Games available in most casinos are commonly

called casino games. In a casino game, the players gamble casino

chips on various possible random outcomes or combinations of outcomes. Casino games are also available in online

casinos, where permitted by law. Casino games can also be played outside casinos

for entertainment purposes like in parties or in school competitions, some on machines

that simulate gambling.==Categories==

There are three general categories of casino games: table games, electronic gaming machines,

and random number ticket games such as keno. Gaming machines, such as slot machines and

pachinko, are usually played by one player at a time and do not require the involvement

of casino employees to play. Random number games are based upon the selection

of random numbers, either from a computerized random number generator or from other gaming

equipment. Random number games may be played at a table,

such as roulette, or through the purchase of paper tickets or cards, such as keno or

bingo.==Table games====

Common non-table games=====Gaming machines===

Pachinko Slot machine

Video Lottery Terminal Video poker===Random numbers===

Bingo Keno==House advantage==Casino games generally provide a predictable

long-term advantage to the casino, or “house”, while offering the player the possibility

of a large short-term payout. Some casino games have a skill element, where

the player makes decisions; such games are called “random with a tactical element”. While it is possible through skillful play

to minimize the house advantage, it is extremely rare that a player has sufficient skill to

completely eliminate his inherent long-term disadvantage (the house edge or vigorish)

in a casino game. Such a skill set would involve years of training,

an extraordinary memory and numeracy, and/or acute visual or even aural observation, as

in the case of wheel clocking in roulette or other examples of advantage play. The player’s disadvantage is a result of the

casino not paying winning wagers according to the game’s “true odds”, which are the payouts

that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering

on the number that would result from the roll of one die, true odds would be 5 times the

amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that

the player gets the original amount wagered back. However, the casino may only pay 4 times the

amount wagered for a winning wager. The house edge or vigorish is defined as the

casino profit expressed as the percentage of the player’s original bet. (In games such as blackjack or Spanish 21,

the final bet may be several times the original bet, if the player double and splits.) In American roulette, there are two “zeroes”

(0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared

to the European roulette. The chances of a player, who bets 1 unit on

red, winning is 18/38 and his chances of losing 1 unit is 20/38. The player’s expected value is EV=(18/38

x 1) + (20/38 x -1)=18/38 – 20/38=-2/38=-5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the

average house profit will be 10 x 1 x 5.26%=0.53 units. European roulette wheels have only one “zero”

and therefore the house advantage (ignoring the en prison rule) is equal to 1/37=2.7%. The house edge of casino games vary greatly

with the game, with some games having as low as 0.3%. Keno can have house edges up to 25%, slot

machines having up to 15%, while most Australian Pontoon games have house edges between 0.3%

and 0.4%. The calculation of the roulette house edge

was a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation

is necessary to complete the task. In games which have a skill element, such

as blackjack or Spanish 21, the house edge is defined as the house advantage from optimal

play (without the use of advanced techniques such as card counting), on the first hand

of the shoe (the container that holds the cards). The set of the optimal plays for all possible

hands is known as “basic strategy” and is highly dependent on the specific rules and

even the number of decks used. Good blackjack and Spanish 21 games have house

edges below 0.5%. Traditionally, the majority of casinos have

refused to reveal the house edge information for their slots games and due to the unknown

number of symbols and weightings of the reels, in most cases this is much more difficult

to calculate than for other casino games. However, due to some online properties revealing

this information and some independent research conducted by Michael Shackleford in the offline

sector, this pattern is slowly changing.===Standard deviation===

The luck factor in a casino game is quantified using standard deviations (SD). The standard deviation of a simple game like

roulette can be calculated using the binomial distribution. In the binomial distribution, SD=sqrt (npq

), where n=number of rounds played, p= probability of winning, and q=probability

of losing. The binomial distribution assumes a result

of 1 unit for a win, and 0 units for a loss, rather than -1 units for a loss, which doubles

the range of possible outcomes. Furthermore, if we flat bet at 10 units per

round instead of 1 unit, the range of possible outcomes increases 10 fold.SD (Roulette, even-money

bet)=2b sqrt(npq ), where b=flat bet per round, n=number of rounds, p=18/38, and

q=20/38. For example, after 10 rounds at 1 unit per

round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38)=3.16 units. After 10 rounds, the expected loss will be

10 x 1 x 5.26%=0.53. As you can see, standard deviation is many

times the magnitude of the expected loss.The standard deviation for pai gow poker is the

lowest out of all common casinos. Many, particularly slots, have extremely high

standard deviations. As the size of the potential payouts increase,

so does the standard deviation. As the number of rounds increases, eventually,

the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard

deviation is proportional to the square root of the number of rounds played, while the

expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected

loss increases at a much faster rate. This is why it is impossible for a gambler

to win in the long term. It is the high ratio of short-term standard

deviation to expected loss that fools gamblers into thinking that they can win. It is important for a casino to know both

the house edge and variance for all of their games. The house edge tells them what kind of profit

they will make as percentage of turnover, and the variance tells them how much they

need in the way of cash reserves. The mathematicians and computer programmers

that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in

this field, so outsource their requirements to experts in the gaming analysis field.==See also==

Gambler’s fallacy