Beneath flashing lights and free drinks, casinos stand on a bedrock of mathematics engineered to slowly bleed patrons of their cash. For years mathematically inclined minds have tried to turn the tables, using knowledge of probability and game theory to find ways to beat a rigged system.

Casinos make their money by taking a percentage of all bets made on games that do not require skill, such as roulette and slot machines, or from a percentage of the pot in poker. This revenue is known as the house edge. A casino’s house edge varies with the rules of the game, the number and type of decks used, and other variables. In addition, some casinos earn a commission from high rollers, charging an hourly rate for the use of their tables.

Because casinos have a virtual assurance of gross profit, they frequently offer big bettors extravagant inducements. These may include free spectacular entertainment, luxury hotel rooms and transportation, reduced-fare transportation, and even casino-provided living quarters. Casinos also employ techniques to prevent cheating and theft. Chip tracking systems allow them to oversee bets minute-by-minute, and roulette wheels are electronically monitored regularly to discover statistical deviations from their expected results.

Many American casinos have incorporated traditional Far Eastern games, including sic bo (which became a major hit in Europe during the 1990s), fan-tan and pai gow. In addition, some casinos have added games of local interest, such as two-up in Australia, boule and trente et quarante in France, and baccarat in the United Kingdom.