Casino Math Guide
UNLV Gaming Studies Research Center 2
Mathematics should also overcome the dangers of superstitions. An owner of a major Las
Vegas strip casino once experienced a streak of losing substantial amounts of money to a few
“high rollers.” He did not attribute this losing streak to normal volatility in the games, but to bad
luck. His solution was simple. He spent the evening spreading salt throughout the casino to
ward off the bad spirits. Before attributing this example to the idiosyncrasies of one owner, his
are atypical only in their extreme. Superstition has long been a part of gambling – from both
sides of the table. Superstitions can lead to irrational decisions that may hurt casino profits. For
example, believing that a particular dealer is unlucky against a particular (winning) player may
lead to a decision to change dealers. As many, if not most, players are superstitious. At best, he
may resent that the casino is trying to change his luck. At worst, the player may feel the new
dealer is skilled in methods to “cool” the game. Perhaps he is even familiar with stories of old
where casinos employed dealers to cheat “lucky” players.
Understanding the mathematics of a game also is important for the casino operator to ensure
that the reasonable expectations of the players are met. For most persons, gambling is
entertainment. It provides an outlet for adult play. As such, persons have the opportunity for a
pleasant diversion from ordinary life and from societal and personal pressures. As an
entertainment alternative, however, players may consider the value of the gambling experience.
For example, some people may have the option of either spending a hundred dollars during an
evening by going to a professional basketball game or at a licensed casino. If the house
advantage is too strong and the person loses his money too quickly, he may not value that
casino entertainment experience. On the other hand, if a casino can entertain him for an
evening, and he enjoys a “complimentary” meal or drinks, he may want to repeat the
experience, even over a professional basketball game. Likewise, new casino games themselves
may succeed or fail based on player expectations. In recent years, casinos have debuted a
variety of new games that attempt to garner player interest and keep their attention. Regardless
of whether a game is fun or interesting to play, most often a player will not want to play games
where his money is lost too quickly or where he has a exceptionally remote chance of returning
home with winnings.
Mathematics also plays an important part in meeting players’ expectations as to the possible
consequences of his gambling activities. If gambling involves rational decision-making, it would
appear irrational to wager money where your opponent has a better chance of winning than you
do. Adam Smith suggested that all gambling, where the operator has an advantage, is irrational.
He wrote “There is not, however, a more certain proposition in mathematics than that the more
tickets [in a lottery] you advertise upon, the more likely you are a loser. Adventure upon all the
tickets in the lottery, and you lose for certain; and the greater the number of your tickets, the
nearer you approach to this certainty.”
Even where the house has an advantage, however, a gambler may be justified if the amount
lost means little to him, but the potential gain would elevate him to a higher standing of living.
For example, a person with an annual income of $30,000 may have $5 in disposable weekly
income. He could save or gamble this money. By saving it, at the end of a year, he would have
$260. Even if he did this for years, the savings would not elevate his economic status to another
level. As an alternative, he could use the $5 to gamble for the chance to win $1 million. While
the odds of winning are remote, it may provide the only opportunity to move to a higher
economic class.
Since the casino industry is heavily regulated and some of the standards set forth by regulatory
bodies involve mathematically related issues, casino managers also should understand the
mathematical aspects relating to gaming regulation. Gaming regulation is principally dedicated