"The Tug of the Newfangled Slot Machines," by Gary Rivlin. The New York Times Magazine, 9 May 2004.
Although the article doesn't dwell on the mathematics behind slot machines, it does note that Anthony Baerlocher, chief game designer at International Game Technology of Reno (I.G.T., the country's largest maker of slot machines), was "trained as a mathematician." Slot machines are the number-one revenue generator in casinos and are the country's most profitable form of adult entertainment. "Today's slot machines feature well-choreographed illusions designed to hide a fundamental truth: at heart they're really nothing more than computers whose chips randomly cycle through hundreds of thousands of numbers every second. A player's fate is determined almost the instant play begins. But to simply display a long string a numbers on a computer screen, along with an accounting of money won or lost, would hardly prove entrancing." So Baerlocher and others at the company witness and analyze slot machine addiction and use probability models---"infrequent random reinforcement, or 'intermittent reward'"---to hook and periodically reward slot machine users. Most of I.G.T.'s development costs are devoted to the glitzy sounds, design, graphics and video effects of the machines. The core team that develops a game consists of Baerlocher, a junior mathematician, and computer programmers. As Baerlocher says, "There are two basic elements to any slot machine: the art and the math."
--- Annette Emerson