Game Protection
Game protection is important to prevent fraudulent and illegal activity of cheating the casino. Game
protection is important to train surveillance, security, management, law enforcement and pit
supervisors, to protect the casino games from cheating. Cheating is illegal at casinos because cheating is
stealing from the casino. Extensive research goes into protecting the casino from cheaters stealing at
their casino. This chapter discusses the types of cheating and collusion. The chapter discusses the
consequences of cheating and it give advice on how to prevent it from happening.
Casino math is important to the casino. Casino math is used to determine the revenue of a casino. All
casino games use math to determine the drop or the expected value of return. The casino has an
advantage. Casino games are games of chance. The probability of winning is in the house favor. The
house has at least a 2% advantage over all casino games. work. Percentages, odds, and probability are
the foundation of the gaming industry. The mathematics underlying the games assures the casinos will
make money. Since games are the products sold by the gaming industry, managers must understand
how the mathematics behind the games produces the expected revenues. Outcomes in games of chance
are, by definition, uncertain. The branch of mathematics used to describe and calculate uncertainty is
called probability.
Casino math is important to the casino. Casino math is used to determine the revenue of a casino. All
casino games use math to determine the drop or the expected value of return. The casino has an
advantage. Casino games are games of chance. The probability of winning is in the house favor. The
house has at least a 2% advantage over all casino games. work. Percentages, odds, and probability are
the foundation of the gaming industry. The mathematics underlying the games assures the casinos will
make money. Since games are the products sold by the gaming industry, managers must understand
how the mathematics behind the games produces the expected revenues. Outcomes in games of chance
are, by definition, uncertain. The branch of mathematics used to describe and calculate uncertainty is
called probability.
Probability reflects how often we expect things to occur and can be interpreted to be the proportion of
times an event will occur overall. That is, the probability of an event is the approximate proportion of
times the event will occur in many repetitions of the random experiment. Probability can be expressed
as a fraction, decimal, or percentage. The probability of heads is 1⁄2, or .50, or 50%. Sometimes
probability is referred to as chance. A person may say that there is a 50% chance of getting heads when
tossing a coin.
Odds are another way to express probability. Whereas probability represents the relationship between
the desired event and all events, odds describe the relationship between a desired event and all non-
desired events. As a rule, odds are stated against an event in casinos.
Permutations refer to the number of diverse ways in which objects can be arranged in order. In a
permutation, each item can appear only once, and each order of the items’ arrangement constitutes a
separate permutation. Combinations refer to the number of ways that a set of items can be selected
from a group, without regard to the order in which the members of the set are arranged.
Expectation, or expected value, represents how much money a player can expect to win or lose overall
on a particular wager. If the player’s expectation is negative, as is typical for most bets made in a casino,
the player can expect to lose money. Expected value is a function of both the probabilities of winning
and losing the bet, as well as the amount won or lost. The following formula can be used to calculate the
expected value of a wager.
House advantage (HA) is the most used indicator of the value of a particular game or bet. From the
casino’s perspective, the house advantage represents how much, in terms of percentage of the money
wagered, the casino can expect to retain. The house advantage represents the long run percentage of
the wagered money that will be retained by the casino. House advantage and theoretical win
percentage are the same thing, hold percentage is win over drop, win percentage is win over handle,
win percentage approaches the house advantage as the number of plays increases, and hold percentage
is equivalent to win percentage for slots but not table games.
House advantage (HA) is the most used indicator of the value of a particular game or bet. From the
casino’s perspective, the house advantage represents how much, in terms of percentage of the money
wagered, the casino can expect to retain. The house advantage represents the long run percentage of
the wagered money that will be retained by the casino. House advantage and theoretical win
percentage are the same thing, hold percentage is win over drop, win percentage is win over handle,
win percentage approaches the house advantage as the number of plays increases, and hold percentage
is equivalent to win percentage for slots but not table games.
Those who subscribe to this fallacy believe that the “law of averages” will rescue them during a losing
streak by turning things around. Player's experience, or attribute to themselves, good luck when they
are winning and bad luck when they are losing. As with hot and cold streaks, however, luck is merely a
natural statistical fluctuation in one direction or another – good luck is a fluctuation of successful bets
and bad luck is a fluctuation of unsuccessful bets. It is a fallacy to think that luck exists as a tangible
quantity.
The critical difference is in the amount of information a casino can accurately record on the play of table
games versus the play of slot machines. Someday, casinos will have the ability to track every transaction
that occurs in the casino, whether it is the amount of each bet at a blackjack table or the quality of a
video blackjack player’s play. But until technology meets these needs in a cost-efficient manner, the
casino must rely on limited or less-than-perfect information to do its analyses. This is particularly true
with table games where the casino does not have the advantage of the advanced player tracking
systems.
When a casino player approaches a table game to play, he usually exchanges cash for chips. After giving
the player the chips, the dealer will drop the cash into the drop box attached to the underside of a table
game. Some players are not cash players but will gamble using credit instruments or “markers.” A
marker is an instrument used to document the extension of credit to a player. In this case, the player
will sign a credit instrument in the amount of the chips received at the table. Like the cash received, the
credit instruments also are placed in the drop box. Besides cash and credit instruments, the drop box
contains foreign chips, and credit and fill slips. Foreign chips are chips from other casinos played or
exchanged by players. A credit slip (not related to credit extended to a player) is an instrument used to
document a transfer of (usually excess) chips from a table game to the cashier – a game credit. A fill slip
is an instrument used to document a transfer of chips from the cashier to a table game.
As with the above description of win, this refers to the actual win percentage, and not theoretical or
expected win percentage. Actual win percentage represents the fraction of money wagered that is
retained by the casino over a given period or number of trials. The theoretical win percentage is the
house advantage, or the long-run average percentage of money wagered that is retained by the casino.
For many trials, the actual win percentage should approximate the theoretical win percentage. For slots
and other gaming devices, the actual win percentage is known. For table games, however, win
percentage is difficult to measure since handle is usually unknown.
For table games, however, where handle and drop are not equal, hold percentage is different from win
percentage. The actual fraction of money wagered at a table game that the casino retains is not the hold
percentage, but the win percentage – win divided by handle. As mentioned above, table game handle is
difficult to measure and therefore the win percentage is unknown. Hold percentage is a known measure
of the “win rate” for table games and is used as a rough gauge of how these games are performing. Hold
percentage for table games is represented by game revenue, i.e., the drop plus the change in chip
inventory, divided by drop.
Hold percentage is a theoretical amount that can be set to any value with the computer program that
controls the machine. Whatever this theoretical hold, the actual percentage will vary but will be close to
the theoretical amount after many plays. Assessing the likelihood of a certain difference between actual
and theoretical win is possible because of the random selection of outcomes. The volatility section can
be expected between actual and theoretical win for slot machines.
The volatility index is the basis for calculating how much variation can be expected and for determining
whether an observed hold percentage on a given machine is normal or unusual for a given number of
plays. In general, the larger the volatility index, the greater fluctuations will be in actual hold
percentage.
The volatility index is the basis for calculating how much variation can be expected and for determining
whether an observed hold percentage on a given machine is normal or unusual for a given number of
plays. In general, the larger the volatility index, the greater fluctuations will be in actual hold
percentage.
Most casinos will track both theoretical win and observed losses. The reason for this is simply that some
players will lose most if not all their bankroll quickly either because they are extremely bad players, or
they experience an incredible streak of bad fortune. Although the house advantage represents the
average outcome in any game, there is a bell-shaped (normal) distribution of outcomes centered on the
expected house win. Some players will end up at the lower end of the house win distribution with a
large player win. Others, merely “unlucky,” will be at the upper end, with a resulting large player loss
and house win. Some casinos will grant comps or rebates if the player loses all or more (often 80% or
more) of their credit line or front money deposit even if they do not meet the criteria that the casino
sets for minimum theoretical loss.
Probabilities are often described as the very backbone of gambling mathematics. In addition, probability
in gambling mathematics can be used when determining the conditions for acquiring certain results or
even some financial expectations of a game in the long term. Probabilities could also be helpful when
determining how favorable a certain game would be and is it worth playing. This aspect of the matter is
usually expressed as odds, as well as a fraction or a decimal fraction. Still, casino players should know
odds and probabilities are different things. Players will need be aware of some details to calculate the
probability of a certain event.
Players will need be aware of some details to calculate the probability of a certain event. First, they will
need a full count of the number of individual elements in the sample space. In addition, they will need to
know the number of the individual elements related to the event. Once a player knows these values,
they will be able to define the probability of the event.
The most general definition of odds is the probability of a certain event happening in comparison to the
probability of the same event not happening. Odds are considered as ratios of the player's chances of
losing to the likelihood of winning. In other words, they are the average frequency of a player's eventual
loss to the average frequency of a win. As already mentioned above, odds are often mistaken with
probabilities, but they are not the same thing. The term “odds” could also be used as a substitute of the
true odds that are the actual chances of winning. There are also payout odds, which represent the ratio
of payout for each unit bet.
The most general definition of odds is the probability of a certain event happening in comparison to the
probability of the same event not happening. Odds are considered as ratios of the player's chances of
losing to the likelihood of winning. In other words, they are the average frequency of a player's eventual
loss to the average frequency of a win. As already mentioned above, odds are often mistaken with
probabilities, but they are not the same thing. The term “odds” could also be used as a substitute of the
true odds that are the actual chances of winning. There are also payout odds, which represent the ratio
of payout for each unit bet.
