Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott
“The Four Horsemen of Aberdeen”
The Four Horsemen of Aberdeen: Roger Baldwin, Will Cantey, James McDermott and Herbert Maisel
The “Four Horsemen of Aberdeen”” (Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott) were inducted into the Blackjack Hall of Fame in 2008 by the unanimous decision of the current living members of the Hall of Fame, including (alphabetically) Johnny Chang, Al Francesco, James Grosjean, Tommy Hyland, Max Rubin, Arnold Snyder, Edward O. Thorp, and Stanford Wong.
The Four Horsemen were inducted for their pioneering work in publishing, in 1956, the first accurate basic strategy for the game of blackjack. The strategy was first published in an article in the Journal of the American Statistical Association; later the strategy was published for a mass audience in the 1957 book Playing Blackjack to Win .
Ed Thorp credits Baldwin, Cantey, Maisel and McDermott with being the impetus for his own research into the game. The four mathematicians provided Thorp with all of their data in 1958, which ultimately led to the publication of Thorp’s Beat the Dealer in 1962.
Although the Four Horsemen did not realize it at the time, the strategy they published in 1957, which also included the first legitimate card-counting system, was the first published blackjack strategy to provide a player advantage over the house with a flat bet. Recent computer simulation carried out by ETFan at Blackjack Forum Online, using the PowerSim blackjack simulation software, shows that the strategy provided a player edge of 0.1%.
One of the particularly impressive things about the Four Horsemen’s accomplishment was that they determined an accurate basic strategy using only desk calculators (or what used to be commonly called “adding machines”), as they began their work while in the Army in 1953, and computers were not available to them at that time. Although the game of blackjack had been played in casinos for 200 years, and although all of the other common casino-banked games had been mathematically analyzed by this time, blackjack had not been analyzed because all of the experts agreed that the game was simply too complicated.
Although the Four Horsemen were never widely known by the public, blackjack aficionados and professional players have always revered the four mathematicians as legends.
Here are a few comments about the Four Horsemen from the members of the Blackjack Hall of Fame:
James Grosjean: “I must have heard a thousand different players tell someone at a blackjack table ‘The book says this’ or “The book says that.’ These guys are the book.”
Johnny Chang: “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.”
Al Francesco: “Without these guys, none of us would even be here.”
Cardoza Publishing has published a 50th anniversary edition of the Four Horsemen’s Playing Blackjack to Win , along with interviews and other historical information about these men who changed blackjack history. Arnold Snyder has provided an Introduction for the book, and Ed Thorp has written the Foreword, in which he states: “To paraphrase Isaac Newton, if I have seen farther than others it is because I stood on the shoulders of four giants.”