The seventeenth century mathematician and physicist Blaise Pascal invented the world’s first digital calculator, experimented with creating an artificial vacuum, and was an early student of projective geometry (which is concerned with such projections as a globe onto a flat plane), but he is mostly remembered today for his triangle (an immensely pattern-laiden representation of binomial coefficients) pioneering work on gambling. Among other things, Pascal is often credited with inventing the game of roulette. The origins of roulette are murky, but it’s at least possible; Pascal’s final work as a mathematician was on the cycloid, the curve formed by a point on the rim of a circle as it rolls, and he was one of the first modern mathematicians to seriously study probability. Along with Fermat (of Last and Little Theorem fame), Pascal solved the "problem of points": how to divide up a pot between two players if the game ended early. This, along with his work on the dice problem (how many times do we expect to roll of a pair of dice before we get a given combination?) laid the foundation for the scientific study of probability. All sorts of questions about dice began to fall to mathematicians as they learned more about probability and Gaussian distributions.

Dice bets were relatively complex; Samuel Pepys needed to consult Isaac Newton to get a sense of the odds on one that he had thought of. Roulette, on the other hand, is about as simple as a game of chance can get. A wheel is divided into 38 slices; each one is given a number (1 through 36, 0, and 00) and a color (the non-zero numbers are evenly divided into red and black; zero and double zero are green). The wheel is spun, and then a small ball is spun along the wheel in the opposite direction. Eventually it comes to a halt in one of the numbered divisions. Bettors can bet on red or black, high or low, even or odd, and be paid even money, giving the house a 2 in 38 edge, as the even-money bets lose on zeros and double zeroes. (Louis Blanc introduced the "European wheel", which lacks the double zero and thus offers better odds; the bettors attracted to Blanc’s wheel built the gaming industry in Monte Carlo.)

Roulette is not a game for winners; Einstein purportedly said that the way to win at roulette was to figure out how much you’d bet on the game over the course of your entire life, put it all down at once on one bet, and pray. Unless you’re one of a bunch of physics geeks who think you can use predict the physics of roulette (using a computer built into a shoe) like the Santa Cruz grad students featured in Thomas Bass’ The Eudaemonic Pie, the longer you play, the more likely you are to lose your shirt. The house edge is relentless.

If two players, with different amounts of money, are betting the same amount of money at a game time after time, what are the odds that player A will run out money first? And what are the odds that player A will have run out of money in a certain number of hands? This is known as the "gambler’s ruin" problem. When one player has both an advantage at the game and vastly more resources than the other, the odds of the richer player being "ruined" are vanishingly small. The man who broke the bank at Monte Carlo was exploiting a physical flaw in a wheel; Charles Wells, who won a million pounds through repeated winning bets, later lost it all and died impoverished.

Perhaps at the end Wells remembered Pascal’s final contribution to the world of gambling. After a brush with death (in a carraige accident), Pascal spent much of his last decade of life doing good works, defending Jansenism, and writing about religion. In his Pensées, he laid forth Pascal’s Wager: since if God exists, belief will be infinitely rewarded and unbelief infinitely punished, and if God does not exist, neither the believer nor the unbeliever will be rewarded, one must logically attempt to believe. Blaise Pascal died of cancer at the age of 39; his epitaph reads, in part, "He tasted good and bad fortune, that he might be known in every thing for what he was," a gambler to the last.