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 available in online casinos, where permitted by law. Casino games can also be played outside of casinos for entertainment purposes, some on machines that simulate gambling.

[edit] Categories of casino games

There are three general categories of casino games: table games, electronic gaming machines, and random number ticket games such as Keno and simulated racing. 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.

[edit] Common table games

[edit] Cards

[edit] Dice / Tiles

[edit] Random numbers

[edit] Common non-table games

[edit] Gaming machines

• Pachinko
• Slot machine
• Video Lottery Terminal
• Video poker

[edit] Random numbers

• Bingo
• Keno

[edit] 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 house 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.

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 5 to 1 probability of any single number appearing. However, the casino may only pay 4 times the amount wagered for a winning wager.

The house edge (HE) or vigorish is defined as the casino profit expressed as a 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.)

Example: In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets $1 on red, his chance of winning $1 is therefore 18/38 and his chance of losing $1 (or winning -$1) is 20/38.

The player's expected value, 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 rounds, play $1 per round, the average house profit will be 10 x $1 x 5.26% = $0.53. Of course, it is not possible for the casino to win exactly 53 cents; this figure is the average casino profit from each player if it had millions of players each betting 10 rounds at $1 per round.

The house edge of casino games vary greatly with the game. Keno can have house edges up to 25%, slot machines can have 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%.

[edit] 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. Therefore,

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 per round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38) = $3.16. 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 range is six times the standard deviation: three above the mean, and three below. Therefore, after 10 rounds betting $1 per round, your result will be somewhere between -$0.53 - 3 x $3.16 and -$0.53 + 3 x $3.16, i.e., between -$10.01 and $8.95. (There is still a 0.1% chance that your result will exceed a $8.95 profit, and a 0.1% chance that you will lose more than $10.01.) This demonstrates how luck can be quantified; we know that if we walk into a casino and bet $5 per round for a whole night, we are not going to walk out with $500.

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, such as Mike Shackleford, the "Wizard of Odds".

[edit] See also

• Gambler's fallacy

Online casinos, also known as virtual casinos or internet casinos, are online versions of traditional ("brick and mortar") casinos. Online casinos enable gamblers to play and wager on casino games through the Internet.

Online casinos generally offer odds and payback percentages that are comparable to land-based casinos. Some online casinos claim higher payback percentages for slot machine games, and some publish payout percentage audits on their websites. Assuming that the online casino is using an appropriately programmed random number generator, table games like blackjack have an established house edge. The payout percentage for these games are established by the rules of the game.

Reliability and trust issues are commonplace and often questioned. Many online casinos lease or purchase their software from well-known companies like Microgaming, Realtime Gaming, Playtech, and CryptoLogic Inc in an attempt to "piggyback" their reputation on the software manufacturer's credibility. These software companies either use or claim to use random number generators to ensure that the numbers, cards or dice appear randomly.

[edit] Online casino types

Online casinos can be divided into three groups based on their interface: web-based casinos, download-based casinos, and more recently live casinos. Some casinos offer multiple interfaces.

[edit] Web-based online casinos

Web-based online casinos are websites where users may play casino games without downloading software to the local computer. Games are mainly represented in the browser plugins Macromedia Flash, Macromedia Shockwave, or Java and require browser support for these plugins. Also, bandwidth is needed since all graphics, sounds and animations are loaded through the web via the plugin. Some online casinos also allow gameplay through a plain HTML interface.

[edit] Download-based online casinos

Download-based online casinos require the download of the software client in order to play and wager on the casino games offered. The online casino software connects to the casino service provider and handles contact without browser support. Download-based online casinos generally run faster than web-based online casinos since the graphics and sound programs are located within the software client, rather than having to be loaded from the Internet. On the other hand, the initial download and installation of a download-based online casino client does take time. As with any download from the Internet, the risk of the program containing malware does exist.

[edit] Live-based casinos

Live-based casino gaming allows web players to interact with games played in a real world casino environment. Online players can see, hear, and interact with live dealers at tables in casino studios worldwide.

[edit] Games offered

A typical selection of gambling games offered at an online casino might include:

• Baccarat
• Blackjack
• Craps
• Roulette
• Online slot games
• Online poker

[edit] Bonuses

[edit] Signup bonuses

Many online casinos offer signup bonuses to new players making their first deposit. These bonuses normally match a percentage of the player's deposit with a dollar maximum, and almost all online casino signup bonuses require a minimum amount of wagering before allowing a cash out. Gameplay at specific casino games might be excluded from the wagering requirement calculation.^{[citation needed]}

A fictional signup bonus offer follows as an example:

• The online casino offers new players a deposit matching bonus of 100%, up to $100
• The player must wager 25 times the total amount of the deposit plus the bonus before withdrawing
• Wagers on baccarat, craps, roulette, and sic bo do not count towards meeting wagering requirements

For this particular example, this would mean that a player depositing $100 would start with $200 in his account. The player must make $5000 ($200 × 25) in wagers before being allowed to make a withdrawal.

Some bonuses require no deposit to claim them. Types of no deposit bonuses include^{[citation needed]}:

• A no deposit in pure monetary form, for example $10.
• Free spins no deposit, this is where they allow free spins on particular games, and then allow you to keep the winnings.
• Play for a predetermine period of time with x amount of dollars.

[edit] Cashable bonuses

The most common form of casino bonuses is the cashable bonus.^{[citation needed]} Cashable bonuses can be cashed out after completing a wagering requirement. A casino might offer a 100% match bonus up to $100 with a wagering requirement of $2000. After wagering $2000 in the casino, the player is able to cash out the $100 bonus.^{[citation needed]}

Cashable bonuses often restrict play on certain games.^{[citation needed]} Wagers made on roulette, baccarat, craps, and sic bo usually do not count towards the wagering requirement because these bets give the player the opportunity to simultaneously bet on winning and losing outcomes, greatly reducing variance.^{[citation needed]} For example, betting on both red and black in roulette. Wagers on games with a low house edge, like blackjack and video poker, are also often excluded. Some casinos increase the wagering requirement above the default for low-house-edge games.

On games without raises or doubles, the expected loss while completing a wagering requirement is wagering requirement * house edge. This makes the expected gain of a cashable bonus equal to bonus - wagering requirement * house edge. House edge is defined in terms of initial bet, so the above equation does not apply to games with raises and doubles where the final bet size may be larger than the initial bet. The equation becomes bonus - wagering requirement * average loss per wager. WizardofOdds.com has proposed calling the latter average loss per wager variable "element of risk".^[1] For a more precise estimate, one must also consider the benefit from being able to bet the bonus prior to completing the wagering requirement. This effect becomes noticeable when making large bets, such as betting the full balance (deposit and bonus) in a single bet. After considering this benefit and "element of risk", the formula for return becomes bonus - average wagering * element of risk.^[2] If games without raises or doubles are played and the bonus is not given until completing wagering, then the formula can be simplified as bonus - wagering requirement * house edge.

[edit] Sticky bonuses

Non-cashable bonuses are often called "sticky bonuses".^[3] Sticky bonuses can be bet, but cannot be cashed out. When the player makes a withdrawal, the sticky bonus is typically removed from the withdrawal total. A player might receive a 100% match sticky bonus on a $100 deposit with a wagering requirement of $2000. While meeting the $2000 wagering requirement, the player could bet both the deposit and the sticky bonus. When cashing out, the $100 bonus would be removed from the balance. If the player cashed out $300, $100 would be subtracted out, leaving $200. The player is not allowed to cash out a balance of below $100 since no cash would remain after the bonus is removed.

The average return of a sticky bonus is sometimes expressed in terms of a target gain. Average return = (chance of reaching target) * (target - bonus - deposit - wagering requirement * house edge) - (chance of not reaching target * deposit). With a target of 2x(bonus+deposit) and 50% chance of reaching the target, the equation reduces to 50% * (bonus - wagering requirement * house edge). Expressing in terms of chance of bust and "element of risk", the formula for return becomes bonus * chance of bust - average wagering * element of risk.^[4]

The sticky bonus described above that is removed after wagering is sometimes known as a "phantom bonus." There are other variations of a sticky bonus in which you do not need to exceed your original balance to make a withdrawal. Instead any win is immediately cashable.^[5]

[edit] Cash back bonuses

Cash back bonuses are given following a player loss. A portion of the player's loss is returned, often as cash. For example, a casino might offer a 25% cash back bonus each week. Any player who had a loss over the course of the week, would receive 25% of his loss back. Any player who had a win over the course of the week would not receive a bonus. Cashback bonuses are rare.^[6]

[edit] Comp points

Main article: Comps (casino)

Comps are commonly available at land-based casinos, but also exist online. Comp points can usually be exchanged for cash, prizes, or other comps.^[7] The amount of cash given per wager is usually very small and often varies with game selection. A casino might offer three comp points for each $10 wagered on slots and one comp point for each $10 wagered on blackjack. The casino might give $1 for each 100 comp points. This example is equivalent to returning 0.3% of wagers on slots and 0.1% of wagers on blackjack.

[edit] Bonus hunting

Bonus hunting (also known as bonus bagging or bonus whoring) is a type of advantage gambling where turning a profit from casino, sportsbook and poker room bonus situations is mathematically possible. For example, the house edge in blackjack is roughly 0.5%. In the example above, $5000 in wagering with a house edge of 0.5% will result in an expected loss of $25. Since the player received a $100 signup bonus, after subtracting the expected loss of $25, the player has an expected profit of $75.

[edit] Casino games

Online casinos offer players signup bonuses as incentives to play. These are usually one-off bonuses for signing up to the casino and opening an account. The terms and conditions attached to each bonus vary but share two common features:

• Restricted games or bets.
• Wagering requirements.

Wagering requirements prevent players from withdrawing the bonus money immediately after receiving it. Before the bonus money can be withdrawn the player must wager a certain amount of money on unrestricted games. The wagering can be spread out over many bets. To meet a $2000 wagering requirement, a player could make 1000 $2 bets on blackjack, provided blackjack is not a restricted game.

Games like blackjack and video poker have a low house advantage. The house advantage for blackjack is ~0.5%. So in the example above, by playing $2000 worth of blackjack with a house advantage of 0.5%, a player is, expected to lose $10 in total. But the expected value is an average value and may be less than the actual value. Risk of ruin is an important topic that comes into play.

Assuming that the player only loses an amount close to the expected loss, and the bonus awarded to the player after meeting this wagering requirement is greater than $10 then the player profits. The process is mathematically calculated. Bad luck could cause a player to lose more than $10 playing blackjack in this situation. The run of luck is subject to variance and follows a normal distribution.

[edit] Sports betting

By taking advantage of 'free' bet promotions, users can back the event, and then lay the event on a betting exchange, at similar or same odds, thus ensuring that their 'free' bet is not a bet at all, instead more like a financial trade. No matter the outcome, it is possible (by using a betting / arb calculator) to calculate both the possible outcomes before the sporting event has started. By inputting the odds, the bet calculator then tells you what amount to bet, to ensure that whether the bet wins or loses, the return is the same.

[edit] Poker

See the online poker article for a discussion of poker bonuses.

[edit] Bonus abuse

A large portion of online casino disputes relate to bonuses.^[8] Casinos may label players who win using bonuses as "bonus abusers." Both players and casinos may commit fraud. An example of player fraud is creating multiple accounts and using the accounts to claim a sign-up bonus several times. An example of casino fraud is changing terms of a bonus after a player has completed the wagering requirements, then requiring the player to meet the new bonus terms.^{[citation needed]}

[edit] Fraudulent online casino behavior

Fraudulent behavior on the part of online casinos has been documented. The most commonly reported behaviors are refusal to pay withdrawals or cheating software with rigged payouts. An online casino with multiple confirmed cases of fraudulent behavior is often called a rogue casino by the online casino player community.^[9]

One commonly reported behavior related to refusal to pay withdrawals is the refusal to pay withdrawals promptly. A rogue casino may intentionally delay a withdrawal in hopes that the player will continue gambling with the money in the account and lose it all back. Other rogue online casinos attempt to not pay their customers by retroactively applying unfair terms to their house rules.

Cheating software appears to be less common than payout problems.

Some casino software has been mathematically proven to cheat, such as Elka System/Oyster Gaming and Casino Bar.^[10] Screen shots from the back office of an older brand of software indicated the odds could be adjusted by the operator.

Many casino gambling portals and player forums maintain blacklists of rogue casinos.^[9][11][12] While some carry more authority than others, most blacklists constitute individual webmaster and player opinions rather than anything official from any type of regulating body.

[edit] Fraudulent player behavior

Common fraudulent behavior from online casinos players includes the signing up for multiple casino accounts using different identities in order to claim a bonus offer multiple times, a practice known as "gnoming". Another form of fraudulent behavior might be the use of a graphics editing software like Adobe Photoshop to create a false winning slot machine game screenshot in an attempt to tell the casino they hit a jackpot and didn't get paid for it.

Online casinos usually lock the player accounts for these people. Some observers believe that online casinos share fraudulent player blacklists.^[13]

[edit] Legality

See online gambling for a discussion of the legality of playing at an online casino.

[edit] See also

• Comps (casino)
• Problem gambling
• eCOGRA

[edit] Notes

[edit] External links

• Open Directory online casino listings