Most of the article was filled with mathematical notations, the sort of longhand formulas typical in an era when a single computer would fill an entire room and statisticians did calculations on slide rules.

Nobody knew at the time, but that arcane little treatise would rattle a multi-billion-dollar industry.

Once upon a time there was no card counting and no basic strategy. Blackjack players made choices intuitively, or they followed "expert" advice that was generally incorrect. Players lost a lot of money making bonehead moves like splitting tens. And casinos cleaned up on games that (we would find out decades later) were mathematically beatable.

These days, some players still make bonehead moves, but people who study the game know that blackjack has an optimal strategy. In fact, we tend to take that strategy for granted, as if it’s always been around and as if the moves are obvious. Card counting and other "overlay" tactics (used in conjunction with basic strategy) dominate most strategy discussions.

But splitting 8-8 against a 9 or 10 is not intuitive, nor is doubling on soft 15 against a 5. These are just two out of dozens of novel moves that were discovered when basic strategy was developed. Indeed, it’s helpful to take a closer look at basic strategy, particularly its history and the writings of its creators, because that material can help us better analyze and understand the game today.

Roger Baldwin, Wilbert E. Cantey, Herbert Maisel, and James P. McDermott were four soldier-mathematicians who worked at Aberdeen Proving Ground in Maryland during the early 1950s.

Baldwin was a private. One night he was playing blackjack with some friends, and as the cards were being dealt, Baldwin had a revelation. He realized that the game is theoretically beatable when the dealer’s moves are predictable (as they are in the casino version of the game). The inquisitive soldier decided to solve the strategic riddle. At first, he tackled the mathematics problem on his own, but he was quickly overwhelmed with its complexity. Baldwin needed a calculator, a rare commodity in those days (back then it was called an "adding machine"). So he asked Cantey, a sergeant at the proving ground, to let him use one of the army’s calculators. Cantey wanted an explanation for the favor, and the story tumbled out. The sergeant was intrigued. He decided to work on the problem, too.

Cantey brought McDermott and Maisel onboard, and soon the four mathematicians were spending nights and weekends trying to crack the secret of blackjack. It took them a year and a half. And what they discovered then, still defines the game.

Of course, if you’re a blackjack professional and you live the contest every day, then you’re always thinking about these issues. But if you’re a semi-pro or a casual player, this wisdom from across five decades has particular value.

For example, quoting from "The Optimum Strategy in Blackjack" on the very first page:

"… in selecting a variation of the game of blackjack for analysis, the best that could be done was to consider rules that were common but not universal."

In other words, rule variations in the game were a substantial issue at the beginning. And they still are to this day. After five decades of research and refinements, some players still incorrectly play a strategy optimized for one set of rules on a game with different rules. Be honest, you’ve probably done this a few times yourself just for the sake of convenience. Of course, the sky won’t fall if you use an incorrect strategy for a few hours, but if you’re going to play a game regularly, then it pays real money to study that particular game and know the optimal moves. Consider the difference between doubling on an 11 against an ace. You should do it if the dealer hits soft 17 in a multiple-deck game (four or more decks). But don’t do it if the dealer stands on soft 17. One bet has a positive expectation, and the other is a pure gamble.

Here’s another point that involves doubling. The article says, "The fact that the player should double down so frequently may surprise many people… One may even go so far as to say that doubling-down is the most neglected, under-rated aspect of blackjack strategy."

This is pure strategic poetry! Doubling situations are always long-term profitable. You must correctly double down as per basic strategy if you want a long-term chance of beating the casino.

More wisdom: "The most surprising aspect of the optimum strategy for unique hands is the low value of M(D) (hands that should not be hit when the dealer shows a 6 or less)… Also unexpected is the great "discontinuity" in M(D) as D (the dealer’s hand) goes from 6 to 7. "

Essentially, they’re saying that everything changes dramatically when the dealer’s hand shows 7 or more. This is sage wisdom. It’s the fulcrum upon which most good players hang their visualizations of the contest, and the "decision tree" of basic strategy. If the dealer shows 7 or more, then it’s a whole other ball game.

One more example:

"The detailed strategy for splitting nines, sevens, sixes, fours, threes, and twos probably defies the intuition of even the most experienced players."

These are the nuts and bolts of basic strategy. When you play these hands correctly, you squeeze out extra profit (or lower your potential loss) in ways that makes long-term winning possible.

Ironically, few people noticed or understood the importance of basic strategy when it was first introduced, and a subsequent book on the subject by the four mathematicians (published in 1957) was mostly ignored. It wasn’t until Edward O. Thorp’s book Beat the Dealer came out in 1962 that players and casino owners realized the significance of basic strategy. Thorp explained and expanded on the original basic strategy, and he introduced the advanced strategy of counting cards. This triggered substantial changes in the game, which substantially changed basic strategy into basic strategies designed for a plethora of variations.

So blackjack these days is very different from the contest back in 1950.

I will leave you with one poignant example. In 1950s Las Vegas, blackjack was always dealt from a single deck, and it was not uncommon for a dealer to play out the deck to the very last card. Wow!

Think about the profits you could have made playing those games with a modern strategy. It’s nice to imagine!