How I Invented Ace Prediction – Ed Thorp

Ed ThorpBy David McDowell.

The big thrill,” said Ed Thorp, “came from learning things nobody else in the world had ever known.[i]  Edward Oakley Thorp was a 28-year-old Assistant Professor at New Mexico State University when he came up with the idea of Ace Prediction:  “I believe that I began to think in detail about non-random shuffling in 1961 and 1962.  My initial thoughts were that it could very substantially affect the odds of many games.”1)EDITOR NOTE: This article is an excerpt from the book Blackjack Ace Prediction by David McDowell, which was originally published in 2004.

     “This was confirmed by the subsequent work I did.  I had a two-pronged attack:  build mathematical models to approximate real shuffling, and do empirical studies of real shuffling.  While doing this, I wanted a simple, practical method for exploiting this and the idea of Ace locating, using neighboring cards, occurred to me.  Why Aces?  Because an Ace is the best card for the player to get as one of his initial two cards at Blackjack.”

     “I tried it out at home and it worked well.  I didn’t focus on using it at the casinos because many other projects with higher priority were going on in my life at the same time.

    Among Thorp’s “other projects” were inventing with Claude Shannon[ii] (1916–2001)  the world’s first wearable computer to successfully predict roulette outcomes in Las Vegas, and writing the world’s best-selling gambling book, Beat the Dealer,[iii] which contained the first mathematical system ever discovered for beating a major casino game—card counting at blackjack.

     Paul O’Neil, writing of Thorp’s exploits in Life magazine in 1964, observed:  “Thorp delved into a stratum of impure chaos—a phenomenon involving both pattern and lack of pattern—to which comparatively little attention had ever been paid.[iv]

     While Thorp’s book made the New York Times best-seller list, his Ace Prediction theory remained the closely guarded secret of a handful of high-stakes professional blackjack players for more than 20 years. 

     The idea of predicting Aces first appeared in Thorp’s 1973 academic paper, “Nonrandom Shuffling with Applications to the Game of Faro,”[v] in which he wrote:  “ … nonrandomness yields simple winning strategies at Blackjack, Baccarat and Faro (Thorp and Walden, unpublished)[vi] ”  After outlining his non-random shuffling theories, Thorp commented:  “Note … the immediate application to ace-location …[vii]

     In 1997, Arnold Snyder, blackjack author and publisher, asked Professor Thorp if he had explored non-random shuffling more thoroughly in the seventies.  Thorp replied: “I did.  Most of it never got written up.  It is mostly in my mind and in a few sketch notes.

     Richard Reid, Webmaster of www.bjmath.com, (a website to which Thorp contributed) asked the professor if his “simple winning strategies” would ever be published.  “They may,” Thorp replied, “appear in a future reprint of [his book] The Mathematics of Gambling.[viii]

[i] O’Neil, Paul, “The Professor Who Breaks the Bank,” Life Magazine, Chicago, Illinois: Time, Inc., March 27, 1964, p. 84.
[ii] Calderbank, Robert and Neil J. A. Sloane,  “Obituary: Claude Shannon,” Nature, Vol. 410, No. 768, 2001.
[iii] Thorp, Edward O., Beat the Dealer: A Winning Strategy for the Game of Twenty-One, New York: Blaisdell Publishing Company, 1st ed., 1962.
[iv] O’Neil, 1964, p. 91.
[v] Thorp, Edward O., “Nonrandom Shuffling with Applications to the Game of Faro,” Journal of the American Statistical Association, Vol. 68, No. 344, December, 1973, p. 844.
[vi] Thorp, Edward O. and William E. Walden, “The Solution of Games by Computer,” (unpublished manuscript), 1963.
[vii] Thorp, 1973, p. 464.
[viii] Thorp, Edward O., The Mathematics of Gambling.  Secaucus, New Jersey: Lyle Stuart, March, 1985.

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Footnotes

Footnotes
1EDITOR NOTE: This article is an excerpt from the book Blackjack Ace Prediction by David McDowell, which was originally published in 2004.

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