large bank capital requirements to free up credit. 4/1/20—ISM manufacturing down to 49.1. 4/2/20—Global virus infections top 1M; 51K dead. 4/2/20—Jobless claims to 6.65M for week ending March 28: 10M people unemployed over the last two weeks. 4/3/20—ISM nonmanufacturing at 52.5, a 4.8 point decline; employment in leisure and hospitality plummeted by 7.7 million jobs, or 47%. 4/3/20—Payrolls -701K; unemployment jumps to 4.4%; first net loss of jobs since Sept. 2010. 4/6/20—Boris Johnson moved into intensive care. 4/6/20—Fed further expands lending and credit facilities.

Frequently Asked Questions in Quantitative Finance
by Paul Wilmott
Published 3 Jan 2007

These ideas would find a use in finance almost three decades later. See Sobol’ (1967), Faure (1969), Hammersley and Handscomb (1964), Haselgrove (1961) and Halton (1960). Figure 1-1: They may not look like it, but these dots are distributed deterministically so as to have very useful properties. 1968 Thorp Ed Thorp’s first claim to fame was that he figured out how to win at casino Blackjack, ideas that were put into practice by Thorp himself and written about in his best-selling Beat the Dealer, the “book that made Las Vegas change its rules.” His second claim to fame is that he invented and built, with Claude Shannon, the information theorist, the world’s first wearable computer.

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Paul Wilmott On Quantitative Finance by Paul Wilmott “Paul Wilmott On Quantitative Finance, Second Edition, is even better than his unsurpassed First Edition. He combines the insights of an incisive theorist with his extensive practical experience. His teaching style is clear and entertaining. I recommend the book to everyone in the ‘quant’ community, from beginner to expert, both for learning and for reference.” Ed Thorp Publisher John Wiley & Sons Publication date 2006 Format Hardback, three volumes in slip case, + CD ISBN 0470018704 A research-level book containing the tried and trusted techniques, the analysis of models and data, and cutting-edge material. Contains models and research that cannot be found in other textbooks.

Hedge Fund Market Wizards
by Jack D. Schwager
Published 24 Apr 2012

Contents Foreword Preface Acknowledgments Part One: Macro Men Chapter 1: Colm O’Shea Addendum: Ray Dalio’s Big Picture View Chapter 2: Ray Dalio Chapter 3: Larry Benedict Chapter 4: Scott Ramsey Chapter 5: Jaffray Woodriff Part Two: Multistrategy Players Chapter 6: Edward Thorp Chapter 7: Jamie Mai Chapter 8: Michael Platt Part Three: Equity Traders Chapter 9: Steve Clark Chapter 10: Martin Taylor Chapter 11: Tom Claugus Chapter 12: Joe Vidich Chapter 13: Kevin Daly Chapter 14: Jimmy Balodimas Chapter 15: Joel Greenblatt Conclusion Epilogue Appendix A Appendix B About the Author Index Other Books by Jack D.

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Although segmenting the data to reserve unseen data for testing is a necessary condition to avoid misleading results, it is not a sufficient condition as Woodriff goes on to explain. 7In 2011, QIM changed the exact calculation it used to reduce leverage during periods of poor performance, but the new formulation was similar in both conceptual and practical terms. It is, therefore, simpler to talk about their leverage reduction as one process. Part Two MULTISTRATEGY PLAYERS Chapter 6 Edward Thorp The Innovator Can the markets be beat? Not unless you are lucky, according to proponents of the efficient market hypothesis (EMH), which assumes that the markets discount all known information and immediately reflect all new information. What about traders who have achieved exceptional track records including some of those profiled in this book?

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See Options QE2 (quantitative easing) Quadrant conceptualization Quantitative Foundation Quantitative Investment Management (QIM) Ramsey, Scott Random Character of Stock Prices (Cootner) Recessions vs. deleveragings Regan, James Related market price actions Relative Strength Index (RSI) Reminiscenses of a Stock Operator Research in Motion Ltd. (RIMM) Return on capital Reversal vs. correction Ridgeline Partners Rights issues Risk and volatility Risk arbitrage Risk management Edward Thorp Jaffray Woodriff Joe Vidich Larry Benedict Martin Taylor Michael Platt Thomas Claugus Risk vs. volatility RMH Warrants and Low Price Stock Survey (Fried) Rock Tenn Rohm & Haas Roulette system Russian financial crisis of 1998 Schwager, Zachary Schwartz, Marty Secondary variables Sentiment Seykota, Ed Shannon, Claude Sharpe ratio Shaw, David Short-term trading Silver Singer, Paul Slavin, Robert Société Générale Solvency vs. liquidity Soros, George South Korean stock market Soviet Union.

Age of Context: Mobile, Sensors, Data and the Future of Privacy
by Robert Scoble and Shel Israel
Published 4 Sep 2013

About 2.7 billion people are now nodes on the global network, and while it sounds strange, that connectedness empowers each of us. What Started in Vegas… Where wearables are concerned, Moore’s miniaturization is extremely important. If they don’t get small enough to be unobtrusive, people won’t wear them. Small was fundamental to the colorful story of how wearable computers were developed. Edward O. Thorp, an MIT professor whose specialty was mathematical probability, had invented a successful clandestine system for counting cards and winning big at blackjack tables. Growing bored, he took on the larger challenge of predicting the number where a ball spinning on a roulette wheel would land. He devised a clever system that he concealed from the scrutiny of Mob-controlled security guards in Las Vegas casinos.

Radical Uncertainty: Decision-Making for an Unknowable Future
by Mervyn King and John Kay
Published 5 Mar 2020

They were arrested, and only after a nine-month investigation did police conclude that no offence had been committed: Section 17 of the Gaming Act 1845 forbade ‘unlawful devices’, but the suspects had not interfered with the outcome of the game. 5 They had, however, prevented the achievement of a ‘level playing field’ on which the objective frequency distribution was known and was the same for all players. Many gamblers believe they have a system. What distinguished the Ritz players was that they really did. So did Edward Thorp, a mathematics professor at MIT, who in the 1960s used statistical analysis to devise a winning strategy for blackjack. Blacklisted by operators, he wore false beards and other disguises to gain access to Las Vegas casinos. Ultimately, he found easier and more profitable applications of his skills on Wall Street. 6 Regulators of securities markets restrict the activities of traders with superior information for superficially different but substantively similar reasons.

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But the prediction that people routinely engage in such transactions is plainly false, and no prudent individual would even think of behaving in that way. A very few professional gamblers are successful because they have observed anomalies, or studied the processes of apparent games of chance particularly carefully – Edward Thorp and the Ritz patrons – and the organisers of gambling establishments are anxious to identify them and exclude them from their casinos. But most regular gamblers are sad people, some in the grip of addiction, some suffering from persistent delusions about their own skill. It is true that when experimental subjects are asked to come up with subjective probabilities using these pignistic methods they can sometimes be persuaded to do so, usually with the aid of pressure from their professors and modest financial compensation for their cooperation.

Think Twice: Harnessing the Power of Counterintuition
by Michael J. Mauboussin
Published 6 Nov 2012

For the stock market, see Didier Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton, NJ: Princeton University Press, 2003); for terrorist acts, see Aaron Clauset and Maxwell Young, “Scale Invariance in Global Terrorism,” arXiv:physics, May 1, 2005; and for power grid, see Jie Chen, James S. Thorp, and Ian Dobson, “Cascading Dynamics and Mitigation Assessment in Power System Disturbances Via a Hidden Failure Model,” Electrical Power and Energy Systems 27 (2005): 318–326. 26. Shankar Vedantam, “Vote Your Conscience. If You Can.” Washington Post, December 31, 2007, A3. 27. Edward O. Thorp, The Mathematics of Gambling (Hollywood, CA: Gambling Times, 1984); J. L. Kelly Jr., “A New Interpretation of Information Rate,” Bell System Technical Journal, 1956, 917–926; and William Poundstone, Fortune’s Formula: The Untold Story of the Unscientific Betting System that Beat The Casinos and Wall Street (New York: Hill and Wang, 2005). 28.

The Idea Factory: Bell Labs and the Great Age of American Innovation
by Jon Gertner
Published 15 Mar 2012

Baker told his colleagues that he never wanted such a fate to befall someone like Shannon. 26 Shannon also believed a smart gambler could take advantage of certain inefficiencies in gaming systems, an idea that led him to travel to various Nevada casinos around this time with a mathematician and investor named Ed Thorp. Their intent was to beat the house in roulette and cards. Many of these exploits are detailed in William Poundstone’s book Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (New York: Hill & Wang, 2005). 27 Arthur Lewbel, author interview. 28 Claude Shannon, “Scientific Aspects of Juggling,” in Collected Papers, edited by N.

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I likewise suggest Googling “The Essential Message,” an unpublished MIT thesis on Shannon by Erico Marui Guizzo, which is an insightful look into how he created information theory. Finally, no list of books on Shannon would be complete without Fortune’s Formula, William Poundstone’s entertaining narrative of how in the 1960s Shannon and his friend Ed Thorp tried to beat the Las Vegas casinos and Wall Street. John Pierce wrote many technical books that are still available through used booksellers; with Mike Noll, he also wrote Signals, a useful and accessible introduction to the science of communications. Alas, one of Pierce’s most captivating pieces of writing was My Career as an Engineer, an autobiography (unpublished in the United States) that he wrote—very quickly, I’m sure—for a small Japanese publisher upon receiving the Japan Prize in 1985.

100 Baggers: Stocks That Return 100-To-1 and How to Find Them
by Christopher W Mayer
Published 21 May 2018

(See Poundstone’s book for a good look at the debates. Also, Michael Mauboussin has a summary discussion in a 2006 paper titled “Size Matters.” You can find it free online.) For me, the big obstacle is that in the stock market, you can’t know your odds or your edge with any certainty. You must guess. Nonetheless, the idea is alluring. Ed Thorp used it in his hedge fund, Princeton/Newport. Started in 1974, it averaged 19 percent returns for nearly 30 years without a down year. How much of that is due to Kelly’s formula and how much to Thorp’s own genius is hard to say. Thorp’s example is not a lonely one. Many great investors seem to intuitively use Kelly’s formula.

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age
by Paul J. Nahin
Published 27 Oct 2012

Interestingly, however, and in contradiction to his Omni declaration of “no interest in money”—a sentiment he repeated in a 1990 Scientific American profile (“I’ve always pursued my interests without much regard to financial value”)—at MIT he did develop a strong interest in making money. More technically, in what is called portfolio management, the sort of activity that is the heart and soul of pension and mutual funds. At first ignored by financial professionals, Shannon’s ideas (along with those of his Bell Labs colleague John L. Kelly Jr. and the mathematician Ed Thorpe) have today been enthusiastically embraced. The Transactions on Information Theory began publishing papers on portfolio theory in the 1980s, and many PhDs in information theory have since found employment with Wall Street investment firms. Shannon himself became wealthy by applying his ideas to his personal finances, a story you can read at length in the 2005 book by William Poundstone, Fortune’s Formula.

Safe Haven: Investing for Financial Storms
by Mark Spitznagel
Published 9 Aug 2021

Ironically, even Harry Markowitz, the original architect of modern portfolio theory in 1952, had become a proponent of the geometric mean criterion by 1959 (and very much so by 1976); but it was too late, as his modern portfolio theory framework had already taken hold—and the rest is history. Perhaps most notable was the magisterial work of Ed Thorp, who has both written about it and put it into practice since the 1960s. Much more recently, Ole Peters has written exhaustive and insightful papers on non‐ergodicity's implications for economic theory. And, of course, Nassim Taleb took up the point in his 2018 book Skin in the Game of the non‐ergodicity of the one‐period ensemble average versus the multi‐period time average.

How to Predict the Unpredictable
by William Poundstone

That jargon is meaningful to professionals (though no one could figure out how Madoff made it pay the way he claimed). At least some clients got statements that ostensibly listed every trade. That should have made it possible to figure out Madoff’s system, assuming he had one. At least one person tried. In 1991 hedge fund manager Ed Thorp — also known as the inventor of blackjack card counting — was asked for his opinion on a company’s investments. Thorp saw that the returns for the account with Madoff were fantastic. Curious, Thorp asked Madoff for more detail on his trades. He got it and quickly determined that something was fishy.

What the Dormouse Said: How the Sixties Counterculture Shaped the Personal Computer Industry
by John Markoff
Published 1 Jan 2005

Years later, however, when people would ask about the inventive ideas in Smalltalk, Ingalls would joke, “Well, where do you think these ideas came from?!” Ingalls demonstrated the new feature to one of the large weekly meetings of the PARC researchers in the fall of 1974. The gatherings were known as “Dealers” and had been instituted by Taylor, who took the name from the book Beat the Dealer by Edward O. Thorp, the MIT professor who had developed a system for winning at blackjack. Taylor was taken by the image of a nerdy math professor beating the house. The meetings became forums for both technical presentations and a kind of group interview system for job candidates. The demonstration of BitBlt had a dramatic impact both inside and outside of Kay’s group.

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing
by Burton G. Malkiel
Published 10 Jan 2011

Other things being the same, this should make stock prices fall. But with higher expected inflation, investors may reasonably project that corporate earnings and dividends will also increase at a faster rate, causing stock prices to rise. A fuller discussion of inflation, interest rates, and stock prices is contained in chapter 13. * Edward O. Thorp actually did find a method to win at blackjack. Thorp wrote it all up in Beat the Dealer. Since then, casinos switched to the use of several decks of cards to make it more difficult for card counters and, as a last resort, they banished the counters from the gaming tables. * If such a regularity was known to only one individual, he would simply practice the technique until he had collected a large share of the marbles.

Smarter Than You Think: How Technology Is Changing Our Minds for the Better
by Clive Thompson
Published 11 Sep 2013

Perlow describes similarly positive effects in Sleeping with Your Smartphone (Boston: Harvard Business Press, 2012), in documenting how a group of consultants with the Boston Consulting Group agreed to stay off their devices for a set number of hours per day, which they called predictable time off, and which in saner times was referred to as evenings and weekends. “an overarching ability to watch and understand your own mind”: Maggie Jackson and Bill McKibben, Distracted: The Erosion of Attention and the Coming Dark Age (Amherst, NY: Prometheus Books, 2008), Kindle edition. The first wearable was cocreated in 1960 by Claude Shannon: Edward O. Thorp, “The Invention of the First Wearable Computer,” Proceedings of the 2nd IEEE International Symposium on Wearable Computers (1998): 4–8, accessed March 23, 2013, graphics.cs.columbia.edu/courses/mobwear/resources/thorp-iswc98.pdf. Critics have already noted how unsettling it might feel: Mark Hurst, “The Google Glass Feature No One Is Talking About,” Creative Good (blog), February 28, 2013, accessed March 24, 2013, creativegood.com/blog/the-google-glass-feature-no-one-is-talking-about/; Adrian Chen, “If You Wear Google’s New Glasses You Are an Asshole,” Gawker, March 3, 2013, accessed March 24, 2013, http://gawker.com/5990395.

Making It Happen: Fred Goodwin, RBS and the Men Who Blew Up the British Economy
by Iain Martin
Published 11 Sep 2013

It was noticed after he had gone that someone had ordered that the RBS and NatWest logos in the portrait be painted over. 8 ‘Royal Bank of Scotland saviour takes his final curtain call’, Independent, 29 April 2006. 9 The current Cameron of Lochiel is Donald, Johnny Cameron’s elder brother. 10 ‘Heimlich Institute honors RBS for lifesaving ad’, Heimlich Institute, 21 September 2004. 11 Sutherland visited the Kremlin as part of a delegation in 2003, although BP’s investment in Russia via TNK-BP later descended into an extremely bitter row with the Russian government. Chapter 10 1 ‘Greenwich’s outrageous fortune’, Vanity Fair, July 2006. 2 Edward O. Thorp was one such pioneer in America, a Maths professor who perfected a gambling system and wrote the best-selling books Beat the Dealer and then Beat the Stock Market. In the early 1970s he applied his talents to creating a hedge fund, Princeton Newport Partners. 3 When Genius Failed: The Rise and Fall of Long-term Capital Management, Roger Lowenstein, 2000. 4 ‘$363m is average pay for top hedge fund managers’, USA Today, 26 May 2005. 5 Kruger founded Five Mile Capital. 6 Angelo Mozilo built Countrywide, plunged deep into sub-prime and after the crisis was targeted by the US authorities.

Systematic Trading: A Unique New Method for Designing Trading and Investing Systems
by Robert Carver
Published 13 Sep 2015

As I discussed in chapter two, many negative skew strategies have fantastic SR in back-test, but I advise you to run them at half the risk you’d use for a more benign trading system. Column B of table 25 shows the recommended percentage volatility target for negative skew systems. 106. At the time of writing I’m using a 25% volatility target, reflecting my relatively low appetite for risk. 107. Here is famous Kelly fan, hedge fund manager and Blackjack card counter Ed Thorpe: “My experience has been that most cautious … investors who use Kelly find the frequency of substantial bankroll reductions to be uncomfortably large.” (Quoted in Fortune’s Formula.) 146 Chapter Nine. Volatility targeting TABLE 25: WHAT VOLATILITY TARGET SHOULD STAUNCH SYSTEMS TRADERS USE? Recommended percentage volatility target Realistic backtested SR (A) Skew>0 (B) Negative skew 0.25 12% 6% 0.40 20% 10% 0.50 25% 12% 0.75 37% 19% 1.0 or more 50% 25% The table shows the recommended percentage volatility target for those who can backtest their dynamic trading systems, depending on the skew of returns (columns) and achievable back-tested Sharpe ratios (SR) (rows) after making adjustments to simulated results from table 14 on page 90.

Fortunes of Change: The Rise of the Liberal Rich and the Remaking of America
by David Callahan
Published 9 Aug 2010

He grew up in Minnesota, the son of a math professor, and moved to California when his father became the founding c03.indd 74 5/11/10 6:18:36 AM the eco rich 75 chairman of the math department at UC–Irvine. Gelbaum was a math prodigy as a teenager, taking math classes at UC–Irvine while still in high school before he started full-time at the university as a math major. When he graduated, he got a job with a math professor named Edward Thorp who was starting a hedge fund that used mathematical formulas to predict stock prices. Gelbaum worked with Thorp for the next seventeen years. Later he helped start a new hedge fund using mathematical formulas. His business success, he once told a reporter, “was all a matter of chance. It certainly wasn’t because I worked 5,000 times as hard as the average person or was 5,000 times smarter than the average person.”14 (It is not clear that Gelbaum ever gave the Sierra Club the full $100 million, since he announced in 2009 that he was suspending gifts to the group after he suffered market setbacks.

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Eleventh Edition)
by Burton G. Malkiel
Published 5 Jan 2015

By following any technical strategy, you are likely to realize short-term capital gains and pay larger taxes (as well as paying them sooner) than you would under a buy-and-hold strategy. Thus, simply buying and holding a diversified portfolio suited to your objectives will enable you to save on investment expense, brokerage charges, and taxes. *Edward O. Thorp actually did find a method to win at blackjack. Thorp wrote it all up in Beat the Dealer. Since then, casinos switched to the use of several decks of cards to make it more difficult for card counters and, as a last resort, they banished the counters from the gaming tables. †If such a regularity was known to only one individual, he would simply practice the technique until he had collected a large share of the marbles.

How I Became a Quant: Insights From 25 of Wall Street's Elite
by Richard R. Lindsey and Barry Schachter
Published 30 Jun 2007

Normative portfolio theory is concerned with the properties of utility functions and prescribes utility functions that achieve specified long-term goals such as maximizing the expected rate of compound return. For an excellent discussion, JWPR007-Lindsey May 18, 2007 356 11:41 note s see Edward O. Thorp: “Portfolio Choice and the Kelly Criterion,” reprinted in W. T. Ziemba & R. G.Vickson (eds.): Stochastic Optimization Models in Finance, Academic Press, 1975. 3. Myron J. Gordon: Finance, Investment and Macroeconomics: The Neoclassical and a Post Keynesian Solution (London: Edward Elgar, 1994). 4.

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation
by Richard Bookstaber
Published 5 Apr 2007

It was clear to Bamberger that he would last about as long as it took Tartaglia to understand the computer code behind the trading system. They had one conversation and that was it. While many who were at Morgan Stanley at the time can retell the story of Bamberger’s discovery of stat arb, its epilogue remains a blank page. Bamberger headed off to Princeton Newport, where he continued to pursue the strategy with the legendary Ed Thorp for a year, made a small fortune, and then disappeared from the world of trading. This move was a natural. Thorp was the first great analytically oriented trader. An MIT mathematician, he was the author of Beat the Dealer (Random House, 1966), which introduced the concept of card counting to blackjack.

No One Would Listen: A True Financial Thriller
by Harry Markopolos
Published 1 Mar 2010

When he surrendered in 2008, it was estimated he was running roughly $65 billion. You do the sad math. About three years later Neil confirmed this to be a viable scenario. By that time he was working at Benchmark Plus in Tacoma, Washington. His employer was friendly with an extraordinarily successful investor named Edward Thorp, who had conducted due diligence on behalf of another institution many years earlier. As he told Neil’s boss, he’d gotten ahold of some of Madoff’s trade tickets and compared them to OPRA tapes. He was nice about it, but said he found some discrepancies— meaning he was unable to match all the reported trades against the OPRA data.

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
by Satyajit Das
Published 15 Nov 2006

The convertible investors didn’t get their money back; instead, they got back shares in the defaulted company. So the convertible did convert after all, there just wasn’t any blue sky – it was the dark abyss below. So, who was fooling whom? Strippers You can strip down cars. It’s the same with convertibles. Convertible stripping dates back to the 1960s. A famous 1967 book by Edward Thorp and Sheen Kassouf, Beat the Market, set out the principles of convertible arbitrage. Thorp was already well known for another book, Beat the Dealer, which set out the process of card counting in blackjack. Thorp and Kassouf outlined the idea of breaking up a convertible bond into its bond and equity parts and hedging and trading them separately.

A First-Class Catastrophe: The Road to Black Monday, the Worst Day in Wall Street History
by Diana B. Henriques
Published 18 Sep 2017

Granville, Stock Market Predictor, Dies at 90,” New York Times, September 18, 2013. it encouraged investors to buy: Granville had issued an equally dramatic weekend “buy” recommendation months earlier, in April 1980; when the market opened for Monday trading, the Dow surged up 30 points on heavy trading. See Jerome Baesel, George Shows, and Edward Thorp, “Can Joe Granville Time the Market?” Journal of Portfolio Management (Spring 1982), p. 5. worked into the night making telephone calls: Kristin McMurran, “When Joe Granville Speaks, Small Wonder That the Market Yo-Yos and Tickers Fibrillate,” People, April 6, 1981. His message to those elite followers: Granville was a middling stock picker over the long run, but he was fair at calling overall market turns.

Stock Market Wizards: Interviews With America's Top Stock Traders
by Jack D. Schwager
Published 1 Jan 2001

For various reasons, the vast majority of the high-quality work that appears in the open literature can't be used in practice to actually beat the market. Conversely, the vast majority of the research that really does work will probably never be published. But there are a few successful quantitative traders who from time to time publish useful information, even when it may not be in their own selfinterest to do so. My favorite example is Ed Thorpe, who was a real pioneer in the field. He was doing this stuff well before almost anyone else. Ed has been remarkably open about some of the money-making strategies he's discovered over the years, both within and outside of the field of finance. After he figured out how to beat the casinos at blackjack, he published Beat the Dealer.

Investing Amid Low Expected Returns: Making the Most When Markets Offer the Least
by Antti Ilmanen
Published 24 Feb 2022

For excellent books with as broad coverage as this one, see Lussier (2013), Ang (2014), and Pedersen (2015). I also recommend viewing the Words from the Wise series in aqr.com, where we interviewed many luminaries (John Bogle, Charley Ellis, Robert Engle, Marty Leibowitz, Harry Markowitz, Richard Thaler, Ed Thorp, and Roger Urwin) who have influenced our thinking. For two other wonderful sets of interviews and profiles of modern finance giants, see Towle (2014) and Lo-Foerster (2021). Chapter 2 The Secular Low Expected Return Challenge Expected returns in all major asset classes have fallen to near historic lows.

Troublemakers: Silicon Valley's Coming of Age
by Leslie Berlin
Published 7 Nov 2017

Taylor called the featured presenter the “dealer” because the speaker set the terms much as a dealer sets out the rules of a poker game. Soon enough, the meetings themselves came to be called Dealers. “Dealer” also had a more antagonistic connotation. Taylor had read the popular 1962 how-to guide on card counting, Edward O. Thorp’s Beat the Dealer. He hoped that meeting participants would use their expertise to poke holes in a presenter’s work in the same way that card counters used continuous computations to get the edge on a blackjack dealer. Nearly every presentation was interrupted by mutters or even shouts of disagreement from people sprawled in the soft chairs on the floor.

Bernie Madoff, the Wizard of Lies: Inside the Infamous $65 Billion Swindle
by Diana B. Henriques
Published 1 Aug 2011

Madoff estimated that client account balances totaled $5 billion in 1987; if so, the annual investment returns he claimed to be producing would have pushed that number, conservatively, to about $8 billion by the early 1990s. 93 the harder it would be for savvy investors to believe: Indeed, as early as 1991, the pioneering quantitative analyst Edward Thorp looked at the results Madoff was producing for a pension fund client and found some red flags, including a day in April 1991 when Madoff’s reported trades in Procter & Gamble options were more than ten times the total number of P&G options traded that day. See Scott Patterson, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (New York: Crown Business, 2010), p. 63. 94 a pair of sceptical investors had sent two documents: Kotz Report, pp. 42–44, and Kotz Report, Exhibit 113, p. 1. 94 The fact sheet was on the letterhead of a financial adviser in San Francisco: Ibid., p. 43. 95 “relatives, friends and former clients”: Ibid. 95 he had received a call from his friend Richard Glantz: Avellino-Bienes SEC Transcript, pp. 12–14. 95 one of the earliest subcontractors: The elder Glantz was a partner with accountant Steven Mendelow in the Telfran fund, an indirect Madoff feeder fund that invested through Avellino & Bienes.

New Market Wizards: Conversations With America's Top Traders
by Jack D. Schwager
Published 28 Jan 1994

No, I got a job selling time on large computers. However, that position was essentially a marketing slot, and I was interested in doing analytical work. After about a year, I left to take a job in operations research for Kaiser Cement. At that time, I got interested in playing blackjack by reading a book called Beat the Dealer by Ed Thorp. From 1971 to 1975, I went to the Nevada casinos regularly. Did you live in Nevada at the time? No, I lived in California. But I would take a blackjack trip every chance I got. I probably spent about five days a month in Nevada during that time. In a sense, I owe everything that I have to the state of Nevada.

Extreme Money: Masters of the Universe and the Cult of Risk
by Satyajit Das
Published 14 Oct 2011

The insurer’s profit was the difference between statistical loss experience, based on historical knowledge of claims, and the premiums paid, plus investment income on the premiums. Applying insurance theory to options proved difficult. Louis Bachelier applied random walk models to pricing options. Paul Cootner and Paul Samuleson worked on the problem. In their 1967 book Beat the Market, mathematicians Sheen Kassouf and Edward Thorp outlined the relationship between the price of an option and the price of the underlying stock. Thorp, whose interest was gambling and beating the casino at roulette and baccarat, developed a model, anticipating the Black-Scholes equation. With a background in physics and mathematics, Fischer Black worked at Arthur D.

The Rough Guide to New York City
by Martin Dunford
Published 2 Jan 2009

One of the most interesting painter galleries in the district, this space exhibits great stuff from the likes of David Konigberg, Willy Lenski, and Sonya Sklaroff. Barbara Gladstone Gallery 515 W 24th St T 212/206-9300, W www.gladstonegallery.com. Paintings, sculpture, and photography by hot contemporary artists like Matthew Barney and Rosemarie Trockel. Edward Thorp 210 Eleventh Ave, 6th floor T 212/691-6565, Wwww.edwardthorpgallery .com. Mainstream contemporary American, South American, and European painting and sculpture. Highlights of their roster include painter Matthew Blackwell and sculptor Deborah Butterfield. Feature 5276 Bowery T212/675-7772, Wwww .featureinc.com.

The Rough Guide to New York City
by Rough Guides
Published 21 May 2018

Moved into these new Norman Foster-designed premises in 2016. Tues–Sat 10am–6pm. David Zwirner 537 W 20th St, between Tenth and Eleventh aves; also 519, 525 and 533 W 19th St 212 727 2070, davidzwirner.com; subway C, E to 23rd St. High-quality shows from major players such as Richard Serra, Lisa Yuskavage and Yayoi Kusama. Tues–Sat 10am–6pm. Edward Thorp Gallery 210 Eleventh Ave, 6th floor, between W 24th and W 25th sts 212 691 6565, edwardthorpgallery.com; subway C, E to 23rd St. Mainstream contemporary American, South American and European painting and sculpture. Highlights of their roster include painter Matthew Blackwell and sculptor Deborah Butterfield.