A note on what is known
The history of game strategy is full of colorful stories, and many of them are told with more confidence than the evidence allows. This article sticks to developments that are well documented and says less where the record is thin. Games themselves are very old, and people have played with dice and tokens for thousands of years, but we know little about how ancient players thought about their choices. Systematic written analysis comes much later.
Early writing on dice and cards
One of the earliest known works on the mathematics of games is by the Italian physician and scholar Gerolamo Cardano. He wrote a treatise on games of chance in the sixteenth century, usually dated to around the 1560s, though it was not published until 1663, after his death. In it he reasoned about the number of ways dice can land and compared favorable and unfavorable outcomes. His work contains errors and uneven passages, but it shows an attempt to count possibilities rather than rely on superstition.
The idea that outcomes could be counted systematically is the root of everything that followed. It separated two things that had been tangled together: what the dice do, which is random, and what a player chooses to do, which is not.
Pascal, Fermat and the problem of points
A commonly cited turning point is a correspondence in 1654 between the French mathematicians Blaise Pascal and Pierre de Fermat. They worked on a puzzle about how to fairly divide the stakes of an interrupted game, known as the problem of points. Their solution rested on considering all the ways the game could have continued and giving each player a share that matched their chances. That reasoning is an early form of what we now call expected value.
Shortly afterward, the Dutch scientist Christiaan Huygens published a short book on reasoning in games of chance, in 1657. It was widely read and helped spread the new approach. Later in that century and the next, Jacob Bernoulli’s posthumous Ars Conjectandi, published in 1713, and Abraham de Moivre’s The Doctrine of Chances, first published in 1718, carried the subject further. De Moivre’s book was written with gamblers in mind and set out methods for calculating odds.
None of this made games easier to beat. What it did was give people a vocabulary for understanding why some bets and plays cost more than others. Games with a built-in disadvantage for the player stay that way, however well they are understood. Knowing the house edge explains the cost of playing; it does not remove it.
Game theory and the study of opponents
Dice and roulette involve no opponent who responds to you. Many games do, and analyzing those required a different set of tools. In 1928 John von Neumann proved a minimax theorem for two-player zero-sum games, and in 1944 he and Oskar Morgenstern published Theory of Games and Economic Behavior. In 1950 John Nash introduced the equilibrium concept that bears his name.
For card games like poker, these ideas matter because the best play often involves randomizing between options, so that opponents cannot easily exploit a fixed pattern. This is the core of game theory as players meet it. The history here is of mathematics gradually being applied to games with hidden information and competing decisions, rather than to simple chance.
Blackjack as a case study
Blackjack is a well-documented example of how analysis changed a game. In 1956, a group of US Army researchers published a paper describing a computed basic strategy for the game. Then in 1962, the mathematician Edward Thorp published Beat the Dealer, which explained how card counting could, under particular conditions, shift the odds because the cards remaining in the deck change as play goes on. The mathematical reason why card counting is possible is that cards already dealt are not replaced.
Casinos responded by changing procedures, such as using more decks and shuffling earlier, and by excluding players they suspected of counting. The episode is useful as history because it shows both sides: analysis revealed a real mathematical feature, and the environment then adapted. It is not a recommendation. Counting is difficult, casinos can refuse play, and most players who try informal methods will not overcome the built-in house edge.
Computers and solved games
From the late twentieth century, computers began to reshape strategy in games of perfect information and later in those with hidden information. A few well-documented milestones:
- In 1997, IBM’s Deep Blue defeated the world chess champion Garry Kasparov in a match.
- In the early 1990s, Gerald Tesauro’s TD-Gammon program, which learned largely by playing against itself, reached a strong level at backgammon.
- In 2016, DeepMind’s AlphaGo defeated the professional Go player Lee Sedol.
- In 2015, researchers at the University of Alberta reported that heads-up limit Texas hold’em, a particular two-player poker variant, had been essentially solved. Later programs, such as Libratus in 2017, played top professionals in heads-up no-limit poker over a large number of hands.
These results mattered less as announcements about machines and more as sources of new ideas. Players studied unusual moves and revised long-held beliefs about what was sound. They also showed that even in games with hidden information, strong play is a matter of balanced strategy rather than guesses.
What the long view suggests
Across these developments the pattern is consistent. First people noticed that chance has structure. Then they learned to separate what is random from what is chosen. Then they began to model opponents and, eventually, to build machines that could search or learn good play. Each step turned some part of a game from mystery into something that could be studied.
What did not change is that chance remains chance. Better understanding changes how you decide, not the odds in games designed with a house advantage. Gambling can be harmful, and no historical development turns it into a reliable source of income. If it is becoming a problem, a local support service can help.