# The Four Horsemen of Aberdeen

Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott could easily be considered the fore fathers of card counting, as they were the first men to publish a book that included accurate basic strategy and card counting methods. They weren't the first men to try to work out these calculations, but they were the first men who were successfully able to do so.

Arnold Snyder, an established blackjack player in his own right, wrote this about the Four Horsemen, "The strategy devised by these four men has since been published in millions of books. Hundreds of thousands of blackjack players all over the world depend on it." This quote is taken directly from the cover of the latest edition of their book.

## How Basic Strategy was First Developed

The U.S. Army's Aberdeen Proving Ground was established in Hartford Country, Maryland shortly after the United States entered World War I. This unit was established to test the effectiveness of military weapons before they were sent to the soldiers in combat. They would also apply stress tests to the vehicles used overseas, to make sure they were equipped to handle extreme conditions.

All four of these men were stationed in Aberdeen, Maryland. To deal with the everyday stress that being in the military entails, the men found themselves spending the majority of their free time playing poker. After playing that for several weeks, the men decided to switch over to a game they were less familiar with: blackjack. They took some time to discuss which set of rules they would use, as many people had played slightly different versions of the games in the past.

While Roger Baldwin listened to the other men talk about what set of rules would be appropriate, he started to think about how knowing the dealer's limitations would make it possible to calculate accurate probabilities of how likely a player is to win or lose depending on the cards in their hand. Robert Baldwin had his Master's Degree in Mathematics from the University of Columbia at the time, so if anyone could calculate these probabilities, it would be him.

The team finally agreed to use the rules followed by most Las Vegas casinos; the dealer would stand on 17 but must hit on 16. Now knowing this information, Baldwin was curious about how he would go about calculating these probabilities. He took a piece a paper and started developing fundamental formulas, quickly realizing this task would not be something he could accomplish on his own.

He asked his Army Sergeant, Wilbert Cantey, if he could use the "adding machine" located on base during his free time. These adding machines can do the same types of functions as an average desk calculator. They were nothing fancy, but they would help speed up the process.

Cantey agreed to allow Baldwin to use the adding machines, if he was allowed to help with the calculations. Cantey spent the first few years of his life in seminary school, but he eventually got kicked out because he spent too much time hustling people at the card tables. Forced to change majors, he too decided to dedicate his college years to studying mathematics. He later became a mathematics teacher, whose favorite subject just happened to be statistics. Needless to say, he was the perfect person for the job.

Baldwin knew this project wasn't going to be easy, so not only did he have Cantey help him, but he sought the help of two other soldiers as well: Herbert Maisel and James McDermott. McDermott had a Master's Degree from Columbia University, so he was highly qualified to do the calculations. Although Maisel was still working on his degree at the time, he would later become a professor at Georgetown University and was still a huge asset to the group.

This whole process took a lot longer than any of these four men had anticipated. There were many instances where they wanted to give up, where they wanted to scratch everything they had and just start over, but they persevered through it all. In a little under two year's time, their work was finally complete.

## Playing Blackjack to Win: A New Strategy for the Game of 21

By 1956, the four men were ready to share their finished work with the world, publishing their findings in a journal of the American Statistical Association. This article was eleven pages long and was titled, "The Optimum Strategy in Blackjack." Less than a year later, the four men published a limited quantity of their book called, Playing Blackjack to Win: A New Strategy for the Game of 21.

Nowadays, people can purchase this book for about fifteen dollars, but back in the day the most expensive version of the book was a measly \$1.75. Although we have to take infatuation into consideration, we will point out the fact that many people weren't aware of all the benefits this book had to offer when it first came out.

"Chapter 10: Using the Exposed Cards to Improve Your Chances," would be considered the first legitimate blackjack card counting system ever published. It set the foundation for Thorp's revolutionary 10-count system. This early system didn't come without its flaws though, as critics would say that they overlooked the simple fact that tens and aces were more valuable to players than actual low cards.

This book was officially re-published in 2008, with some added features to make it even more of a classic. A new foreword was added to the book by the best-selling author, Edward O. Thorp, who used this book to write, Beat the Dealer. Arnold Snyder also added a new introduction for the book, as he's very thankful for the impact this book has had on the world of blackjack.

## Testing these Number for Accuracy

As mentioned above, Thorp based his book, Beat the Dealer, off of the Four Horsemen's initial calculations. Looking over these four men's work for the first time was an overwhelming experience, as the strategies they recommended were unheard-of. For example, they claimed that hard totals of 12 should be hit against 2 and 3 and that soft totals of 18 should be hit against 9 and 10 only. Normally, the opposite would be recommended.

To determine whether or not their strategies were accurate, Thorp plugged their calculations into the highly advanced computers at MIT. When it came to their advice on knowing when to hit or stand, their calculations were proven to be 100% accurate. They did make some minor errors when it came to their hard doubling and pair splitting strategies, but it would only have had a small negative impact on a player's overall winnings.

Even though their calculations set the necessary ground work for other card counting strategies, they would still be considered outdated today. This is because at the time they were working on their calculations, casinos only used a single deck for each game of blackjack. Since then, casinos have started using more decks to hinder these systems from working. It would be rare to find a casino that uses less than four decks a game nowadays.

## Inducted into the Blackjack Hall of Fame

The Four Horsemen were inducted into the Blackjack Hall of Fame at Max Rubin's 12th Annual Blackjack Ball. Three out of the four horsemen were able to make it to this esteemed event. Baldwin, Cantey, and McDermott made an appearance, but Maisel regrettably couldn't make it to Las Vegas that weekend, as he had to stay home to take care of his wife who was recovering from a recent surgery.

Upon receiving this award, Baldwin said, "I must confess that my knowledge of blackjack history had been limited and really only went through the first edition of 'Beat the Dealer.' I was amazed and very impressed at what had happened since." Baldwin went back to grad school after he retired from the military, eventually working in the applied statistics and data processing field until retirement.

Cantey shared, "It was an honor, in so many ways, to be able to use mathematics to figure out the game of blackjack." He spent the majority of his career doing confidential research for the government. He has since retired, and his health just isn't what it used to be. The doctors and his family both advised him to stay home that weekend, but he refused to miss out on this opportunity.

McDermott dedicated thirty-two years of his life working for IBM in market research and business planning after the book was published. "The Four Horsemen of the Apocalypse were death, famine, pestilence and war. Let's hope those are the names the gambling casinos give to you guys. Let's keep it going from here," he said to inspire the crowd that night.

The four men still get together on occasions to reminisce about the old days, and talk about how much has changed over the years. What makes these men unique is the fact that they did all of these calculations and research for educational purposes only, as not one of them ever used their techniques to take money from the casinos.

Article Details

Author: Nicole Miller
Updated: August 2016

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