Roger Baldwin was an Army private in 1953 playing blackjack in the barracks at the Aberdeen Proving Ground in Maryland when another serviceman said something that piqued his curiosity: that dealers at casinos in Nevada were required to draw a card when their hands totaled 16 or less, but that they could stick with their hands at 17.
The rule was more than a morsel of knowledge for Mr. Baldwin to pack away for a future trip to Las Vegas. For him, who had earned a master’s in statistics from Columbia University that year, it was the spark to devise a new strategy to win at blackjack.
“After learning that the dealers had a fixed strategy, I thought maybe we could beat this game,” Mr. Baldwin later recalled.
The strategy, which was conceived by Mr. Baldwin and three Army friends, turned out to be a game-changer. It led Edward O. Thorp, a mathematics professor and blackjack expert, to validate their calculations on an IBM 704 computer at the Massachusetts Institute of Technology and to write the best-selling 1962 book, “Beat the Dealer: A Winning Strategy for the Game of Twenty-One,” which helped bring the Army group to public renown.
Mr. Thorp recalled the influence of the men’s strategy in his 2017 memoir, “A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market.” “The Baldwin group,” he wrote, showed that the advice of the reigning experts was poor, unnecessarily giving the casinos an extra two percent advantage.”
Arnold Snyder, a renowned author of blackjack books, said by phone: “No one actually knew what the right strategy was because it hadn’t been calculated. They figured out what to do if your hand totals 15 and the dealer has an 8 up: do you hit or do you stand?”
Mr. Baldwin died on Jan. 10 at his home in Riverhead, on Long Island, his daughter, Deborah Baldwin, said. He was 91. He was the last surviving member of the quartet that became known to blackjack aficionados as the “Four Horsemen of Aberdeen.”
Roger Rauschenbusch Baldwin was born on Nov. 22, 1929, in Manhattan. His father, Stephen Raushenbush, was an economist; his mother, Evelyn (Preston) Raushenbush, was a social reformer and union activist. When they divorced, she married Roger N. Baldwin, the founder of the American Civil Liberties Union, who adopted Roger and his brother, Carl.
Mr. Baldwin grew up in a townhouse in Greenwich Village; graduated from Cornell University with a bachelor’s degree in 1951 and received his master’s from Columbia before entering the Army.
In the age before the personal computer, he started his blackjack theorizing modestly, working out some formulas on his own for a few months before collaborating with three other soldiers with mathematical backgrounds — Wilbert Cantey, Herbert Maisel and James McDermott.
For the next 18 months they spent their free time — a thousand man-hours by their count — using Army desk calculators with the goal of optimizing a blackjack player’s odds of beating the dealer’s hand without going over 21 — the object of the game.
Using probability theory, they focused on essential aspects of blackjack, all in pursuit of a practical, statistically sound strategy that would help players figure out what to do when they saw the dealer’s upcard, his exposed card.
The group’s numbers-crunching underwent some adjustments after Mr. Baldwin made a weeklong field trip to Las Vegas in June 1954 to watch blackjack being played in 16 casinos.
The Baldwin group unveiled their research in the Journal of the American Statistical Association in September 1956. Of the casino games poker, roulette, craps and blackjack, they wrote, “blackjack is by far the most neglected in the scientific literature of gambling.”
Referring to the rules about dealers that had aroused Mr. Baldwin’s interest, they added: “The fixed and known nature of the dealer’s strategy is vital in reducing the mathematical and computational problems in analyzing blackjack to manageable proportions.”
A year later, the group expanded the article into a book, “Playing Blackjack to Win: A New Strategy for the Game of 21,” with a foreword written by Charles Van Doren, a friend of Mr. Baldwin’s who had won $129,000 on the television quiz show “Twenty-One,” which was based on blackjack. Mr. Van Doren would later admit that the show was rigged and that he had received questions and answers in advance.
In the foreword, Mr. Van Doren wrote: “I only hope the dealers in Las Vegas don’t start changing the rules to cope with the new crop of blackjack players descending on them with copies of ‘Playing Blackjack to Win’ sticking out of their pockets.”
The book did not sell well but was reissued in 2008, with help from Mr. Snyder, the blackjack author.
In addition to his daughter, Deborah, Mr. Baldwin is survived by three other daughters, Lauren and Geraldine Baldwin and Carole Ann Geronimo; 12 grandchildren; and two great-grandchildren. His wife, Patricia (Devine) Baldwin, died in 1986; his daughter Susan died in 1998, and his son, Roger Jr., died in 2017.
Mr. Baldwin did not profit much from his blackjack work and did not become a Las Vegas habitué. Rather, he was a systems administrator for Union Carbide, Brookhaven National Laboratory on Long Island and the City of New York.
But his group’s contribution to gambling did not go unnoticed.
In 2008, Mr. Baldwin, Mr. Cantey, Mr. McDermott and Mr. Maisel were inducted into the Blackjack Hall of Fame.
At the time, Mr. Baldwin admitted that he had paid little attention to blackjack in decades. He told The Tech, the campus newspaper of the Massachusetts Institute of Technology, that his knowledge of the game had “ended with the first edition of ‘Beat the Dealer.’”
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