The Four Horsemen of Aberdeen

The first mathematically correct blackjack strategy was not produced by a professional gambler or a computer. It was worked out on mechanical desk calculators by four US Army enlisted men at the Aberdeen Proving Ground in Maryland and published in September 1956 in the Journal of the American Statistical Association. Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott, later nicknamed the “Four Horsemen of Aberdeen”, gave the game its first basic strategy and gave Edward Thorp the foundation for Beat the Dealer.

Who they were

All four were serving in the Army in the early 1950s. The Wikipedia article on the group records that Baldwin was stationed at Aberdeen Proving Ground, the Army’s oldest active proving ground, where the others also worked. Las Vegas Advisor’s account says they met there as enlistees in the early 1950s. They had mathematical training rather than casino experience: Cantey went on to a career as a statistician, Maisel later chaired the computer science department at Georgetown University, and McDermott spent 33 years as an IBM executive.

The question they took on was tractable but enormous: with 52 cards, ten distinct dealer upcards, a dealer who must draw to 17, and player options to hit, stand, double and split, the number of cases to evaluate ran into the hundreds of thousands. Nobody had evaluated them; the “right play” for most hands was folklore.

How they computed it

They had no computer. The group used the desk calculators on the base, machines that the Las Vegas Advisor article describes as “crude mechanical calculators” that “used to be called ‘adding machines’”. The work meant tabulating the dealer’s probability of reaching each final total from each upcard, then the player’s expectation for standing, hitting, doubling and splitting with every starting hand against every upcard.

Hand computation forced approximations. The dealer’s drawing sequence and the effect of removing the player’s cards from the deck could not be followed exactly across every branch, so some expectations were estimated rather than enumerated. Those shortcuts explain the small errors later found in their doubling and splitting recommendations. The hit-or-stand table, which carries most of the value of basic strategy, came out right.

What they produced was a complete, total-dependent strategy: for each player hand and dealer upcard, the action with the highest expected return. It is recognisably the same chart a player learns today. The method, choosing the action that maximises expectation given the dealer’s fixed rules, is exactly the method still used; see how basic strategy is derived.

The 1956 paper

The bibliographic record held by Crossref gives the details:

Publishing in a statistics journal rather than a gambling magazine mattered. It put the strategy on the record with its derivation, where mathematicians could check it. One of them did.

Playing Blackjack to Win (1957)

The journal paper was not written for players, so the following year the four produced a popular version, Playing Blackjack to Win, published by M. Barrows & Co. in 1957 with a foreword by Charles Van Doren. The Wikipedia article records that the 5,000-copy print run sold out and that the book was reprinted in 2008 with a foreword by Thorp. Arnold Snyder notes that original copies are scarce because the “plastic spiral binding and the cheap pulp paper have not held up well”.

The book contained more than the strategy. Snyder points out that its chapter on “partial casing”, adjusting play according to cards already seen, is the first published card-counting idea, five years before Beat the Dealer. He also calls the method “very crude” and says it “simply wasn’t much of a winner”. The idea that deck composition changes correct play was there; the machinery to exploit it was not.

How accurate was it?

Snyder’s assessment, in the Las Vegas Advisor piece, is the clearest published verdict:

When Thorp re-ran the calculations on an IBM 704 computer he confirmed the structure of the strategy and corrected the details. The original paper also reported an estimated house edge for a player following its strategy; the exact figure is not reproduced here because it depended on the paper’s approximations and was superseded by Thorp’s and later computer results. Under the six-deck, dealer-stands-on-soft-17, double-after-split, no-surrender game our strategy chart assumes, correct basic strategy gives a house edge of roughly 0.4% (BlackjackInfo’s rule table lists 0.44% for six decks with S17, DAS and no surrender), a figure from modern computation rather than from the 1956 paper.

Thorp’s acknowledgement

Thorp has never been shy about the debt. The Wikipedia article quotes him: “To paraphrase Isaac Newton, if I have seen farther than others it is because I stood on the shoulders of four giants.” He inscribed McDermott’s copy of Beat the Dealer: “Thanks for your paper, which ultimately led to this book.” Las Vegas Advisor’s account says Thorp credits the four as “the impetus for his own research into the game”. Thorp’s own story continues in Edward Thorp and Beat the Dealer.

Recognition and later lives

For decades the four were a footnote. That changed when researchers connected with the Blackjack Ball discovered all four were still alive. On 4 January 2008, at Max Rubin’s 12th annual Blackjack Ball in Las Vegas, they were inducted into the Blackjack Hall of Fame as a group; the Hall’s members page lists “Roger Baldwin, Wilbert Cantey, Herbert Maisel & James McDermott (‘The Four Horsemen of Aberdeen’)” under 2008. The Wikipedia Hall of Fame article notes the group was voted in at the end of 2007 and inducted at the January 2008 Ball, which is why some sources give either year.

Baldwin was the last survivor. The dates and careers are from the Wikipedia article on the group.

Why it still matters

Basic strategy is the base layer of everything else in blackjack: card counting adjusts it, composition-dependent exceptions refine it, and rule changes shift a few of its decisions. The Four Horsemen established that the base layer could be computed rather than guessed, and that a player who followed it faced a house edge well under 1% instead of the several percent that intuitive play gave up. Every chart since, including the one in our trainer, is a descendant of nine pages in a 1956 statistics journal.

Related reading

• History of blackjack
• Edward Thorp and Beat the Dealer
• How basic strategy is derived
• Basic strategy