Games available in most casinos are commonly called casino games. In a casino game, the players gamble cash or 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[edit]
There are three general categories of casino games: gaming machines, table games, and random number games. 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. Tables games, such as blackjack or craps, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. 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 or through the purchase of paper tickets or cards, such as keno or bingo.
Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, which involves random numbers. Casinos may also offer other type of gaming, such as hosting poker games or tournaments, where players compete against each other.
Number One is a 5-reel, 99-line online slot game with bonus spins, instant play, autoplay, video slots, wild symbol, scatter symbol, hold, mobile gaming, sports, celebrities and soccer themes you can play at 130 online casinos. This Game Will Bring You Impeccable Emotions. Microgaming guarantees that once you try to play this free slot game, you will become one of its numerous faithful admirers. One more thing that should be also mentioned is that the game has maximum rates that really impress. Lucky Numbers is worth the attention of the gamblers from all over the world.
Common casino games[edit]
Notable games that are commonly found at casinos include:
Table games[edit]
| Gaming machines[edit] | Random numbers[edit] |
House advantage[edit]
Casino games typically provide a predictable long-term advantage to the casino, or 'house', while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish) in a casino game are referred to as advantage players.
The players' 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 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 × 1) + (20/38 × (−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 × 1 × 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 varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges up to 25%, slot machines having up to 15%.
The calculation of the roulette house edge is 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 it is much more difficult to calculate the house edge than that in 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.[1]
In games where players are not competing against the house, such as poker, the casino usually earns money via a commission, known as a 'rake'.
Standard deviation[edit]
The luck factor in a casino game is quantified using standard deviations (SD).[2] The standard deviation of a simple game like roulette can be calculated using the binomial distribution. In the binomial distribution, SD = √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.[3]
- SD (roulette, even-money bet) = 2b√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 × 1 × √10 × 18/38 × 20/38 = 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss.[4]
The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.
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[edit]
References[edit]
- ^'Michael Shackleford is the wizard of odds'. Observer. Retrieved 13 October 2015.
- ^Hagan, general editor, Julian Harris, Harris (2012). Gaming law : jurisdictional comparisons (1st ed.). London: European Lawyer Reference Series/Thomson Reuters. ISBN978-0414024861.
- ^Gao, J.Z.; Fong, D.; Liu, X. (April 2011). 'Mathematical analyses of casino rebate systems for VIP gambling'. International Gambling Studies. 11 (1): 93–106. doi:10.1080/14459795.2011.552575. S2CID144540412.
- ^Andrew, Siegel (2011). Practical Business Statistics. Academic Press. ISBN978-0123877178. Retrieved 13 October 2015.
The Big Six wheel, also known simply as The Big Six or Wheel of Fortune, is an unequal game of chance, played using a large vertical wheel that can be spun.
Since 13 May 2002, it can be played legally in licensed casinos in the United Kingdom, under The Gaming Clubs (Bankers' Games) (Amendment) Regulations 2002 (Statutory Instrument 2002/1130).
The game is also known in casinos in the United States.
Rules[edit]
The wheel is divided into a number of equal segments separated by spokes or pins. Each segment is associated with a number. The wheel is spun by a dealer, and the winning segment is indicated by a pointer mounted on a flexible piece of rubber or leather, which also rubs against the pins to impart friction and slow the wheel down. Should the player stop the wheel, the segment at the top is the winner.
Variants[edit]
There are a number of variants of the game, that divide the wheel into a different number of segments, use different symbols in the segments, and have different odds if a symbol is selected.
Money wheel[edit]
This variant is the most common in casinos in the United States. The symbols are $1, $2, $5, $10 and $20 bills — and two special symbols, a joker and the casino logo. The $1 bills pay at odds of 1 to 1, the $2 bills at 2 to 1, the $5 bills at 5 to 1, and so on. The joker and the logo pay at odds of 40 to 1 or 45 to 1, depending on local gaming regulations or the practice of the casino.
The house advantage or edge (the proportion of the stakes that the casino expects to win on average) of this game is one of the highest of most casino games. In the United States it ranges from 11.1% on the $1-bill bet to more than 24% on the joker or logo (when it pays at 40 to 1). In Australia the house edge is 7.69% on all bets, so that the payouts on a 52-segment wheel are 47:1, 23:1, 11:1, 5:1, 3:1 and 1:1.
Dice wheel[edit]
The symbols on the wheel represent some of the 216 possible combinations of three dice. Sometimes the same combination appears in more than one segment. Players wager on the numbers 1 through 6. If the number appears on one of the dice in the winning segment, the dealer pays at 1 to 1; on two of the dice, 2 to 1; on all three of the dice, 3 to 1.
One example of a dice wheel, manufactured by H. C. Evans & Co. of Chicago (or its successor), is divided into 54 segments. Each of the triples appears four times. The following doubles each appear four times: 2, 1, 1; 2, 2, 1; 4, 3, 3; 5, 4, 4; 6, 5, 5; and 6, 6, 3. The following combinations each appear three times: 3, 2, 1; and 6, 5, 4.
In the example above, there are 54 possible outcomes for a single spin of the wheel. For a specific number:
- There are 7 possible outcomes where only one die will match the number
- There are 4 possible outcomes where only two dice will match
- There are 4 possible outcomes where all three dice will match
At odds of 1 to 1, 2 to 1 and 3 to 1 respectively for each of these types of outcome, the expected loss as a percentage of the stake wagered is:
1 - [(7/54) * 2 + (4/54) * 3 + (4/54) * 4] = 22.2%
The symbolism of the game is redolent of chuck-a-luck or sic bo, games of chance played with three dice. However, the house advantage or edge is greater than for chuck-a-luck, which itself has a higher house advantage than other casino games.
Online Number Game
This variety is seldom seen in casinos, but frequently seen as a carnival game, or at a charity 'Monte Carlo night' fund-raiser. A similar game, the 'Big Nine' wheel, has five numbers on each segment, and also three special symbols, appearing on three spaces each, which pay 10:1 odds.
United Kingdom, Australia and New Zealand[edit]
A legal game in a licensed casino in the United Kingdom, Australia or New Zealand involves a wheel at least 1.5 metres in diameter divided into 52 segments, each marked with one of seven symbols (referred to as A to G). The table below sets out the frequency of the symbols, their probability, the associated odds specified, and the house advantage or edge.
| Symbol | Number of segments | Probability of winning | Odds offered in UK | House edge in UK | Odds offered in AUS & NZ | House edge in AUS & NZ |
|---|---|---|---|---|---|---|
| A | 1 out of 52 | 1.9% | 50 to 1 | 1.9% | 47 to 1 | 7.7% |
| B | 1 out of 52 | 1.9% | 50 to 1 | 1.9% | 47 to 1 | 7.7% |
| C | 2 out of 52 | 3.9% | 20 to 1 | 19.2% | 23 to 1 | 7.7% |
| D | 4 out of 52 | 7.7% | 10 to 1 | 15.4% | 11 to 1 | 7.7% |
| E | 8 out of 52 | 15.4% | 5 to 1 | 7.7% | 5 to 1 | 7.7% |
| F | 12 out of 52 | 23.1% | 3 to 1 | 7.7% | 3 to 1 | 7.7% |
| G | 24 out of 52 | 46.2% | 1 to 1 | 7.7% | 1 to 1 | 7.7% |
Other variants[edit]
Other variants, using different symbols and odds, are relatively rare in the United States.
One variant called 'Mississippi Derby' was used for a short time at the Grand Casino in Gulfport, Mississippi. (The casino was destroyed in 2005 by Hurricane Katrina.) The symbols were combinations of three of a number of different horses, arranged to represent a winner, a second-placed horse and a third-placed horse. (The horses were represented in three concentric rings, with the winner on the outer ring.) Players wagered on particular horses to 'win', 'place' or 'show', as with betting in horse racing. The payoffs varied from horse to horse, depending on how many times and where the horse appeared on the rings. Odds ranged from 40 to 1 for the 'longshot' to win, down to 1-2 for the 'favorite' to show.
References[edit]
Regulation in the United Kingdom
Casino Number Game Online
Regulation in New Zealand