Mathematics in gambling and casino games

Mathematics in Gambling, Casino Games

An Examination of the Ways in Which Mathematics are Used in Gambling and Casino Games Today

Introduction common misperception exists among many gamblers that the odds are somehow with them after a series of several losses at a slot machine, or that a seven might be more likely to come up on the roll of the dice if one has not been rolled in awhile. Gaming machines and dice, though, do not have a memory and it is impossible to predict what the next outcome of these types of gaming event might be based on the previous outcomes. Despite these constraints, there are some casino games that offer better odds of winning than others and in some of these, the careful application of mathematics can help the gambler achieve even more successful outcomes. This paper provides an overview of casinos and casino games and a discussion of vigorish, or the amount of advantage the house has over the gambler. An analysis of how mathematics and statistics can be used to further improve these chances is followed by a summary of the research in the conclusion.

Review and Discussion

Background and Overview. The casino of the 21st century may also be called a gambling, or gaming, house or club; these are places where people can risk their money against a common gambler, known as "the banker," or "the house." Casinos around the world have an almost a uniform character (Casinos 2004). According to Barker and Britz (2000), casinos are able to calculate their handle for slot operations because the revenue accounting of the win-to-handle ratio is accurately known. Drop and handle are frequently confused terms; however, there is an important distinction between the two. "Handle is the total amount wagered, or bet: A chip may be wagered (bet) many times before the game goes to a decision and the chip is won or lost" (Barker & Britz 6). Video gaming machines are set to report the coins/cash going in and the coins or payouts going out; however, the handle for table games is calculated differently. Barker and Britz point out that there is no way of accounting for how much each player bets on each turn of the cards, roll of the dice, or spin of the wheel. As a result, casinos begin their mathematical calculations of what they have been winning or losing with the drop; this is the amount of money used at the table to buy chips. The amount of cash and credit that is collected at each table is then compared with the amount of chips remaining at the table when the final count is complete; however, the total amount a player wagers is not always equal to the amount of cash exchanged for chips, a point that is well recognized by money launderers. "A player could exchange $1,000 in cash for chips at a table, lose $100, and then cash in $900 at the cage. Nine hundred dollars would be successfully laundered. Casinos, or at least many, constantly monitor for this practice, but it does occur. Nevertheless, the drop and the handle are the starting point for the calculation of the win" (Barker & Britz 6).

If gamblers do not understand these terms, or misuse them, the consequences can be severe; Barker and Britz cite the example of a slot player who began with a bankroll of $100 and played a three-coin quarter machine with an average 93.27% payoff. "He would begin with the $100 and get back $93.27 (theoretically) the first time he ran his money through the machine. If he continued to play until his $100 bankroll was gone, he would have put his money through the machine 71 times for a total of 1,967 plays on the machine" (7). The gambler's total wager (handle) would then be $1,475; however, the win (gambling revenue) for the casino would be $100, the amount of the player's original bankroll (Barker & Britz 2000). According to the International Gaming and Wagering Business (IGWB, 1998, 5), a player could statistically generate a handle of $10,000 at a table game with a casino advantage of 1% before losing a bankroll of $100 (in Barker & Britz 7). This casino advantage is known as the "vigorish," which is discussed further below.

Vigorish. John Winn is credited with inventing the book, the quarter charge that evolved into the 5% charge, and is responsible for the game of open craps (the Vigorish 2002). Because the 5% charge resulted in such dependable revenues, and was.".. so strong, gamblers took the word 'vigor,' added a syllable of jargon as they have a habit of doing when they would rather the laymen couldn't follow their conversation, and called it 'The Vigorish'" (the Vigorish 2002). Video gaming machines are able to be fine-tuned to accommodate different levels of vigorish, but on table games, the vigorish is set and the gambler must take advantage of improved mathematical odds whenever they are available - because they are; for example, there are a wide range of different bets than can be made on the craps table. "That's why it is the exciting game that it is. However, only the pass line and come bets are truly recommended" (the Vigorish 2002).