Four Horsemen of the Apocalypse (blackjack)

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Four Horsemen of the Apocalypse is the name given by gambling authors[1] to the four U.S. Army engineers who first discovered in the 1950s the best playing strategy in the casino game of Blackjack that can be formulated on the basis of the player's and the dealer's cards. The so-called Basic Strategy, which was subsequently refined through the use of computers and combinatorial analysis, loses the least money to the casino in the long term.


In 1953, Roger Baldwin, a private in the U.S. Army with a master's degree in mathematics from Columbia University, stationed in Aberdeen Proving Ground, the U.S. Army's oldest active proving ground,[2] was playing dealer's choice poker in the barracks. After a player acting as dealer selected Blackjack, someone remarked that the dealer, as they do in the Las Vegas casinos, would have to stand on 17 and hit on 16.[1] Baldwin was intrigued by this news enough to embark on a project during his off-work hours to discover the optimal playing strategy for the player on the basis of the player's and the dealer's cards, as well as the rules dictating the dealer's play. For this, Baldwin asked the help of Wilbert Cantey, a sergeant at the facility, who had left the seminary because of his hustling at pool and cards and pursued a master's degree in Mathematics. They enlisted the help of privates Herbert Maisel, who later became a professor at Georgetown University, and James McDermott, who had a master's from Columbia University.[1]

For their project, the four Army men used only the desk calculators available at the military base, which were called at the time “adding machines.” The result of their work was presented in an analytical study in the Journal of the American Statistical Association, in September 1956,[3] and subsequently in a book titled Playing Blackjack to Win that was published in 1957.[4] The book, with a foreword written by TV quiz-show star Charles Van Doren, contained a pull-out strategy chart with sections on Draw or Stand, Doubling Down, and Splitting Pairs.[3]

The book did include, in a chapter titled "Using the Exposed Cards to Improve Your Chances", the first valid card-counting system ever published, but their method was not strong enough to offer a positive-expectation strategy for the player, although it did offer the least costly strategy in the game of casino Blackjack.[5] A gambling expert has claimed that any player who uses the Four Horsemen's basic strategy today "would not be giving up more than a few hundredths of a percent [of expected value] over perfect basic strategy."[5]


The four originators of Blackjack's Basic Strategy went on with their lives away from casinos and gambling, dedicating themselves to scientific research, teaching and business.[6] But their work caused an immediate sensation in gambling research as well as among professional gamblers. MIT Professor of Mathematics Edward O. Thorp tested their strategy on the university's IBM computers and found it to be accurate "within a couple of hundredths of a percentage point."[1] Thorp went on to formulate the first strong card counting strategy and tested it in actual casino play, in trips he took to Las Vegas, often accompanied by Claude Shannon, the so-called "father of information theory".[7]

The existence of a casino-beating system spread throughout the American gambling and casino circles, and in 1962, E. O. Thorp published his "seminal" work Beat The Dealer, widely considered to be the original Blackjack manual.[8] The book sold over 700,000 copies and earned a place in the New York Times bestseller list. The publication and subsequent notoriety of the book was the cause at the time behind many casinos changing the rules and conditions of how Blackjack was offered – for example, they stopped dealing single-deck Blackjack down to the last card.[9] After players began complaining, most casinos went back to the previous rules and conditions. The tables were soon full of casual gamblers who believed that by they could now "beat the house," even though most of them never strictly followed Thorp's "complicated," two-parallel-counts system, or even the simpler systems that subsequently appeared, such as High-Low, and the casinos started winning more money than before Thorp's book had appeared.[9]

Thorp's work in turn inspired the research and the exploits of professional blackjack players such as Stanford Wong, Ken Uston, and the MIT Blackjack Teams of the 1990s, as well as many others.[1]


In 1965, in an early recognition of the impact that the work of the four U.S. Army men would have on the game of 21, gambling author Dr. Allan N. Wilson labelled them "The Four Horsemen of the Apocalypse"[10] in his book The Casino Gambler’s Guide.[11]

On the night of 4 January 2008, during Max Rubin's 12th annual Blackjack Ball, held in Las Vegas, the Four Horsemen were inducted into the Blackjack Hall of Fame.[1]

During the Ball's festivities, Stanford Wong commented: "Thorp never would have got there without the work of these guys. If Thorp never got there, I don't know that any of us would be here. I don't know how many millions of dollars just the people in this room have made as a result of the work that these guys did." And Max Rubin stated, “If it wasn't for them, not one of us would be in this room."[1] Former member of the MIT Team Johnny Chang said, "When I first read the 1957 article they wrote that appeared in the Journal of the American Statistical Association with an accurate basic strategy, I couldn't fathom how they had accomplished this using desk calculators. It just seemed impossible."[12]

Later in 2008, on the 50th anniversary of its first edition, the book Playing Blackjack to Win was reprinted in the US,[4] with a foreword written by E. O. Thorp, and an introduction by Arnold Snyder.[4] In his foreword, Thorp wrote: "To paraphrase Isaac Newton, if I have seen farther than others it is because I stood on the shoulders of four giants.[4]

See also[edit]


  1. ^ a b c d e f g "They invented basic strategy" by Jeff Haney, Las Vegas Sun, 4 January 2008
  2. ^ Aberdeen Proving Ground Archived 2017-04-29 at the Wayback Machine, Army Alliance website
  3. ^ a b "Legendary Blackjack Analysts Alive But Still Widely Unknown" by Joseph P. Kahn, The Boston Globe, 22 February 2008, reprinted in The Tech
  4. ^ a b c d Baldwin, Roger, Wilbert Cantey, Herbert Maisel, and James McDermott. Playing Blackjack to Win: A New Strategy for the Game of 21; original edition: 1957; reprinted by Cardoza, 25 November 2008; 978-1580422512
  5. ^ a b "Blackjack History: Baldwin, Cantey, Maisel and McDermott and the First Accurate Blackjack Basic Strategy" by Arnold Snyder, Blackjack Forum, 1997
  6. ^ "Aberdeen Four Horsemen made movie 21 possible" by Bill Ordine, The Baltimore Sun, 7 April 2008
  7. ^ "Claude Shannon, the Father of the Information Age, Turns 1100100" by Siobhan Roberts, The New Yorker, 30 April 2016
  8. ^ Edward Thorp - Blackjack Player, Blackjack Hero website
  9. ^ a b Snyder, Arnold. Blackbelt in Blackjack : Playing 21 as a Martial Art; Cardoza; revised edition: 1 February 2005; 978-1580421430
  10. ^ Wilbert Cantey Biography, Cardoza website
  11. ^ Wilson, Allan W. The Casino Gambler's Guide ; Harper & Row; 1965; ASIN B000PHSG8Q
  12. ^ The Blackjack Hall of Fame Honors Professional Gamblers, Blackjack Science, 2015

External links[edit]