Thorp, Edward
From Wilmott Wiki
Edward Oakley Thorp (born 1932) is a mathematician and statistical arbitrage hedge fund manager. His first claim to fame was as the discoverer of a winning strategy for the gambling game of blackjack, and inventor of card counting. He also worked with Claude Shannon in the late 1950s and early 1960s on the world's first pocket-sized computer. This was built to forecast the resting place of the ball in roulette. Their system gave them an expected profit of 44% per spin of the wheel.
In the late 1960s Ed Thorp worked with Sheen Kassouf on the pricing of convertibles bonds and together they invented delta hedging and discovered what are now known as the Black-Scholes formulae. Thorp used this work to start a convertible arbitrage hedge fund.
Degrees
- Ph.D. (Mathematics), University of California, Los Angeles, 1958
- M.A. (Physics), University of California, Los Angeles, 1955
- B.A. (Physics), University of California, Los Angeles, 1953
Bibliography
Books
- Beat the Dealer: A Winning Strategy for the Game of Twenty-One, Random House, New York, 1962 ISBN 0-394-70310-3
- Elementary Probability, Wiley, New York, 1966
- Beat the Market: A Scientific Stock Market System, (with Sheen Kassouf) Random House, New York, 1967 ISBN 0-394-42439-5
- The Mathematics of Gambling, Gambling Times, 1984.
Papers and articles
Functional Analysis
- Note on linear operators. Journal fur die reine and angewandte Mathematik 203 (1959), 110-112. (MR22 #4954), (Z90 90).
- Projections onto the substance of compact operators. Pacific Journal of Mathematics 10 (1960), 693-699. (MR22 #4955), (Z119, 319).
- The range as range space for compact operators. (with S. Goldberg), Journal fur die reine und angewandte Mathematik 211 (1962), 133-115. (MR26 #4182), (Z106, 308).
- On some open questions concerning strictly singular operators. (with S. Goldberg), Proceedings of the American Mathematical Society 14 (1963), 334-336. (MR26 #2892), (Z115, 33).
- Finite dimensional normed spaces. Journal of the London Mathematical Society (1964), 211-214. (MR29 #1523).
- Internal points of convex sets. Journal of the London Mathematical Society (1964), 1959-1960. (MR28 #4340).
- Banach spaces congruent to their conjugates. Journal of the London Mathematical Society (1964), 703-705. (MR29 #5092), (Z199, 440).
- The range as range for compact operators II. Jornal fur die reine und angewandte Mathematik 217 (1964), 69-78. (MR 30 #5168)
- Operator representation theorems. (with R. Whitley), Illinois Journal of Mathematics 9 (1965), 595-601. (MR31 #6126).
- The strong maximum modulus theorem for analytic functions into a Banach space. (with R. Whitley), Proceedings of the American Mathematical Society 18 (1967) 640-646. MR 35 #5643), (Z185, 201).
- Partially bounded sets of infinite width. (with R. Whitley), Journal fur die reine und angewandte Mathematik 248 (1971), 117-122. (MR43 #5291), (Z212, 144).
- Attempt at a strongest vector topology. American Mathematical Monthly, (May 1965)
Game Theory
- A favorable strategy for twenty-one. Proceedings of the National Academy of Sciences 47 (1961), 110-112. (MR #B846).
- A partial analysis of Go. (with W.E. Walden), The (British) Computer Journal 7:3 (1964), 203-207. (MR33 #2424), (Z123, 340). Also included in Computer Games II, David N. L. Levy editor, Springer-Verlag, 1988.
- A favorable side bet in Nevada Baccarat. (with W.E. Walden), Journal of the American Statistical Association 61, Part I (1966), 313-328.
- Repeated independent trials and a class of dice problems. (Mathematical Note), American Mathematical Monthly (August-September 1964), 778-781. (Z123, 364).
- Optimal gambling systems for favorable games. Review of International Institute of Statistics 37:3 (1969), 273-293. (Z191, 497).
- Solution of a Poker variant. Information Sciences 2/2 (1970), 299-301. (MR S42 #8925), (Z205, 232).
- A computer-assisted study of Go on M x N boards. (with W.E. Walden), Lecture Notes in Operations Research and Mathematical Systems in Theoretical Approaches to Non-numerical Problem Solving, Vol. 28, R. Banerji and M.D. Masarovic, eds., Springer-Verlag, New York, 1970, 303-343; later revised version, Information Sciences 4:1 (1972), 1-33 (MR45 #8684), (Z228.68028). Also in Computer Games II, David N. L. Levy editor, Springer-Verlag, 1988.
- Non-random shuffling with applications to the game of Faro. Journal of the American Statistical Association, 842-847, December 1973. Much expanded version appears in: Gambling and Society, edited by W. Eadington, Charles C. Thomas, Springfield, Illinois, 1975, as: Probabilities and Strategies for the Game of Faro, pp. 531-560.
- The fundamental theorem of card counting with applications to Trente et Quarante and Baccarat. (with W.E. Walden) International Journal of Game Theory 2 (1973), 109-119. (Z258.90054)
- Backgammon: Part I, The Optimal Strategy for the Pure Running Game. working paper, Proceedings of the Second Annual Conference on Gambling, Lake Tahoe, 1975. ms 42 + pp. See news report on this paper in: Beating the Game, an article by Dietrick E. Thomsen, Science News, Vol. 107, March, 1975.
- Blackjack Systems. working paper, Proceedings of the Second Annual Conference on Gambling, Lake Tahoe, 1975, ms. 15 + pp. See news report on this paper in: Beating the Game, an article by Dietrick E. Thomsen, Science News, Vol. 107, March 1975.
- End Positions in Backgammon. in Computer Games I, David N.L. Levy editor, Springer-Verlag 1987, pp. 44-61.
- The Gambling Times Guide to Blackjack, Stanley Roberts with Edward O. Thorp, et al.; E. Thorp’s part is pp. 11-38.
- Blackjack: Betting the Klondike’s Free Ride. with Peter Griffin. Finding the Edge: Mathematical Analysis of Casino Games, edited by Olaf Vancura, Judy A. Cornelius and William R. Eadington. Institute for the Study of Gambling and Commercial Gaming, 2000.
- Does Basic Strategy Have the Same Expectation for Each Round? Finding the Edge: Mathematical Analysis of Casino Games, edited by Olaf Vancura, Judy A. Cornelius and William R. Eadington. Institute for the Study of Gambling and Commercial Gaming, 2000. An earlier version appeared in Blackjack Forum XIII #2, pp. 27-44, June 1933. RGE Publishing, 414 Santa Clara Ave., Oakland, CA 94610.
Probability and Statistics
- The metrization of statistical metric spaces. (with B. Schwiezer and A. Sklar), Pacific Journal of Mathematics 10 (1960), 673-675. (MR22 #5956).
- Best possible triangle inequalities for statistical metric spaces. Proceedings of the American Mathematical Society 11 (1960), 734-740. (MR22 #10068), (Z125 370)
- Generalized topologies for statistical metric spaces. Fundamenta Mathematicae 51 (1962), 9-21. (MR25 #3507) (Z105 115).
- Poincare’s conjecture and the distribution of digits in tables. (with R. Whitley), Composito Mathematica 23, (1971), 233-250. Summary also appears, Contributed Papers, 27th Session of the International Statistical Institute, London, September 1969, pp. 399-401. (MR44 #5281), (Z215. 357).
Mathematical Finance
- Portfolio choice and the Kelly criterion. Proceedings of the 1971 Business and Economics Section of the American Statistical Association 1972, 215-224. To be reprinted in Investment Decision-Making, edited by J. Bicksler. Reprinted in Stochastic Optimization Models in Finance, Academic Press, edited by W.T. Ziemba. S.L. Brumelle, and R.G. Vickson, 1975, pp. 599-620
- The Capital Growth Model: An Empirical Investigation. (with James Bicksler), Journal of Financial and Quantitative Analysis, March 1973, Vol. VIII, No. 2, pp. 273-287
- Extensions of the Black-Scholes Option Model. Contributed Papers 39th Session of the International Statistical Institute, Vienna Austria, August 1973, pp. 1029-1036.
- Concave utilities are distinguished by their optimal strategies. (with R.J. Whitley), Colloquia Mathematica Societatis Janos Bolyai 9. Progress in Statistics, Proceedings of the European Meeting of Statisticians, Budapest, 1972. Edited by J. Grani, S. Sarkadi, and I. Vincze. North Holland, 1974, pp. 813-830.
- The Stefan Problem for the Heat Equation with Applications to Economics. in Open Questions in Mathematics, Vol. II, 1980, Dagmar Henney, ed.
- Options in Institutional Portfolios: Theory and Practice. Proceedings, Seminar on the Analysis of Security Prices, Vol. 20, No. 1, May 15-16, 1975 (Center for Research Security Prices, Graduate School of Business, University of Chicago) pp. 229-251.
- Common Stock Volatilities in Option Formulas. Proceedings, Seminar on the Analysis of Security Prices, Vol. 21, No. 1, May 13-14 1976 (Center for Research in Security Prices, Graduate School of Business, University of Chicago), pp. 235-276.
- A Public Index for Listed Options. Proceedings, Seminar on the Analysis of Security Prices, Vol. 22, No. 1, May 12-13, 1977 (Center for Research in Security Prices, Graduate School of Business, University of Chicago), pp. 1699-205.
- Hedging Interest Rate Risk. A report for the Energy Fuels Corporation. April, 1977, 68 + pp.
- Indexes for Valuing Listed Options (Continued). Proceedings, Seminar on the Analysis of Security Prices, Vol. 22, No. 2, November 3-4, 1977, 19 + pp.
- The Probability that a Matrix has a Saddle Point. Information Sciences on Vol. 19, pp. 91-95 (1979)
- The Cost of Liquidity Services in Listed Options. with J. Baesel and G. Shows. Journal of Finance, Vol. 38, No. 3, p 989, June 1983.
- Granville’s Record in Predicting the DJIA: Some Statistical Tests. with J. Baesel and G. Shows. 15 + pp. Journal of Portfolio Management (Spring, 1982).
- Options on Commodity Forward Contracts. Management Science, Vol. 31, No. 10, October 1985
- The Kelly Criterion and the Stock Market. with Louis M. Rotando. American Mathematical Monthly, December, 1992.
- Risk Arbitrage in the Nikkei Put Warrant Market of 1989-1990. with J. Shaw and W.T. Ziemba. 2, pp. 243-271, 1995.
- The Kelly Criterion in Blackjack, Sports Betting and the Stock Market. Finding the Edge: Mathematical Analysis of Casino Games, edited by Olaf Vancura, Judy A. Cornelius and William R. Eadington. Institute for the Study of Gambling and Commercial Gaming, 2000. Later Version in Handbook of Asset and Liability Management in two volumes. North Holland, 2006. Editors Stavros A. Zenios and William T. Ziemba.
- A Perspective on Quantitative Finance: Models for Beating the Market. The Best of Wilmott Vol. 1, Incorporating the Quantitative Finance Review, Wiley, Chichester England 2005
- The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market. Handbook of Asset and Liability Management, Volume 1. Edited by S.A. Zenios and W.T. Ziemba ©2006 Published by Elsevier B.V. DOI: 10.1016/S1872-0978(06)01009-X
General Interest
- A Professor Beats the Gamblers. The Atlantic Monthly, June 1962. Reprinted in The Gambler’s Bedside Book, John K. Hutchens, ed., Tapliniger, New York, 1977, pp. 166-177.
- Professor Thorp Tosses a Coin. Cosmopolitan, 1964.
- The Legacy of Beat the Dealer, Wilmott website, posted September 24, 2002
- The Invention of the First Wearable Computer, Second International Symposium on Wearable Computers, Pittsburgh, Pennsylvania, October 19-20, 1998. IEEE Computer Society, Los Alamitos, CA. Reprinted in Noesis, the Journal of the Mega Society, Issue #176, February 2005.
- How many beans in the jar? Popular Mechanics, November 1965.
- On Optimal Doubling in Backgammon (Review). Management Science, 1976-1977.
- Approximate Planetary Positions. High School Science Bulletin, January 15, 1963.
- Finding the Speed of Light in a Prism. High School Science Bulletin, January 15, 1963.
- Exponential versus Factorial. Elementary Problem E1860, American Mathematical Monthly, 1966.
- Equivalence Classes of Poker Hands. Elementary Problem, E1865, American Mathematical Monthly, 1966.
Wilmott columns
- What I Knew and When I Knew It – Part 1, September 2002, pp. 44-45. Reprinted in Noesis, the Journal of the Mega Society, Issue #177, June 2005.
- What I Knew and When I Knew It – Part II, December 2002, pp. 44-45. Reprinted in Noesis, the Journal of the Mega Society
- What I Knew and When I Knew It – Part II , January 2003, pp. 42-43. Reprinted in Noesis, the Journal of the Mega Society
- The Distribution of Stock Price Changes – Part I, March 2003, pp. 26-27.
- The Distribution of Stock Price Changes – Part II, May 2003, pp. 42-43.
- How Rich is Rich? – Part 1, July 2003, pp. 44-45.
- How Rich is Rich? – Part II, September 2003, pp. 32-33.
- A Million Dollars for Mathematics – Part I, November 2003, pp. 34-35.
- A Million Dollars for Mathematics – Part II, January 2004, pp. 38-40.
- A Million Dollars for Mathematics – Part III, March 2004, pp. 32-33.
- A Theory of Inefficient Markets – Part I, May 2004, pp. 38-40.
- A Theory of Inefficient Markets – Part II, July 2004, pp. 46-47.
- Statistical Arbitrage – Part I, August 2004, pp. 44-45.
- Statistical Arbitrage – Part II, November 2004, pp. 48-49.
- Statistical Arbitrage – Part III, January 2005, pp. 36-37
- Statistical Arbitrage – Part IV, March 2005, pp. 66-67
- Statistical Arbitrage – Part V, May 2005, pp. 46-47
- Statistical Arbitrage – Part VI, July 2005, pp. 34-36
- Inefficient Markets, September 2005, pp. 36-38
- Bridge With Buffett. November 2005
- Berkshire Hathaway. January 2006
Articles in Gambling Times
- End Positions in Backgammon. Reprinted in Gammon Magazine preview issue. September, 1978.
- End Positions in Backgammon II. October 1978.
- End Positions in Backgammon III. November 1978.
- The World Championship of Blackjack. December 1978.
- Systems for Roulette I. January/February 1979.
- Systems for Roulette II. March 1979.
- Systems for Roulette III. April 1979.
- Physical Prediction of Roulette I. May 1979.
- The Black and White Classic Invitational Backgammon Tournament. June 1979.
- Physical Prediction of Roulette II. July 1979.
- Physical Prediction of Roulette III. August 1979.
- Backgammon Tournament Play: Game Theory Solves Expert’s Puzzle. September 1979.
- Physical Prediction of Roulette IV. October 1979.
- Letters from Readers. November 1979.
- The Kelly Money Management System. December 1979.
- Letters from Readers. January 1980.
- Getting Rich. February 1980.
- Blackjack – Beware the Short Shoe. March 1980.
- Counting Every Card in the Deck. Aril 1980.
- Roulette: The Dealer’s Signature Fallacy. May 1980.
- Cheating at Blackjack. June/July 1980.
- Letters from Readers. August 1980.
- Roulette and the Dealer’s Signature. September 1980.
- The Love Boat. October 1980.
- The Love Boat (continued). November 1980.
- The Horse Hedge Method. December 1980.
- Blackjack with a Ten-less Deck. January 1981.
- Part I: J.E. Granville Prophet of Profits. March 1981.
- Part II: J.E. Granville Prophet of Profits. April 1981.
- Granville Shakes the World. May 1981.
- Granville Shakes the World II. June 1981.
- Granville Shakes the World III. July 1981.
- Horse Racing and Letters. August 1981.
- Granville at UCI September 1981.
- Granville at UCI II. October 1981.
- Granville at UCI III. November 1981.
- The House Take in the Options Market
- A Proposition Bet with Dice. December 1981.