Picture a poker game in an army barracks in Maryland in 1953. Someone mentions that at Las Vegas blackjack tables, dealers follow fixed house rules, hitting on 16 and standing on 17. These limits shape the game’s pace, leaving little room for personal judgment. For visitors planning an evening around casino entertainment and local craft beer, understanding the rules can make it easier to balance time at the tables with a stop at a nearby brewery or taproom.
A private named Roger Baldwin, who held a master’s in mathematics, realised that a game with a fixed dealer could be solved. With three fellow soldiers and the base’s desk calculators, he did exactly that, producing the first accurate basic strategy for blackjack. Their 1956 work has held up remarkably well, and the clearest way to see it is to set it beside the strategy players use today.
Their 1956 Chart Against Today’s Basic Strategy
The four men analysed the single-deck game dealt on the Las Vegas Strip in the 1950s. Blackjack author Arnold Snyder later checked their book against modern basic strategy for that game and called it devastatingly accurate. The comparison below covers the key decisions he examined:
| Situation | 1956 advice | Verdict today |
|---|---|---|
| Hit and stand decisions overall | Full chart for hard and soft totals | 100% accurate for the single-deck game, according to Arnold Snyder |
| Hard 12 against a dealer 2 or 3 | Hit | Correct |
| Soft 18 against a dealer 9 or 10 | Hit, and only against those cards | Correct |
| Pair of 8s against a dealer 9 or 10 | Split | Correct, and one of their most surprising findings |
| Hard 8 against a dealer 5 or 6 | Do not double | A borderline double in single-deck games |
| Pairs of 2s or 3s against a dealer 2, and 3s against a 3 | Split | Correct only where doubling after a split is allowed |
| Player’s overall expectation | Estimated at -0.62% | Thorp’s computer work put it at -0.21% for a complete deck |
The overall expectation shows where hand calculation reached its limits. Baldwin and his colleagues estimated the player’s disadvantage at 0.62%, while Edward Thorp’s computer work at MIT later put the figure for a complete deck at 0.21%, largely by removing approximations the soldiers had been forced to make.
How Four Soldiers Got There
Baldwin secured permission from Sergeant Wilbert Cantey to use the adding machines at Aberdeen Proving Ground. Privates Herbert Maisel and James McDermott joined the research team. Baldwin and McDermott held master’s degrees from Columbia, Cantey had left seminary to study mathematics, and Maisel had no college degree. Known as Preach, Cantey had reportedly left the seminary partly because of his gambling activities at pool and cards.
Over 18 months, the four men analyzed blackjack hands during their free time. Their findings appeared in a statistical journal in September 1956. The following year, they published Playing Blackjack to Win, a 92-page book priced at $1.75 with an introduction by quiz-show celebrity Charles Doren. All 5,000 copies of the first printing sold, but McDermott earned just total royalty income of $23, according to the Las Vegas Sun. Baldwin’s conclusion was that the casino still held the long-term advantage.
Why Their Logic Still Works Online
The concept of basic strategy is simple: if the dealer is dealt with in a certain way, then there is a best answer that every player’s decision can be worked out. The same concept applies to software blackjack, where the dealer plays according to a set of instructions and the cards are dealt from a virtual shuffled shoe.
The rulebook will change from table to table, and the changes will add up to move the house edge more than most players realize. A 6:5 payoff to blackjack, instead of 3:2, takes about 1.4 percentage points; allowing doubles after a split takes about 0.15 back; and giving a dealer soft 17s takes about 0.22 back.
Deck count is important as well, with a single-deck game having about 0.6 points more house edge than eight decks of the same game under the same rules. Each blackjack table of an online casino, like crusino, has a set of rules that indicates what the casino pays on the natural, if the dealer stands on soft 17 or not, and if doubling after splitting is permitted. Those details determine the version of the strategy chart that is in use prior to any card being dealt.
The Errors, and Why They Barely Matter
Snyder’s review found that the soldiers made few mistakes, and most were narrow misses even by today’s standards. This attention to detail also highlights the value of precision in craft brewing, where small adjustments to fermentation temperature, ingredient ratios, or timing can influence the final beer.
- Hard doubling: they did not advise doubling 8 against a dealer 5 or 6, a borderline play that only pays in single-deck games.
- Soft doubling: they missed a few soft doubles, which Snyder judged minor in dollar terms.
- Pair splitting: three of their splits with 2s and 3s are correct only when doubling after a split is allowed.
- Card counting: their counting method did not recognise how strongly tens and aces favour the player, and it offered no betting advice.
- The expectation: their 0.62% estimate of the player’s disadvantage was roughly three times Thorp’s later computer figure.
Snyder estimated that a player using their strategy would give up only a very small percentage margin against perfect basic strategy. For calculations done by hand in an army barracks, that margin is astonishingly small.
From Their Notebooks to Beat the Dealer
The bigger legacy came through Edward Thorp, a young mathematician who borrowed the four men’s notebooks and checked their findings on an IBM 704 at MIT. His 1961 paper, A Favorable Strategy for Twenty-One, confirmed how close they had come and pushed the analysis further.
The soldiers had already published a counting method in their 1957 book, which Snyder called the earliest published card-counting method proven effective for casino blackjack. It adjusted 16 plays based on recently seen tens and low cards, but it was too weak to tip the game in the player’s favour.
Thorp built counting systems strong enough to do that and tested them in Las Vegas, often with Claude Shannon. Beat the Dealer, published in 1962, sold more than 700,000 copies and pushed many casinos to change their rules, most of which were later restored. As Thorp put it years afterwards, the soldiers did not realise the game was really beatable.
Recognition Fifty Years Late
For decades the four men were little known outside blackjack circles. Allan N. Wilson nicknamed them the Four Horsemen of the Apocalypse in a 1965 book on casino gambling, and the name stuck among card counters. When McDermott found their names on gambling websites many years later, he emailed Snyder, who was astonished that all four were still alive. Max Rubin’s annual Blackjack Ball in Las Vegas honored them with a place in the Blackjack Hall of Fame on January 4, 2008. The book’s 50th-anniversary edition was subsequently published with a foreword by Thorp.
Cantey had to persuade his family and his doctor to let him travel, and Maisel stayed home to care for his wife after surgery. Baldwin said he was amazed and very impressed by how far the field had come since their barracks calculations. Their working lives had taken them far from the barracks, with Cantey becoming a government statistician, Maisel chairing Georgetown’s computer science department and McDermott spending more than three decades at IBM. Cantey died later in 2008, McDermott in 2018 and Maisel in 2019. Baldwin, the last of the group, died in January 2021 at the age of 91.
Understanding Blackjack Rules
Blackjack’s basic strategy was worked out years before computers were used to solve the game of blackjack, and the game is still essentially the same today on most hands. They made a few mistakes, but just hundredths of a percent, and their notebooks provided Thorp with the basis for card counting.
The take-away is that strategy can help lower the house edge, but can’t eliminate it, and table rules are as important as personal ones. If you’re heading to Las Vegas for a night out playing with blackjack and microbrews, budgeting for your entertainment is the perfect way to make it enjoyable and balanced. Online/offline players can also reach out to Gambling Help Online for free and confidential assistance when gambling starts to have an impact on their finances and/or well-being.
FAQ
How accurate was the Four Horsemen’s basic strategy?
Remarkably so, since Arnold Snyder found their hit and stand decisions matched modern strategy and estimated that their few errors cost only just a very small percentage margin point.
Did the Four Horsemen invent card counting?
They published the first valid card-counting method in 1957, but it was too weak to give players an edge. Edward Thorp built on their work to create far stronger systems in Beat the Dealer.
Does basic strategy beat the house?
No, basic strategy only minimises the house edge under a given set of rules. Beating the game over time requires card counting or unusually favourable rules.
