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Casino – How Mathematicians Help Casinos Succeed

Casino is one of Martin Scorsese’s finest works and arguably the most realistic portrayal of gambling in modern history. Unlike other movies that depict Sin City, it digs beneath the shiny varnish of flashing lights and free cocktails to expose an intricate web of corruption that had its tendrils reaching into the worlds of politicians, Teamsters unions, Chicago mob mafia members, and more. The movie is based on the non-fiction book Casino: Love and Honor in Las Vegas by Nicholas Pileggi, who co-wrote the screenplay with the director.

While casinos are opulent places of glitz and glamour, they’re also engineered to slowly bleed their patrons of money. To that end, they rely on mathematics and game theory to ensure their profits. For years mathematically inclined minds have tried to turn the tables, using knowledge of probability and game theory to exploit weaknesses in the rigged system. Physicists have been especially adept at this, and the resulting work has helped shave billions of dollars off the house edge of games like blackjack and Spanish 21.

As a result, casinos employ gaming mathematicians and analysts to help them calculate the probabilities of winning or losing, as well as their respective variances. These are the underlying numbers that allow a casino to make calculated decisions about which machines to put out on the floor, how much cash to keep in reserve, and whether or not to offer certain bonuses. These numbers are crucial for the health of a casino and can make or break its profitability.