history of games of chance

Astragali and lot-casting

The earliest randomising devices were animal ankle bones, which land in four distinguishable positions and appear in graves and gaming contexts across the ancient Mediterranean and Near East. Cubic dice follow, and by the classical period they are unremarkable objects. Alongside play, lot-casting served divination and the allocation of offices and property, and the two uses are hard to separate.

That double role matters, because it is the origin of a long ambivalence. A device that could assign an inheritance or select an official was not obviously frivolous, and legal treatment of gaming has carried the tension between chance as a social instrument and chance as a pastime ever since.

Lotteries as public finance

The number lottery in its recognisable form emerges in the Italian city-states, where drawing names or numbers to fill offices was adapted into a wagering format — the Genoese model, in which players stake on numbers drawn from a fixed pool. It spread across Europe because it solved a fiscal problem: it raised money from willing participants without a tax.

That fiscal logic has recurred continually. Public works, universities and civic building projects were financed by lotteries in many countries, periods of abuse produced prohibition, and fiscal pressure produced revival. The modern state lottery is a late chapter in a very old pattern rather than a new invention.

The founding correspondence

Probability as a formal subject begins in the middle of the seventeenth century, in an exchange between Blaise Pascal and Pierre de Fermat about the problem of points: how to divide a stake fairly when a game is interrupted before it finishes. The answer — divide it proportionally to each player's chance of eventually winning — required a way of counting future possibilities, and produced one.

Christiaan Huygens set the argument out systematically shortly afterwards and introduced expectation as an explicit quantity. Earlier, Gerolamo Cardano had written a treatise on games of chance built on his own experience, which went unpublished for a century. Once expectation existed, the house edge became computable — but the games had by then been profitable for a very long time without it.

The casino and the modern industry

Licensed public gaming houses appear in seventeenth-century Venice, and the nineteenth century produced the European spa casino, the destination resort built around games. Roulette in its modern form dates from this period, and the removal of the second zero on some wheels is a competitive decision from it — a rare case of a game's arithmetic being changed to attract custom.

Bookmaking developed separately, out of horse racing, as a business of pricing rather than counting. Machine gaming arrived at the end of the nineteenth century and was transformed twice: by electromechanical then electronic operation, and by the virtual reel mapping that decoupled displayed symbols from their probabilities. Each of those transitions widened the gap between what a game looks like and what it computes, and each of them is what the regulatory apparatus described in the next entry was built to close.