Oddsmaking is an important aspect of gambling. Even the earliest dice players could figure out that the probability of a six being thrown on cube-shaped die was 1-in-6, or perhaps slightly higher or lower if the die were lopsided. But how did 14th century bet-takers calculate 10-to-1 odds on the acquittal of King Henry VIII’s wife, Anne Boleyn, and her brother when they were put on trial for treason and incest? Until the 16th century, predicting the likelihood of events was much more of an art than a science. Mathematics had yet to catch up.
In the mid-1500s, an eccentric Italian gambler named Girolamo Cardano wrote several treatises on probability as it applies to games of chance, covering dice, cards, backgammon and even astragali. Between 1613 and 1623, astronomer Galileo Galilei was commissioned by his Tuscan patron to write a paper on the odds related to throwing three dice. Later in the 17th century, mathematical giants no less than Blaise Pascal and Pierre de Fermat (the inventor of calculus) would turn their genius to solving problems concerning dice and coin flips.
In less than a century, mankind’s study of probability theory erupted into a full-blown science. Luminaries from the Netherland’s top physicist Christiaan Huygens to France’s math scholar Pierre Rémond de Montmort and Switzerland’s numbers maven Jakob Bernoulli leapt at the opportunity to pen books on games of chance. And a hungry public lapped them up, particularly “professional” gamblers who, until the 17th century, had been largely “going with gut instinct” when wagering.
With new math to show the way to winnings, mercantile gambling emerged. Unlike social gambling, it was a serious business, conducted for profit, not just for fun. Using the newly available knowledge of gaming odds, an enterprising fellow could set up a table with some dice, draw a crowd, offer odds, and expect to walk away with more money than he started out with, almost every single time.
On a larger scale, organisations could make use of the new understanding of odds, too. Lotteries had been around since Roman times, but in the 16th and 17th centuries, they proliferated. Suddenly churches were using prize drawings to raise funds. In Belgian, Holland, and northern France, money, gold and jewelry were offered in lottery draws.
In Italy, in particular, merchants saw lotteries as an opportunity to get more for their goods. Why sell a carpet for several hundred ducats, when a thousand potential buyers could be found to part with one ducat each for a chance at winning it? The Rialto district of Venice quickly went mad for these types of drawings, which in turn led to another modern aspect of gambling—government regulation.
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