Edward Thorp: The Mathematician Who Beat Blackjack

Edward Thorp did not invent card counting, but he proved it worked.

1958 to 1961: the Los Angeles calculation

Edward Oakley Thorp, born in Chicago on August 14, 1932, was teaching mathematics at the University of California, Los Angeles in the late 1950s. The problem of blackjack came to his attention through a 1956 paper by Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott, published in the Journal of the American Statistical Association, which established the correct basic strategy for the dealer's standing-on-all-seventeens rule set. The Baldwin paper concluded that even with perfect basic strategy, the house retained a small edge of roughly 0.6 percent.

Thorp suspected that the composition of the remaining deck, as cards were dealt from a single-deck shoe, should alter that conclusion. Working on the IBM 704 at the Massachusetts Institute of Technology after his move there in 1959, he calculated the effect of removing specific cards from the deck. The results confirmed his suspicion. The removal of low cards, particularly fives, shifted the expected value toward the player. A system that tracked the composition of the remaining deck and sized bets accordingly could produce a positive expected return.

1961: Washington and the field test

Thorp presented his findings at the January 1961 meeting of the American Mathematical Society in Washington, D.C. The presentation attracted the attention of the press and, critically, of a professional gambler named Manny Kimmel, who agreed to finance a field test of the system. In the summer of 1961 Thorp and Kimmel traveled to Reno, Lake Tahoe, and Las Vegas with a bankroll of 10,000 US dollars. Over several sessions Thorp played Kimmel's money, using the system he had developed. The bankroll grew to 21,000 US dollars. The system worked in practice.

1962: Beat the Dealer

Thorp published Beat the Dealer: A Winning Strategy for the Game of Twenty-One through Random House in November 1962. The book laid out basic strategy rigorously, introduced the Ten Count system, and explained in plain language why a card counter held an edge against the house. It was the first mass-market work on beating a casino game using mathematics. It sold in the hundreds of thousands of copies and remains in print.

The casino industry's response was immediate and defensive. Las Vegas Strip properties altered blackjack rules in the spring of 1964, removing the player's ability to double down on certain hands and disallowing aces from being split. Player reaction was severe enough that many of the rule changes were rolled back within weeks, because mass-market players avoided the changed games. The episode demonstrated the tension that would shape the industry for the next sixty years. Casinos could not simply make blackjack unwinnable without destroying its appeal to the recreational majority.

1966: the revised edition and the High-Low count

Thorp published a revised edition of Beat the Dealer in 1966, which introduced the High-Low counting system developed in collaboration with Julian Braun of IBM. High-Low is simpler to use than the Ten Count: the player adds one to the running count for each low card seen (two through six), subtracts one for each high card (ten through ace), and uses the true count, the running count divided by the number of decks remaining, to adjust bet sizes. The system traded a small amount of theoretical edge for a large amount of usability, and it became the basis for almost every subsequent counting system taught in books and training programs.

1967 to 1979: Thorp leaves blackjack and enters finance

Thorp's later career shifted from gambling to finance. In 1967, with Sheen Kassouf, he published Beat the Market, which applied his probabilistic thinking to warrant arbitrage. In 1969 he cofounded Princeton Newport Partners, one of the earliest quantitative hedge funds, which generated strong returns for nearly two decades. Thorp continued to publish occasional pieces on gambling, including work on roulette prediction using concealed electronics and on advantage play in baccarat side bets, but his primary work moved to capital markets.

1970s and 1980s: the descendants

Thorp's direct influence on the casino industry in the 1970s and 1980s came through his successors. Ken Uston, a former Pacific Stock Exchange executive, used a big-player team concept in the 1970s, based in part on Thorp's principles and on refinements introduced by Al Francesco. Uston wrote The Big Player in 1977, sued Resorts International in Atlantic City in 1979 after being barred, and won in the New Jersey Supreme Court in 1982 on the question of whether a private casino could bar a non-cheating skilled player. The decision, however, applied only to Atlantic City under the specific New Jersey regulatory regime. Nevada operators retained the right to exclude skilled players.

The MIT Blackjack Team, which operated from roughly 1979 through the late 1990s under various configurations, drew its mathematical foundations from Thorp's work. The team's activities were documented in Ben Mezrich's 2002 book Bringing Down the House and in the 2008 film 21.

Thorp's legacy

Three consequences of Thorp's work are visible in the current industry.

• Multi-deck shoes, introduced at many Las Vegas properties in the late 1960s, were a direct response to counting. More decks reduce the effectiveness of composition-based systems.
• Continuous shuffling machines, which returned used cards to the deck after each hand, were introduced in the 2000s specifically to defeat counting and have since become common at lower-limit blackjack pits.
• The cultural shift in how the public perceives casino games changed. After 1962 it became widely understood that at least one game in the casino could be beaten by a sufficiently dedicated and disciplined player. The idea that mathematics, applied rigorously, could produce an edge against the house became part of popular culture.

Edward Thorp remains alive as of 2026, still publishing, still a figure of affectionate regard in the mathematical and gambling worlds alike. The game he changed has evolved past his original system, but the change he set in motion has not reversed.