**Online casino**, also known as **virtual casino** or **Internet casino**, are online versions of traditional (“bricks and mortar”) casinos. Online casino enable gamblers to play and wager on online casino games through the Internet. It is a prolific form of online gambling.

Online casino generally offer odds and payback percentages that are a bit higher than land-based casinos. Some online casino claims higher payback percentages for slot machines, 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.

Many online casino rent or buy their software from companies like CryptoLogic Inc (now Amaya), International Game Technology, Microgaming, Playtech, Golden Race, and Realtime Gaming.

## Online casino types

Online casino can be divided into two groups based on their interface: web-based and download-only casinos. Some casinos offer both interfaces, both have their merits.

### Web-based online casino

Web-based online casino (also known as flash casinos) are websites where users may play casino games without downloading software to their 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 an HTML interface. Apple devices such as iPod, iPad, and iPhone cannot play Flash games as the technology is not supported.

### Download-based online casino

Download-based online casino 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 casino since the graphics and sound programs are cached by 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 do take time. As with any download from the Internet, the risk of the program containing malware exists.

### Virtual casino games

In a virtual casino game, the outcome of each game is dependent on the data produced by a pseudo random number generator (PRNG). This determines the order of the cards in card games, the outcome of a dice throw, or the results produced by the spinning of a slot machine or roulette wheel.

PRNGs use a set of mathematical instructions known as an algorithm to generate a long stream of numbers that give the impression of true randomness. While this is not the same as true random number generation (computers are incapable of this without an external input source), it provides results that satisfy all but the most stringent requirements for true randomness.

When implemented correctly, a PRNG algorithm such as the Mersenne Twister will ensure that the games are both fair and unpredictable. However, usually, the player has to trust that the software has not been rigged to increase the house edge, as its inner workings are invisible to the user.

Properly regulated online casino are audited externally by independent regulators to ensure that their win percentages are in line with the stated odds, and this can provide a degree of assurance to the player that the games are fair, assuming the player trusts the regulator.

### Live dealer casino games

In a live casino game, a human dealer runs the game in real time from a casino gaming table, which can be seen via a live streaming video link. Players can make betting decisions via a console on their computer screen and can communicate with the dealer using a text chat function.

The results of the physical transactions by the dealer, such as the outcome of the roulette wheel spin or the dealing of cards, are translated into data that can be utilised by the software by means of optical character recognition (OCR) technology. This enables the player to interact with the game in much the same way as they would with a virtual casino game, except for the fact that the results are determined by real-life actions rather than automated processes.

These games are a lot more expensive for websites to host than virtual games, as they involve a heavier investment in technology and staffing. A live casino studio typically employs one or more cameramen, several croupiers running the various games, an information technology manager to ensure that any technical hitches are dealt with swiftly, and a pit boss that acts as an adjudicator in case of disputes between players and croupiers.

In most cases, this requires at least a three-room setup, comprising a live studio, a server/software room, and an analyst’s room. The configuration of these rooms varies from casino to casino, with some having several gaming tables in one room, and some having a single table in each room.

The high running costs involved with operating live dealer games is the reason why online casino only tend to offer a handful of the most popular games in this format, such as roulette, blackjack, sic bo, and baccarat. In comparison, the running costs associated with virtual games are very low, and it is not uncommon for online casinos to offer hundreds of different virtual casino games to players on their site.

Online casino vary in their approach to the hosting of live games, with some providing live games via their own television channel, and others offering the games exclusively via their website. In the case of televised games, players can often use their mobile phone or television remote controls to place bets instead of doing so via a computer connected to the internet. The most common live dealer games offered at online casino are baccarat, blackjack, and roulette.

## Games offered

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

# Baccarat

**Baccarat** or **baccara** (/ˈbækəræt,

There are three popular variants of the game: *punto banco* (or “North American baccarat”), *baccarat chemin de fer* (or “chemmy”), and *baccarat banque* (or *à deux tableaux*). In *punto banco*, each player’s moves are forced by the cards the player is dealt. In *baccarat chemin de fer* and *baccarat banque*, by contrast, both players can make choices. The winning odds are in favour of the bank, with a house edge no lower than around 1 percent.

The origins of the game are disputed, and some sources claim that it dates to the 19th century. Other sources claim that the game was introduced into France from Italy at the end of the 15th century by soldiers returning from the Franco-Italian War during the reign of Charles VIII.

## Valuation of hands

In baccarat, cards have a point value: cards two through nine are worth face value (in points); tens, jacks, queens and kings have no point value (i.e. are worth zero); aces are worth 1 point; jokers are not used. Hands are valued according to the *rightmost digit* of the sum of their constituent cards. For example, a hand consisting of 2 and 3 is worth 5, but a hand consisting of 6 and 7 is worth 3 (i.e., the 3 being the rightmost digit in the combined points total of 13). The highest possible hand value in baccarat is therefore nine.

## Punto banco

The overwhelming majority of casino baccarat games in the United States, United Kingdom, Canada, Australia, Sweden, Finland, and Macau are “punto banco” baccarat and they may be seen labelled simply as “Baccarat”. About 91% of total income from Macau casinos in 2014 came from punto banco. In punto banco, the casino banks the game at all times, and commits to playing out both hands according to fixed drawing rules, known as the “tableau” (French: “board”), in contrast to more historic baccarat games where each hand is associated with an individual who makes drawing choices. The player (*punto*) and banker (*banco*) are simply designations for the two hands dealt out in each coup, two outcomes which the bettor can back; the player has no particular association with the gambler, nor the banker with the house.

Punto banco is dealt from a shoe containing 6 or 8 decks of cards shuffled together; a cut-card is placed in front of the seventh from last card, and the drawing of the cut-card indicates the last coup of the shoe. The dealer burns the first card face up and then based on its respective numerical value, with aces worth 1 and face cards worth 10, the dealer burns that many cards face down. For each coup, two cards are dealt face up to each hand, starting from “player” and alternating between the hands. The croupier may call the total (e.g., “five player, three banker”). If either The player or banker or both achieve a total of 8 or 9 at this stage, the coup is finished and the result is announced: a player win, a banker win, or tie. If neither hand has eight or nine, the drawing rules are applied to determine whether the player should receive a third card. Then, based on the value of any card drawn to the player, the drawing rules are applied to determine whether the banker should receive a third card. The coup is then finished, the outcome is announced, and winning bets are paid out.

### Tableau of drawing rules

If neither the player nor the banker is dealt a total of 8 or 9 in the first two cards (known as a “natural”), the tableau is consulted, first for the player’s rules, then the banker’s.

- Player’s rule
- If the player has an initial total of 0–5, he draws a third card. If the player has an initial total of 6 or 7, he stands.
- Banker’s rule
- If the player stood pat (i.e., has only two cards), the banker regards only his own hand and acts according to the same rule as the player. That means the banker draws a third card with hands 0–5 and stands with 6 or 7.

If the player drew a third card, the banker acts according to the following more complex rules:

- If the banker total is 2 or less, then the banker draws a card, regardless of what the player’s third card is.
- If the banker total is 3, then the banker draws a third card unless the player’s third card was an 8.
- If the banker total is 4, then the banker draws a third card if the player’s third card was 2, 3, 4, 5, 6, 7.
- If the banker total is 5, then the banker draws a third card if the player’s third card was 4, 5, 6, or 7.
- If the banker total is 6, then the banker draws a third card if the player’s third card was a 6 or 7.
- If the banker total is 7, then the banker stands.

The croupier will deal the cards according to the tableau and the croupier will announce the winning hand, either the player or the banker. Losing bets will be collected and the winning bets will be paid according to the rules of the house. Usually, even money or 1–to-1 will be paid on player bets and 95% or 19-to-20 on banker bets (even money with “5% commission to the house on the win”).

Should both the player and banker have the same value at the end of the deal the croupier shall announce “égalité — tie bets win.” All tie bets will be paid at 8-to-1 odds and all bets on player or banker remain in place and active for the next game (the customer may or may not be able to retract these bets depending on casino rules).

In the U.S., the full-scale version of punto banco is usually played at large tables in roped off areas or private rooms separated from the main gaming floor. The game is frequented by high rollers, who may wager tens or hundreds of thousands of dollars on a single hand.

Minimum bets are relatively high, often starting at $100 and going as high as $500. Posted maximum bets are often arranged to suit a player.The table is staffed by a croupier, who directs the play of the game, and two dealers who calculate tax and collect and pay bets. Six or eight decks of cards are used, normally shuffled only by the croupier and dealers.

The shoe is held by one of the players, who deals the cards on the instructions of the croupier according to the tableau. On a player win, the shoe moves either to the highest winning bettor, or to the next person in clockwise order around the table, depending on the casino’s conventions. The shoe may be refused or the croupier may be requested to deal.

### Punto banco odds and strategy

Punto banco has both some of the lowest house edges among casino table games, and some of the highest. The player bet has an attractively low house edge of 1.24%, and the banker bet (despite the 5% commission on the win) is even lower, at 1.06%. Both are just slightly better for the player bet than chances at single-zero roulette, and comparable to playing blackjack without employing strategy.

In contrast, the tie bet which pays 8-to-1 has a high house edge of 14.4%. Most casinos in the United Kingdom pay the tie at 9-to-1, resulting in a more lenient house edge of approximately 4.85%.

Despite having a low house edge, punto banco is not susceptible to advantage play, and despite the superficial similarities to blackjack, card counting is not profitable. In his 1984 analysis (Thorp 1984), Thorp concludes that:

[A]dvantages in baccarat are very small, they are very rare and the few that occur are nearly always in the last five to 20 cards in the pack.

— (Thorp 1984), p. 38

## Punto banco variations

### Midi and Mini punto

Smaller versions of the game are common in more modest settings. In midi punto, the table is only staffed by a single croupier and is generally smaller. In mini punto, the table is no larger than a standard blackjack table, and the cards are dealt by a croupier directly from a standard shoe. Table minimums/maximums are smaller.

### Super 6/Punto 2000

A variation of punto banco exists where even money is paid on winning banker bets (rather than 95%), except when the banker wins with 6, which pay only 50% of the bet. This game goes under various names including *Super 6* and *Punto 2000*. The house edge on a banker bet under Super 6 is 1.46% compared with regular commission baccarat at 1.058%. This is equivalent to increasing the commission by 17.45% to 5.87%. The banker wins with a 6 about 5 times every eight-deck shoe. As well as its increased house edge, the Super 6 variation is used by casinos for its speed, since it partially does away with the time-consuming process of calculating and collecting a commission on winning banker bets except for winning with a 6.

### EZ Baccarat

A variation of punto banco originating in 2004 where even money is paid on winning banker bets, except when the banker wins with a total of 7 after the third card is drawn, which results in a push. The game has two additional options, the *Dragon 7*, a specific bet on the banker to total 7 points with three cards drawn, which pays 40-to-1 instead of pushing, and *Panda 8*, a bet on the player to total 8 points with three cards drawn, which pays 25-to-1.

## Chemin de fer

*Chemin de fer* is a version which first appeared in the late 19th century. It’s name, which is the French term for “railway”, comes from the version being quicker than the original game, the railway being at that time the fastest means of transport. It is still the most popular version in France.

Six decks of cards are used, shuffled together. Players are seated in random order, typically around an oval table; discarded cards go to the center. Play begins to the right of the croupier and continues counterclockwise.

Once play begins, one player is designated as the banker; this player also deals. The other players are “punters”. The position of banker passes counterclockwise in the course of the game. In each round, the banker wagers the amount he wants to risk.

The other players, in order, then declare whether they will “go bank”, playing against the entire current bank with a matching wager. Only one player may “go bank”. If no one “goes bank”, players make their wagers in order. If the total wagers from the players are less than the bank, observing bystanders may also wager up to the amount of the bank.

If the total wagers from the players are greater than the bank, the banker may choose to increase the bank to match; if he does not, the excess wagers are removed in reverse play order.

The banker deals four cards face down: two to himself and two held in common by the remaining players. The player with the highest individual wager (or first in play order if tied for highest wager) is selected to represent the group of non-banker players.

The banker and player both look at their cards; if either has an eight or a nine, this is immediately announced and the hands are turned face-up and compared. If neither hand is an eight or nine, the player has a choice to accept or refuse a third card; if accepted, it is dealt face-up.

Traditional practice – grounded in mathematics, similar to basic strategy in blackjack, but further enforced via social sanctions by the other individuals whose money is at stake – dictates that one always accept a card if one’s hand totals between 0 and 4, inclusive, and always refuse a card if one’s hand totals 6 or 7.

After the player makes his decision, the banker in turn decides either to accept or to refuse another card. Once both the banker and the representative player have made their decision, the hands are turned face-up and compared.

If the player’s hand exceeds the banker’s hand when they are compared, each wagering player receives back their wager and a matching amount from the bank, and the position of banker passes to the next player in order.

If the banker’s hand exceeds the player’s hand, all wagers are forfeit and placed into the bank, and the banker position does not change. If there is a tie, wagers remain as they are for the next hand.

If the banker wishes to withdraw, the new banker is the first player in order willing to stake an amount equal to the current bank total. If no one is willing to stake this amount, the new banker is instead the next player in order, and the bank resets to whatever that player wishes to stake. Many games have a set minimum bank or wager amount.

## Baccarat Banque

In *Baccarat Banque* the position of banker is much more permanent compared to *Chemin de fer*. The shoe contains three inter-shuffled decks. The banker,unless he retires either of his own free will or by reason of the exhaustion of his finances, holds office until all these cards have been dealt.

The bank is at the outset put up to auction, i.e. is given to the player who will undertake to risk the largest amount. In some circles, the person who has first set down his name on the list of players has the right to hold the first bank, risking such amount as he may think proper.

The right to begin having been ascertained, the banker takes his place midway down one of the sides of an oval table, the croupier facing him, with the discard area between. On either side of the banker are the punters (ten such constituting a full table). Any other persons desiring to take part remain standing, and can only play in the event of the amount in the bank for the time being not being covered by the seated players.

The croupier, having shuffled the cards, hands them for the same purpose to the players to the right and left of him, the banker being entitled to shuffle them last, and to select the person by whom they shall be cut. Each punter having made his stake, the banker deals three cards, the first to the player on his right, the second to the player on his left, and the third to himself; then three more in like manner. The five punters on the right (and any bystanders staking with them) win or lose by the cards dealt to that side; the five others by the cards dealt to the left side. The rules as to turning up with eight or nine, offering and accepting cards, and so on, are the same as *Chemin de fer*.

Each punter continues to hold the cards for his side so long as he wins or ties. If he loses, the next hand is dealt to the player next following him in rotation.

Any player may “go bank”, the first claim to do so belonging to the punter immediately on the right of the banker; the next to the player on his left, and so on alternatively in regular order. If two players on opposite sides desire to “go bank”, they go half shares.

A player going bank may either do so on a single hand, in the ordinary course, or a cheval, i.e. on two hands separately, one-half of the stake being played upon each hand. A player going bank and losing may again go bank, and if he again loses, may go bank a third time, but not further.

A player undertaking to hold the bank must play out one hand, but may retire at any time afterwards. On retiring, he is bound to state the amount with which he retires. It is then open to any other player (in order of rotation) to continue the bank, starting with the same amount, and dealing from the remainder of the pack, used by his predecessor. The outgoing banker takes the place previously occupied by his successor.

The breaking of the bank does not deprive the banker of the right to continue, provided that he has funds with which to replenish it, up to the agreed minimum.

Should the stakes of the punters exceed the amount for the time being in the bank, the banker is not responsible for the amount of such excess. In the event of his losing, the croupier pays the punters in order of rotation, so far as the funds in the bank will extend; beyond this, they have no claim. The banker may, however, in such a case, instead of resting on his right, declare the stakes accepted, putting up the needed funds to meet them. In such event the bank thenceforth becomes unlimited, and the banker must hold all stakes (to whatever amount) offered on any subsequent hand, or give up the bank.

## Macao

David Parlett considers Macao as the immediate precursor to baccarat. Its name and rules suggest it may have been brought over by sailors returning from Asia where similar card games have been played since the early 17th century such as San zhang, Oicho-Kabu, and Gabo japgi. Macao appeared in Europe at the end of the 18th century and was popular for all classes. Its notoriety led to King Victor-Amadeus III banning it in all his realms in 1788. It was the most popular game in Watier’s, an exclusive gentlemen’s club in London, where it led to the ruin of Beau Brummell. The match in Arthur Schnitzler’s 1926 novella *Night Games* (*Spiel im Morgengrauen*) contains instructions for Macao under the name of *baccarat*. Its popularity in the United States waned after the early 20th century. The game still has a following in Continental Europe, especially in Russia.

Macao uses two decks of cards shuffled together. Punters place their bets (within the agreed limits) against the banker. Initially, one card is dealt clockwise and face down to every player by the banker. The punters’ objective is to beat the banker’s card value or risk losing their bet. In case of a tie, whoever has the same value with fewer cards wins. The banker wins if there is a tie in both value and number of cards (in an early version, all bets are off). Any punter who receives a natural 9 receives triple the amount of the bet as long as the banker does not have a natural 9 too. Winning with a natural 8 awards double while winning with a 7 or under is only equal to the bet. Players can request additional cards which are dealt face up; if it is a ten or a face card, they can reject it and ask for another. In an early version of this game, going over 9 with extra cards amounts to a “bust” as in blackjack, later versions use modulo 10 arithmetic as in the other games. Beating the banker with a pair only awards an equal amount to the bet. When the deck is exhausted, the player to the banker’s left becomes the new banker.

Victoria is a variation of macao where players are initially dealt two cards. Like macao and baccarat, it was banned in Russia during the 19th century though their rules continued to be printed in game books.

# Blackjack

**Blackjack**, also known as **twenty-one**, is a comparing card game between usually several players and a dealer, where each player in turn competes against the dealer, but players do not play against each other. It is played with one or more decks of 52 cards, and is the most widely played online casino game in the world. The objective of the game is to beat the dealer in one of the following ways:

- Get 21 points on the player’s first two cards (called a “blackjack” or “natural”), without a dealer blackjack;
- Reach a final score higher than the dealer without exceeding 21; or
- Let the dealer draw additional cards until their hand exceeds 21.

Players are each dealt two cards, face up or down depending on the online casino and the table at which you sit. In the U.S., the dealer is also dealt two cards, normally one up (exposed) and one down (hidden). In most other countries, the dealer receives one card face up. The value of cards two through ten is their pip value (2 through 10). Face cards (Jack, Queen, and King) are all worth ten. Aces can be worth one or eleven. A hand’s value is the sum of the card values. Players are allowed to draw additional cards to improve their hands. A hand with an ace valued as 11 is called “soft”, meaning that the hand will not bust by taking an additional card; the value of the ace will become one to prevent the hand from exceeding 21. Otherwise, the hand is “hard”.

Once all the players have completed their hands, it is the dealer’s turn. The dealer hand will not be completed if all players have either busted or received Blackjacks. The dealer then reveals the hidden card and must hit until the cards total 17 or more points. (At most tables the dealer also hits on a “soft” 17, i.e. a hand containing an ace and one or more other cards totaling six.) Players win by not busting and having a total higher than the dealer, or not busting and having the dealer bust, or getting a blackjack without the dealer getting a blackjack. If the player and dealer have the same total (not counting blackjacks), this is called a “push”, and the player typically does not win or lose money on that hand. Otherwise, the dealer wins.

Blackjack has many rule variations. Since the 1960s, blackjack has been a high-profile target of advantage players, particularly card counters, who track the profile of cards that have been dealt and adapt their wagers and playing strategies accordingly.

Blackjack has inspired other casino games, including Spanish 21 and pontoon.

## History

Blackjack’s precursor was *twenty-one*, a game of unknown origin. The first written reference is found in a book by the Spanish author Miguel de Cervantes, most famous for writing *Don Quixote*. Cervantes was a gambler, and the main characters of his tale “Rinconete y Cortadillo”, from *Novelas Ejemplares*, are a couple of cheats working in Seville. They are proficient at cheating at *veintiuna* (Spanish for twenty-one), and state that the object of the game is to reach 21 points without going over and that the ace values 1 or 11. The game is played with the Spanish *baraja* deck, which lacks eights and nines. This short story was written between 1601 and 1602, implying that *ventiuna* was played in Castile since the beginning of the 17th century or earlier. Later references to this game are found in France and Spain.

When twenty-one was introduced in the United States, gambling houses offered bonus payouts to stimulate players’ interest. One such bonus was a ten-to-one payout if the player’s hand consisted of the ace of spades and a black jack (either the jack of clubs or the jack of spades). This hand was called a “blackjack”, and the name stuck to the game even though the ten-to-one bonus was soon withdrawn. In the modern game, a *blackjack* refers to any hand of an ace plus a ten or face card regardless of suits or colours.

The first scientific and mathematically sound attempt to devise an optimal blackjack playing strategy was revealed in September 1956. Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott published a paper titled *The Optimum Strategy in Blackjack* in the Journal of the American Statistical Association. This paper would become the foundation of all future sound efforts to beat the game of blackjack. Ed Thorp would use Baldwin’s hand calculations to verify the basic strategy and later publish (in 1963) his famous book Beat the Dealer.

## Rules of play at online casino

At an online casino blackjack table, the dealer faces five to seven playing positions from behind a semicircular table. Between one and eight standard 52-card decks are shuffled together. At the beginning of each round, up to three players can place their bets in the “betting box” at each position in play. That is, there could be up to three players at each position at a table in jurisdictions that allow back betting. The player whose bet is at the front of the betting box is deemed to have control over the position, and the dealer will consult the controlling player for playing decisions regarding the hand; the other players of that box are said to “play behind”. Any player is usually allowed to control or bet in as many boxes as desired at a single table, but it is prohibited for an individual to play on more than one table at a time or to place multiple bets within a single box. In many U.S. casinos, however, players are limited to playing two or three positions at a table and often only one person is allowed to bet on each position.

The dealer deals cards from his/her left (the position on the dealer’s far left is often referred to as “first base”) to his/her far right (“third base”). Each box is dealt an initial hand of two cards visible to the people playing on it, and often to any other players. The dealer’s hand receives its first card face up, and in “hole card” games immediately receives its second card face down (the hole card), which the dealer peeks at but does not reveal unless it makes the dealer’s hand a blackjack. Hole card games are sometimes played on tables with a small mirror or electronic sensor that is used to peek securely at the hole card. In European casinos, “no hole card” games are prevalent; the dealer’s second card is neither drawn nor consulted until the players have all played their hands.

Cards are dealt either from one or two handheld decks, from a dealer’s shoe, or from a shuffling machine. Single cards are dealt to each wagered-on position clockwise from the dealer’s left, followed by a single card to the dealer, followed by an additional card to each of the positions in play. The players’ initial cards may be dealt face up or face down (more common in single-deck games).

The players’ object is to win money by creating card totals that turn out to be higher than the dealer’s hand but do not exceed 21 (“busting”/”breaking”), or alternatively by allowing the dealer to take additional cards until he/she busts. On their turn, players must choose whether to “hit” (take a card), “stand” (end their turn), “double” (double wager, take a single card and finish), “split” (if the two cards have the same value, separate them to make two hands) or “surrender” (give up a half-bet and retire from the game). Number cards count as their natural value; the jack, queen, and king (also known as “face cards” or “pictures”) count as 10; aces are valued as either 1 or 11 according to the player’s choice. If the hand value exceeds 21 points, it busts, and all bets on it are immediately forfeit. After all boxes have finished playing, the dealer’s hand is resolved by drawing cards until the hand busts or achieves a value of 17 or higher (a dealer total of 17 including an ace, or “soft 17”, must be drawn to in some games and must stand in others). The dealer never doubles, splits, or surrenders. If the dealer busts, all remaining player hands win. If the dealer does not bust, each remaining bet wins if its hand is higher than the dealer’s, and loses if it is lower. If a player receives 21 on the 1st and 2nd card it is considered a “natural” or “blackjack” and the player is paid out immediately unless dealer also has a natural, in which case the hand ties. In the case of a tied score, known as “push” or “standoff”, bets are normally returned without adjustment; however, a blackjack beats any hand that is not a blackjack, even one with a value of 21. Wins are paid out at 1:1, or equal to the wager, except for player blackjacks which are traditionally paid at 3:2 (meaning the player receives three dollars for every two bet) or one-and-a-half times the wager. Many casinos today pay blackjacks at less than 3:2 at some tables; for instance, single-deck blackjack tables often pay 6:5 for a blackjack instead of 3:2.

Blackjack games almost always provide a side bet called insurance, which may be played when dealer’s upcard is an ace. Additional side bets, such as “Dealer Match” which pays when the player’s cards match the dealer’s up card, are sometimes available.

### Player decisions

After receiving an initial two cards, the player has up to four standard options: “hit”, “stand”, “double down”, or “split”. Each option has a corresponding hand signal. Some games give the player a fifth option, “surrender”.

**Hit:**Take another card from the dealer.

*Signal*: Scrape cards against table (in handheld games); tap the table with finger or wave hand toward body (in games dealt face up).

**Stand:**Take no more cards, also known as “stand pat”, “stick”, or “stay”.

*Signal*: Slide cards under chips (in handheld games); wave hand horizontally (in games dealt face up).

**Double down:**The player is allowed to increase the initial bet by up to 100% in exchange for committing to stand after receiving exactly one more card. The additional bet is placed in the betting box next to the original bet. Some games do not permit the player to increase the bet by amounts other than 100%. Non-controlling players may double their wager or decline to do so, but they are bound by the controlling player’s decision to take only one card.

*Signal*: Place additional chips beside the original bet outside the betting box, and point with one finger.

**Split**: If the first two cards of a hand have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box. The dealer separates the two cards and draws an additional card on each, placing one bet with each hand. The player then plays out the two separate hands in turn; except for a few restrictions, the hands are treated as independent new hands, with the player winning or losing their wager separately for each hand. Occasionally, in the case of ten-valued cards, some casinos allow splitting only when the cards have the identical ranks; for instance, a hand of 10-10 may be split, but not one of 10-king. However, usually all 10-value cards are treated the same. Doubling and further splitting of post-split hands may be restricted, and an ace and ten value card after a split are counted as a non-blackjack 21. Hitting split aces is usually not allowed. Non-controlling players may follow the controlling player by putting down an additional bet or decline to do so, instead associating their existing wager with one of the two post-split hands. In that case they must choose which hand to play behind before the second cards are drawn. Some casinos do not give non-controlling players this option, and require that the wager of a player not electing to split remains with the first of the two post-split hands.

*Signal*: Place additional chips next to the original bet outside the betting box; point with two fingers spread into a V formation.

**Surrender**(only available as first decision of a hand): Some games offer the option to “surrender” directly after the dealer has checked for blackjack (see below for variations). When the player surrenders, the house takes half the player’s bet and returns the other half to the player; this terminates the player’s interest in the hand.

*Signal*: The request to surrender is made verbally, there being no standard hand signal.

Hand signals are used to assist the “eye in the sky”, a person or video camera located above the table and sometimes concealed behind one-way glass. The eye in the sky usually makes a video recording of the table, which helps in resolving disputes and identifying dealer mistakes, and is also used to protect the casino against dealers who steal chips or players who cheat. The recording can further be used to identify advantage players whose activities, while legal, make them undesirable customers. In the event of a disagreement between a player’s hand signals and their words, the hand signal takes precedence.

Each hand may normally “hit” as many times as desired so long as the total is not above hard 20. On reaching 21 (including soft 21), the hand is normally required to stand; busting is an irrevocable loss and the players’ wagers are immediately forfeited to the house. After a bust or a stand, play proceeds to the next hand clockwise around the table. When the last hand has finished being played, the dealer reveals the hole card, and stands or draws further cards according to the rules of the game for dealer drawing. When the outcome of the dealer’s hand is established, any hands with bets remaining on the table are resolved (usually in counterclockwise order): bets on losing hands are forfeited, the bet on a push is left on the table, and winners are paid out.

### Insurance

If the dealer’s upcard is an ace, the player is offered the option of taking “insurance” before the dealer checks the hole card.

Insurance is a side bet that the dealer has blackjack and is treated independently of the main wager. It pays 2:1 (meaning that the player receives two dollars for every dollar bet) and is available when the dealer’s exposed card is an ace. The idea is that the dealer’s second card has a fairly high probability (nearly one-third) to be ten-valued, giving the dealer blackjack and disappointment for the player. It is attractive (although not necessarily wise) for the player to insure against the possibility of a dealer blackjack by making a maximum “insurance” bet, in which case the “insurance proceeds” will make up for the concomitant loss on the original bet. The player may add up to half the value of their original bet to the insurance and these extra chips are placed on a portion of the table usually marked “Insurance pays 2 to 1”.

Players with a blackjack may also take insurance, and in taking maximum insurance they commit themselves to winning an amount exactly equal to their main wager, regardless of the dealer’s outcome. Fully insuring a blackjack against blackjack is thus referred to as “taking even money”, and paid out immediately, before the dealer’s hand is resolved; the players do not need to place more chips for the insurance wager.

Insurance bets are expected to lose money in the long run, because the dealer is likely to have blackjack less than one-third of the time. However the insurance outcome is strongly anti-correlated with that of the main wager, and if the player’s priority is to reduce variation, they might choose to pay for this.

Furthermore, the insurance bet is susceptible to advantage play. It is advantageous to make an insurance bet whenever the hole card has more than a chance of one in three of being a ten. Advantage play techniques can sometimes identify such situations. In a multi-hand, face-up, single deck game, it is possible to establish whether insurance is a good bet simply by observing the other cards on the table after the deal; even if there are just 2 player hands exposed, and neither of their two initial cards is a ten, then 16 in 47 of the remaining cards are tens, which is larger than 1 in 3, so insurance is a good bet. This is an elementary example of the family of advantage play techniques known as card counting.

Bets to insure against blackjack are slightly less likely to be advantageous than insurance bets in general, since the ten in the player’s blackjack makes it less likely that the dealer has blackjack too.

## Rule variations and effects on house edge

*Note: where changes in the house edge due to changes in the rules are stated in percentage terms, the difference is usually stated here in percentage points, not percentage; strictly speaking if, say, an edge of 10% is reduced to 9%, the amount is reduced by ten percent, or by one percentage point.*

The rules of online casino blackjack are generally determined by law or regulation, which establishes certain rule variations allowed at the discretion of the online casino. The rules of any particular game are generally posted on or near the table, failing which there is an expectation that casino staff will provide them on request. Over 100 variations of blackjack have been documented.

As with all casino games, blackjack incorporates a “house edge”, a statistical advantage for the casino that is built into the game. The advantage of the dealer’s position in blackjack relative to the player comes from the fact that if the player busts, the player loses, regardless of whether the dealer subsequently busts. Nonetheless, blackjack players using basic strategy will lose less than 1% of their total wagered amount with strictly average luck; this is very favorable to the player compared to other casino games. The loss rate of players who deviate from basic strategy through ignorance is generally expected to be greater.

**Dealer hits soft 17**

- Each game has a rule about whether the dealer must hit or stand on soft 17, which is generally printed on the table surface. The variation where the dealer must hit soft 17 is abbreviated “H17” in blackjack literature, with “S17” used for the stand-on-soft-17 variation. Substituting an “H17” rule with an “S17” rule in a game benefits the player, decreasing the house edge by about 0.2%.

**Number of decks**

- All things being equal, using fewer decks decreases the house edge. This mainly reflects an increased likelihood of player blackjack, since if the players draws a ten on their first card, the subsequent probability of drawing an ace is higher with fewer decks. It also reflects a decreased likelihood of blackjack-blackjack push in a game with fewer decks.

- Casinos generally compensate by tightening other rules in games with fewer decks, in order to preserve the house edge or discourage play altogether. When offering single deck blackjack games, casinos are more likely to disallow doubling on soft hands or after splitting, to restrict resplitting, require higher minimum bets, and to pay the player less than 3:2 for a winning blackjack.

- The following table illustrates the mathematical effect on the house edge of the number of decks, by considering games with various deck counts under the following ruleset: double after split allowed, resplit to four hands allowed, no hitting split aces, no surrender, double on any two cards, original bets only lost on dealer blackjack, dealer hits soft 17, and cut-card used. The increase in house edge per unit increase in the number of decks is most dramatic when comparing the single deck game to the two-deck game, and becomes progressively smaller as more decks are added.

Number of decks | House advantage |
---|---|

Single deck | 0.17% |

Double deck | 0.46% |

Four decks | 0.60% |

Six decks | 0.64% |

Eight decks | 0.65% |

- Late/early surrender

Surrender, for those games that allow it, is usually not permitted against a dealer blackjack; if the dealer’s first card is an ace or ten, the hole card is checked to make sure there is no blackjack before surrender is offered. This rule protocol is consequently known as “late” surrender. The alternative, “early” surrender, gives player the option to surrender *before* the dealer checks for blackjack, or in a no-hole-card game. Early surrender is much more favorable to the player than late surrender. Most medium-strength hands should be surrendered against a dealer Ace if the hole card has not been checked.

For late surrender, however, while it is tempting to opt for surrender on any hand which will probably lose, the correct strategy is to only surrender on the very worst hands, because having even a one in four chance of winning the full bet is better than losing half the bet and pushing the other half, as entailed by surrendering.

- Resplitting
- If the cards of a post-split hand have the same value, most games allow the player to split again, or “resplit”. The player places a further wager and the dealer separates the new pair dealing a further card to each as before. Some games allow unlimited resplitting, while others may limit it to a certain number of hands, such as four hands (for example, “resplit to 4”).
- Hit/resplit split aces
- After splitting aces, the common rule is that only one card will be dealt to each ace; the player cannot split, double, or take another hit on either hand. Rule variants include allowing re-splitting aces or allowing the player to hit split aces. Games allowing aces to be re-split are not uncommon, but those allowing the player to hit split aces are extremely rare. Allowing the player to hit hands resulting from split aces reduces the house edge by about 0.13%; allowing re-splitting of aces reduces house edge by about 0.03%. Note that a ten-value card dealt on a split ace (or vice versa) is a “soft 21” and not a “natural”.
- No double after split
- After a split, most games allow doubling down on the new two-card hands. Disallowing doubling after a split increases the house edge by about 0.12%.
- Double on 9/10/11 or 10/11 only
- Under the “Reno rule”, double down is only permitted on hard totals of 9, 10, or 11 (under a similar European rule, only 10 or 11). Basic strategy would otherwise call for some doubling down with hard 9 and soft 13–18, and advanced players can identify situations where doubling on soft 19–20 and hard 8,7 and even 6 is advantageous. The Reno rule prevents the player from taking advantage of double down in these situations and thereby increases the player’s expected loss. The Reno rule increases the house edge by around one in 1000, and its European version by around two in 1000.
- No hole card and OBO

In most non-U.S. casinos, a ‘no hole card’ game is played, meaning that the dealer does not draw nor consult his or her second card until after all players have finished making decisions. With no hole card, it is almost never correct basic strategy to double or split against a dealer ten or ace, since a dealer blackjack will result in the loss of the split and double bets; the only exception is with a pair of A’s against a dealer 10, where it is still correct to split. In all other cases, a stand, hit or surrender is called for. For instance, holding 11 against a dealer 10, the correct strategy is to double in a hole card game (where the player knows the dealer’s second card is not an ace), but to hit in a no hole card game. The no hole card rule adds approximately 0.11% to the house edge.

The “original bets only” rule variation appearing in certain no hole card games states that if the player’s hand loses to a dealer blackjack, only the mandatory initial bet (“original”) is forfeited, and all optional bets, meaning doubles and splits, are pushed. “Original bets only” is also known by the acronym OBO; it has the same effect on basic strategy and house edge as reverting to a hole card game.

- Altered payout for a winning blackjack
- In many casinos, a blackjack pays only 6:5 or even 1:1 instead of the usual 3:2. This is most common at tables with lower table minimums. Although this payoff was originally limited to single-deck games, it has spread to double-deck and shoe games. Among common rule variations in the U.S., these altered payouts for blackjack are the most damaging to the player, causing the greatest increase in house edge. Since blackjack occurs in approximately 4.8% of hands, the 1:1 game increases the house edge by 2.3%, while the 6:5 game adds 1.4% to the house edge. Video blackjack machines generally pay 1:1 payout for a blackjack.
- Dealer wins ties
- The rule that bets on tied hands are lost rather than pushed is catastrophic to the player. Though rarely used in standard blackjack, it is sometimes seen in “blackjack-like” games such as in some charity casinos.

## Blackjack strategy

### Basic strategy

Each blackjack game has a *basic strategy*, which is playing a hand of any total value against any dealer’s up-card, which loses the least money to the house in the long term.

An example of basic strategy is shown in the table below, and includes the following parameters:^{[9]}

- Four to eight decks
- The dealer hits on a soft 17
- A double is allowed after a split
- Only original bets are lost on dealer blackjack

Player hand | Dealer’s face-up card | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |

Hard totals (excluding pairs) | ||||||||||

17–20 | S | S | S | S | S | S | S | S | S | S |

16 | S | S | S | S | S | H | H | SU | SU | SU |

15 | S | S | S | S | S | H | H | H | SU | H |

13–14 | S | S | S | S | S | H | H | H | H | H |

12 | H | H | S | S | S | H | H | H | H | H |

11 | Dh | Dh | Dh | Dh | Dh | Dh | Dh | Dh | Dh | Dh |

10 | Dh | Dh | Dh | Dh | Dh | Dh | Dh | Dh | H | H |

9 | H | Dh | Dh | Dh | Dh | H | H | H | H | H |

5–8 | H | H | H | H | H | H | H | H | H | H |

Soft totals | ||||||||||

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |

A,9 | S | S | S | S | S | S | S | S | S | S |

A,8 | S | S | S | S | Ds | S | S | S | S | S |

A,7 | Ds | Ds | Ds | Ds | Ds | S | S | H | H | H |

A,6 | H | Dh | Dh | Dh | Dh | H | H | H | H | H |

A,4–A,5 | H | H | Dh | Dh | Dh | H | H | H | H | H |

A,2–A,3 | H | H | H | Dh | Dh | H | H | H | H | H |

Pairs | ||||||||||

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | |

A,A | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |

10,10 | S | S | S | S | S | S | S | S | S | S |

9,9 | SP | SP | SP | SP | SP | S | SP | SP | S | S |

8,8 | SP | SP | SP | SP | SP | SP | SP | SP | SP | SP |

7,7 | SP | SP | SP | SP | SP | SP | H | H | H | H |

6,6 | SP | SP | SP | SP | SP | H | H | H | H | H |

5,5 | Dh | Dh | Dh | Dh | Dh | Dh | Dh | Dh | H | H |

4,4 | H | H | H | SP | SP | H | H | H | H | H |

2,2–3,3 | SP | SP | SP | SP | SP | SP | H | H | H | H |

Key:

**S**= Stand**H**= Hit**Dh**= Double (if not allowed, then hit)**Ds**= Double (if not allowed, then stand)**SP**= Split**SU**= Surrender (if not allowed, then hit)

The bulk of basic strategy is common to all blackjack games, with most rule variations calling for changes in only a few situations. For example, if the above game used the hit on soft 17 rule, common in Las Vegas Strip casinos, only 6 cells of the table would need to be changed: double on 11 *vs.* A, surrender 15 or 17 *vs.* A, double on A,7 *vs.* 2, double on A,8 *vs.* 6, surrender (if not allowed, then hit) on 8,8 *vs.* A. Also when playing basic strategy never take insurance or “even money.”

Estimates of the house edge for blackjack games quoted by casinos and gaming regulators are generally based on the assumption that the players follow basic strategy and do not systematically change their bet size.

Most blackjack games have a house edge of between 0.5% and 1%, placing blackjack among the cheapest casino table games. Casino promotions such as complimentary matchplay vouchers or 2:1 blackjack payouts allow the player to acquire an advantage without deviating from basic strategy.

### Composition-dependent strategy

Basic strategy is based upon a player’s point total and the dealer’s visible card. Players may be able to improve on this decision by considering the precise composition of their hand, not just the point total. For example, players should ordinarily stand when holding 12 against a dealer 4. However, in a single deck game, players should hit if their 12 consists of a 10 and a 2. The presence of a 10 in the player’s hand has two consequences:

- It makes the player’s 12 a worse hand to stand on (since the only way to avoid losing is for the dealer to go bust, which is less likely if there are fewer 10s left in the shoe).
- It makes hitting safer, since the only way of going bust is to draw a 10, and this is less likely with a 10 already in the hand.

However, even when basic and composition-dependent strategy lead to different actions, the difference in expected reward is small, and it becomes even smaller with more decks. Using a composition-dependent strategy rather than basic strategy in a single deck game reduces the house edge by 4 in 10,000, which falls to 3 in 100,000 for a six-deck game.

### Advantage play

Blackjack has been a high-profile target for advantage players since the 1960s. Advantage play is the attempt to win more using skills such as memory, computation, and observation. These techniques, while generally legal, can be powerful enough to give the player a long-term edge in the game, making them an undesirable customer for the casino and potentially leading to ejection or blacklisting if they are detected. The main techniques of advantage play in blackjack are as follows:

#### Card counting

During the course of a blackjack shoe, the dealer exposes the dealt cards. Careful accounting of the exposed cards allows a player to make inferences about the cards which remain to be dealt. These inferences can be used in the following ways:

- Players can make larger bets when they have an advantage. For example, the players can increase the starting bet if there are many aces and tens left in the deck, in the hope of hitting a blackjack.
- Players can deviate from basic strategy according to the composition of their undealt cards. For example, with many tens left in the deck, players might double down in more situations since there is a better chance of getting a good hand.

A card counting system assigns a point score to each rank of card (e.g., 1 point for 2–6, 0 points for 7–9 and −1 point for 10–A). When a card is exposed, a counter adds the score of that card to a running total, the ‘count’. A card counter uses this count to make betting and playing decisions according to a table which they have learned. The count starts at 0 for a freshly shuffled deck for “balanced” counting systems. Unbalanced counts are often started at a value which depends on the number of decks used in the game.

Blackjack’s house edge is usually between 0.5%–1% when players use basic strategy. Card counting can give the player an edge of up to 2% over the house.

Card counting is most rewarding near the end of a complete shoe when as few as possible cards remain. Single-deck games are therefore particularly susceptible to card counting. As a result, casinos are more likely to insist that players do not reveal their cards to one another in single-deck games. In games with more decks of cards, casinos limit penetration by ending the shoe and reshuffling when one or more decks remain undealt. Casinos also sometimes use a shuffling machine to reintroduce the exhausted cards every time a deck has been played.

Card counting is legal and is not considered cheating as long as the counter isn’t using an external device, but if a casino realizes a player is counting, the casino might inform them that they are no longer welcome to play blackjack. Sometimes a casino might ban a card counter from the property.

The use of external devices to help counting cards is illegal in all US states that license blackjack card games.

#### Shuffle tracking

Techniques other than card counting can swing the advantage of casino blackjack toward the player. All such techniques are based on the value of the cards to the player and the casino as originally conceived by Edward O. Thorp. One technique, mainly applicable in multi-deck games, involves tracking groups of cards (also known as slugs, clumps, or packs) during the play of the shoe, following them through the shuffle, and then playing and betting accordingly when those cards come into play from the new shoe. Shuffle tracking requires excellent eyesight and powers of visual estimation but is more difficult to detect since the player’s actions are largely unrelated to the composition of the cards in the shoe.

Arnold Snyder’s articles in *Blackjack Forum* magazine brought shuffle tracking to the general public. His book, *The Shuffle Tracker’s Cookbook,* mathematically analyzed the player edge available from shuffle tracking based on the actual size of the tracked slug. Jerry L. Patterson also developed and published a shuffle-tracking method for tracking favorable clumps of cards and cutting them into play and tracking unfavorable clumps of cards and cutting them out of play.

#### Identifying concealed cards

The player can also gain an advantage by identifying cards from distinctive wear markings on their backs, or by hole carding (observing during the dealing process the front of a card dealt face down). These methods are generally legal although their status in particular jurisdictions may vary.

## Side bets

Many blackjack tables offer a side bet on various outcomes including:

- Player hand and dealer’s up card sum to 19, 20, or 21 (“Lucky Lucky”)
- Player initial hand is a pair (“Perfect pairs”)
- Player initial hand is suited, suited and connected, or a suited K-Q (“Royal match”)
- Player initial hand plus dealer’s card makes a flush, straight, or three-of-a-kind poker hand (“21+3”)
- Player initial hand totals 20 (“Lucky Ladies”)
- Dealer upcard is in between the value of the players two cards (“In Bet”)
- First card drawn to the dealer will result in a dealer bust (“Bust It!”)
- One or both of the players cards is the same as the dealers card (“Match the Dealer”)

The side wager is typically placed in a designated area next to the box for the main wager. A player wishing to wager on a side bet is usually required to place a wager on blackjack. Some games require that the blackjack wager should equal or exceed any side bet wager. A non-controlling player of a blackjack hand is usually permitted to place a side bet regardless of whether the controlling player does so.

The house edge for side bets is generally far higher than for the blackjack game itself. Nonetheless side bets can be susceptible to card counting. A side count, designed specifically for a particular side bet, can improve the player edge. Only a few side bets, like “Lucky Ladies”, offer a sufficient win rate to justify the effort of advantage play.

In team play it is common for team members to be dedicated toward counting only a sidebet using a specialized count.

## Blackjack tournaments

Blackjack can be played in tournament form. Players start with an equal numbers of chips; the goal is to finish among the top chip-holders. Depending on the number of competitors, tournaments may be held over several rounds, with one or two players qualifying from each table after a set number of deals to meet the qualifiers from the other tables in the next round. Another tournament format, Elimination Blackjack, drops the lowest-stacked player from the table at pre-determined points in the tournament. Good strategy for blackjack tournaments can differ from non-tournament strategy because of the added dimension of choosing the amount to be wagered. As in poker tournaments, players pay the casino an initial entry fee to participate in a tournament, and re-buys are sometimes permitted.

## Video blackjack

Some casinos, as well as general betting outlets, provide blackjack among a selection of casino-style games at electronic consoles. Video blackjack game rules are generally more favorable to the house; e.g., paying out only even money for winning blackjacks. Video and online blackjack games deal each coup from a fresh shoe, rendering card counting much less effective.

## Variants of the game

Blackjack is a member of a large family of traditional card games played recreationally all around the world. Most of these games have not been adapted for casino play. Furthermore, the casino game development industry is very active in producing blackjack variants, most of which are ultimately not adopted for widespread use in casinos. The following are the prominent twenty-one themed comparing card games which have been adapted or invented for use in casinos and have become established in the gambling industry.

**Spanish 21**provides players with many liberal blackjack rules, such as doubling down any number of cards (with the option to*rescue*, or surrender only one wager to the house), payout bonuses for five or more card 21s, 6–7–8 21s, 7–7–7 21s, late surrender, and player blackjacks always winning and player 21s always winning, at the cost of having no 10 cards in the deck (though there are jacks, queens, and kings). An unlicensed version of Spanish 21 played without a hole card is found in Australian casinos under the name “Pontoon” (presumably borrowed from the British recreational blackjack-like game “Pontoon” which has substantially different rules).**21st-Century Blackjack**(also known as “Vegas Style” Blackjack) is found in California card rooms. In this form of the game, a player bust does not always result in an automatic loss; depending on the casino, the player can still push if the dealer busts as well, although the dealer typically has to bust with a higher total.**Double Exposure Blackjack**deals the first two cards of the dealer’s hand face up. Blackjacks pay even money, and players lose on ties; also, they can neither buy insurance nor can they surrender their hand (as both dealer’s cards are exposed at the outset).**Double Attack Blackjack**has very liberal blackjack rules and the option of increasing one’s wager after seeing the dealer’s up card. This game is dealt from a Spanish shoe, and blackjacks only pay even money.**Blackjack Switch**is played over two hands whose second cards the player is allowed to interchange. For example, if the player is dealt 10–6 and 5–10, then the player can switch two cards to make hands of 10–10 and 6–5. Natural blackjacks are paid 1:1 instead of the standard 3:2, and a dealer 22 is a push.**Super Fun 21**allows a player to split a hand up to four times. If the player has six cards totaling 20, he automatically wins.

# Roulette

**Roulette** is a casino game named after the French word meaning *little wheel*. In the game, players may choose to place bets on either a single number, various groupings of numbers, the colors red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).

To determine the winning number and color, a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular track running around the outer edge of the wheel. The ball eventually loses momentum, passes through an area of deflectors, and falls onto the wheel and into one of 37 (in French/European style roulette) or 38 (in American style roulette) colored and numbered pockets on the wheel.

## History

The first form of roulette was devised in 18th century France. Many historians believe Blaise Pascal introduced a primitive form of roulette in the 17th century in his search for a perpetual motion machine. The roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game Biribi.

The game has been played in its present form since as early as 1796 in Paris. An early description of the roulette game in its current form is found in a French novel *La Roulette, ou le Jour* by Jaques Lablee, which describes a roulette wheel in the Palais Royal in Paris in 1796. The description included the house pockets, “There are exactly two slots reserved for the bank, whence it derives its sole mathematical advantage.” It then goes on to describe the layout with, “…two betting spaces containing the bank’s two numbers, zero and double zero”. The book was published in 1801. An even earlier reference to a game of this name was published in regulations for New France(Québec) in 1758, which banned the games of “dice, hoca, faro, and roulette”.

The roulette wheels used in the casinos of Paris in the late 1790s had red for the single zero and black for the double zero. To avoid confusion, the color green was selected for the zeros in roulette wheels starting in the 1800s.

In 1843, in the German spa casino town of Bad Homburg, fellow Frenchmen François and Louis Blanc introduced the single *0* style roulette wheel in order to compete against other casinos offering the traditional wheel with single and double zero house pockets.

In some forms of early American roulette wheels, there were numbers 1 through 28, plus a single zero, a double zero, and an American Eagle. The Eagle slot, which was a symbol of American liberty, was a house slot that brought the casino extra edge. Soon, the tradition vanished and since then the wheel features only numbered slots. According to Hoyle “the single 0, the double 0, and eagle are never bars; but when the ball falls into either of them, the banker sweeps every thing upon the table, except what may happen to be bet on either one of them, when he pays twenty-seven for one, which is the amount paid for all sums bet upon any single figure”.

In the 19th century, roulette spread all over Europe and the US, becoming one of the most famous and most popular casino games. When the German government abolished gambling in the 1860s, the Blanc family moved to the last legal remaining casino operation in Europe at Monte Carlo, where they established a gambling mecca for the elite of Europe. It was here that the single zero roulette wheel became the premier game, and over the years was exported around the world, except in the United States where the double zero wheel had remained dominant.

In the United States, the French double zero wheel made its way up the Mississippi from New Orleans, and then westward. It was here, because of rampant cheating by both operators and gamblers, that the wheel was eventually placed on top of the table to prevent devices being hidden in the table or wheel, and the betting layout was simplified. This eventually evolved into the American-style roulette game. The American game was developed in the gambling dens across the new territories where makeshift games had been set up, whereas the French game evolved with style and leisure in Monte Carlo.

During the first part of the 20th century, the only casino towns of note were Monte Carlo with the traditional single zero French wheel, and Las Vegas with the American double zero wheel. In the 1970s, casinos began to flourish around the world. By 2008 there were several hundred casinos worldwide offering roulette games. The double zero wheel is found in the U.S., Canada, South America, and the Caribbean, while the single zero wheel is predominant elsewhere.

The sum of all the numbers on the roulette wheel (from 0 to 36) is **666**, which is the “Number of the Beast”. One legend says that François Blanc made a deal with the devil to obtain the secrets of roulette.

## Rules of play against a casino

Roulette players have a variety of betting options. Placing inside bets is either selecting the exact number of the pocket the ball will land in, or a small range of pockets based on their proximity on the layout. Players wishing to bet on the ‘outside’ will select bets on larger positional groupings of pockets, the pocket color, or whether the winning number is odd or even. The payout odds for each type of bet are based on its probability.

The roulette table usually imposes minimum and maximum bets, and these rules usually apply separately for all of a player’s inside and outside bets for each spin. For inside bets at roulette tables, some casinos may use separate roulette table chips of various colors to distinguish players at the table. Players can continue to place bets as the ball spins around the wheel until the dealer announces *no more bets* or *rien ne va plus*.

When a winning number and color is determined by the roulette wheel, the dealer will place a marker, also known as a dolly, on that winning number on the roulette table layout. When the dolly is on the table, no players may place bets, collect bets, or remove any bets from the table. The dealer will then sweep away all other losing bets either by hand or rake, and determine all of the payouts to the remaining inside and outside winning bets. When the dealer is finished making payouts, the marker is removed from the board where players collect their winnings and make new bets. The winning chips remain on the board.

### California Roulette

In 2004, California legalized a form of roulette known as California Roulette. By law, the game must use cards and not slots on the roulette wheel to pick the winning number.

## Roulette wheel number sequence

The pockets of the roulette wheel are numbered from 0 to 36.

In number ranges from 1 to 10 and 19 to 28, odd numbers are red and even are black. In ranges from 11 to 18 and 29 to 36, odd numbers are black and even are red.

There is a green pocket numbered 0 (zero). In American roulette, there is a second green pocket marked 00. Pocket number order on the roulette wheel adheres to the following clockwise sequence in most casinos:

- Single-zero wheel
- 0-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-18-29-7-28-12-35-3-26
- Double-zero wheel
- 0-28-9-26-30-11-7-20-32-17-5-22-34-15-3-24-36-13-1-00-27-10-25-29-12-8-19-31-18-6-21-33-16-4-23-35-14-2

## Roulette table layout

The cloth-covered betting area on a roulette table is known as the *layout*. The layout is either single-zero or double-zero. The European-style layout has a single zero, and the American style layout is usually a double-zero. The American-style roulette table with a wheel at one end is now used in most casinos. The French style table with a wheel in the centre and a layout on either side is rarely found outside of Monte Carlo.

## Types of bets

In roulette, bets can either be inside or outside bets.

### Inside bets

Name | Description | Chip placement |
---|---|---|

Straight/Single | Bet on a single number | Entirely within the square for the chosen number |

Split | Bet on two vertically/horizontally adjacent numbers (e.g. 14-17 or 8-9) | On the edge shared by the numbers |

Street | Bet on three consecutive numbers in a horizontal line (e.g. 7-8-9) | On the outer edge of the number at either end of the line |

Corner/Square | Bet on four numbers that meet at one corner (e.g. 10-11-13-14) | On the common corner |

Six Line/Double Street | Bet on six consecutive numbers that form two horizontal lines (e.g. 31-32-33-34-35-36) | On the outer corner shared by the two leftmost or the two rightmost numbers |

Trio | A three-number bet that involves at least one zero: 0-1-2 (either layout); 0-2-3 (single-zero only); 0-00-2 or 00-2-3 (double-zero only) | On the corner shared by the three chosen numbers |

Basket/First Four | Bet on 0-1-2-3 (Single-zero layout only) | On the outer corner shared by 0-1 or 0-3 |

Top Line | Bet on 0-00-1-2-3 (Double-zero layout only) | On the outer corner shared by 0-1 or 00-3 |

### Outside bets

Outside bets typically have smaller payouts with better odds at winning. Except as noted, all of these bets lose if a zero comes up.

- 1 to 18 (Low or
*Manque*), or 19 to 36 (High or*Passe*) - A bet that the number will be in the chosen range.
- Red or black (
*Rouge ou Noir*) - A bet that the number will be the chosen color.
- Even or odd (
*Pair ou Impair*) - A bet that the number will be of the chosen type.
- Dozen bet
- A bet that the number will be in the chosen dozen: first (1-12,
*Première douzaine*or P12), second (13-24,*Moyenne douzaine*or M12), or third (25-36,*Dernière douzaine*or D12). - Column bet
- A bet that the number will be in the chosen vertical column of 12 numbers, such as 1-4-7-10 on down to 34. The chip is placed on the space below the final number in this sequence.
- Snake Bet
- A special bet that covers the numbers 1, 5, 9, 12, 14, 16, 19, 23, 27, 30, 32, and 34. It has the same payout as the dozen bet and takes its name from the zigzagging, snakelike pattern traced out by these numbers. The snake bet is not available in all casinos; when it is allowed, the chip is placed on the lower corner of the 34 square that borders the 19-36 betting box. Some layouts mark the bet with a two-headed snake that winds from 1 to 34, and the bet can be placed on the head at either end of the body.

In the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) result in the player losing only half of his/her bet if a zero comes up.

## Bet odds table

The payout (except for the special case of Top line bets), for American and European roulette, can be calculated as

- {\displaystyle \mathrm {payout} ={\frac {1}{n}}(36-n)={\frac {36}{n}}-1,}

where *n* is the number of squares the player is betting on. The initial bet is returned in addition to the mentioned payout. It can be easily demonstrated that this payout formula would lead to a zero expected value of profit if there were only 36 numbers. Having 37 or 38 numbers gives the casino its edge.

Bet name | Winning spaces | Payout | Odds against winning (French) | Expected value (on a $1 bet) (French) |
Odds against winning (American) | Expected value (on a $1 bet) (American) |
---|---|---|---|---|---|---|

0 | 0 | 35 to 1 | 36 to 1 | −$0.027 | 37 to 1 | −$0.053 |

00 | 00 | 35 to 1 | 37 to 1 | −$0.053 | ||

Straight up | Any single number | 35 to 1 | 36 to 1 | −$0.027 | 37 to 1 | −$0.053 |

Row | 0, 00 | 17 to 1 | 18 to 1 | −$0.053 | ||

Split | any two adjoining numbers vertical or horizontal | 17 to 1 | 17 ^{1}⁄_{2} to 1 |
−$0.027 | 18 to 1 | −$0.053 |

Street | any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.) | 11 to 1 | 11 ^{1}⁄_{3} to 1 |
−$0.027 | 11 ^{2}⁄_{3} to 1 |
−$0.053 |

Corner | any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21, etc.) | 8 to 1 | 8 ^{1}⁄_{4} to 1 |
−$0.027 | 8 ^{1}⁄_{2} to 1 |
−$0.053 |

Top line or Basket (US) | 0, 00, 1, 2, 3 | 6 to 1 | 6 ^{3}⁄_{5} to 1 |
−$0.079 | ||

Top line or Basket (European) | 0, 1, 2, 3 | 8 to 1 | 8 ^{1}⁄_{4} to 1 |
−$0.027 | ||

Six line | any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.) | 5 to 1 | 5 ^{1}⁄_{6} to 1 |
−$0.027 | 5 ^{1}⁄_{3} to 1 |
−$0.053 |

1st column | 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

2nd column | 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

3rd column | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

1st dozen | 1 through 12 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

2nd dozen | 13 through 24 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

3rd dozen | 25 through 36 | 2 to 1 | 2 ^{1}⁄_{12} to 1 |
−$0.027 | 2 ^{1}⁄_{6} to 1 |
−$0.053 |

Odd | 1, 3, 5, …, 35 | 1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

Even | 2, 4, 6, …, 36 | 1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

Red | 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 |
1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

Black | 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 |
1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

1 to 18 | 1, 2, 3, …, 18 | 1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

19 to 36 | 19, 20, 21, …, 36 | 1 to 1 | 1 ^{1}⁄_{18} to 1 |
−$0.027 | 1 ^{1}⁄_{9} to 1 |
−$0.053 |

Note that Top line (0, 00, 1, 2, 3) has a different expected value because of approximation of the correct 6 ^{1}⁄_{5}-to-1 payout obtained by the formula to 6-to-1. Note also that 0 and 00 are not odd or even, or high or low.

En prison rules, when used, reduce the house advantage.

## House edge

The *house average* or *house edge or house advantage* (also called the expected value) is the amount the player loses relative for any bet made, on average. If a player bets on a single number in the American game there is a probability of ^{1}⁄_{38} that the player wins 35 times the bet, and a ^{37}⁄_{38} chance that the player loses his bet. The expected value is:

- −1 ×
^{37}⁄_{38}+ 35 ×^{1}⁄_{38}= −0.0526 (5.26% house edge)

For European roulette, a single number wins ^{1}⁄_{37} and loses ^{36}⁄_{37}:

- −1 ×
^{36}⁄_{37}+ 35 ×^{1}⁄_{37}= −0.0270 (2.70% house edge)

The presence of the green squares on the roulette wheel and on the table is technically the only house edge. Outside bets will always lose when a single or double zero comes up. However, the house also has an edge on inside bets because the pay outs (including the original player’s bet) are always set at 36 to 1 when you mathematically have a 1 out of 38 (1 out of 37 for French/European roulette) chance at winning a straight bet on a single number. To demonstrate the house edge on inside bets, imagine placing straight $1 wagers on all inside numbers (including 0 and 00) to assure a win: you would only get back $36, having spent $38. The only exceptions are the five numbers bet where the house edge is considerably higher (7.89% on an American wheel), and the “even money” bets in some European games (French Roulette) where the house edge is halved because only half the stake is lost when a zero comes up. This is commonly called the “la partage” rule, and it is considered being the main difference of European and French roulette. There is also modification of this rule, which is called “en prison” rule. These rules cut the house edge into half (1.35%) in French roulette, when playing even-money bets, as half of the even-money bets are given back for player if the zero is draw in the wheel.

The house edge should not be confused with the “hold”. The hold is the average percentage of the money originally brought to the table that the player loses before he leaves—the actual “win” amount for the casino. The Casino Control Commission in Atlantic City releases a monthly report showing the win/hold amounts for each casino. The average win/hold for double zero wheels is between 21–30%, significantly more than the 5.26% house edge. This reflects the fact that the player is churning the same money over and over again. A 23.6% hold, for example, would imply that, on average, the player bets the total he brought to the table five times, as 23.6% is approximately equal to 100% − (100% − 5.26%)^{5}. For example, a player with $100 making $10 bets on red (which has a near 50/50 chance of winning) is highly unlikely to lose all his money after only 10 bets, and will most likely continue to bet until he has lost all of his money or decides to leave. A player making $10 bets on a single number (with only 1/38 chance of success) with a $100 bankroll is far more likely to lose all of his money after only 10 bets.

In the early frontier gambling saloons, the house would set the odds on roulette tables at 27 for 1. This meant that on a $1 bet you would get $27 and the house would keep your initial dollar. Today most casino odds are set by law, and they have to be either 34 to 1 or 35 to 1. This means that the house pays you $34 or $35 and you get to keep your original $1 bet.

## Mathematical model

As an example, we can examine the European roulette model, that is, roulette with only one zero. Since this roulette has 37 cells with equal odds of hitting, this is a final model of field probability {\displaystyle (\Omega ,2^{\Omega },\mathbb {P} )}, where {\displaystyle \Omega =\{0,\ldots ,36\}}, {\displaystyle \mathbb {P} (A)={\frac {|A|}{37}}} for all {\displaystyle A\in 2^{\Omega }}.

Call the bet {\displaystyle S} a triple {\displaystyle (A,r,\xi )}, where {\displaystyle A} is the set of chosen numbers, {\displaystyle r\in \mathbb {R} _{+}} is the size of the bet, and, and {\displaystyle \xi :\Omega \to \mathbb {R} } determines the return of the bet.

The rules of European roulette have 10 types of bets. First we can examine the ‘Straight Up’ bet. In this case, {\displaystyle S=(\{\omega _{0}\},r,\xi )}, for some {\displaystyle \omega _{0}\in \Omega }, and {\displaystyle \xi } is determined by

- {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega \neq \omega _{0}\\35\cdot r,&\omega =\omega _{0}\end{cases}}.}

The bet’s expected net return, or profitability, is equal to

- {\displaystyle M[\xi ]={\frac {1}{37}}\sum _{\omega \in \Omega }\xi (\omega )={\frac {1}{37}}\left(\xi (\omega ^{\prime })+\sum _{\omega \neq \omega ^{\prime }}\xi (\omega )\right)={\frac {1}{37}}\left(35\cdot r-36\cdot r\right)=-{\frac {r}{37}}\approx -0.027r.}

Without details, for a bet, black (or red), the rule is determined as

- {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega {\text{ is red}}\\-r,&\omega =0\\r,&\omega {\text{ is black}}\end{cases}},}

and the profitability

- {\displaystyle M[\xi ]={\frac {1}{37}}(18\cdot r-18\cdot r-r)=-{\frac {r}{37}}}.

For similar reasons it is simple to see that the profitability is also equal for all remaining types of bets. {\displaystyle -{\frac {r}{37}}}.^{[8]}

In reality this means that, the more bets a player makes, the more he is going to lose independent of the strategies (combinations of bet types or size of bets) that he employs:

- {\displaystyle \sum _{n=1}^{\infty }M[\xi _{n}]=-{\frac {1}{37}}\sum _{n=1}^{\infty }r_{n}\to -\infty .}

Here, the profit margin for the roulette owner is equal to approximately 2.7%. Nevertheless, several roulette strategy systems have been developed despite the losing odds. These systems can not change the odds of the game in favor of the player.

It is worth noting that the odds for the player in American roulette are even worse, as the bet profitability is at worst {\displaystyle -{\frac {3}{38}}r\approx -0.0789r}, and never better than {\displaystyle -{\frac {r}{19}}\approx -0.0526r}.

### Simplified mathematical model

For a roulette wheel with {\displaystyle n} green numbers and 36 other unique numbers the chance of the ball landing on a given number is {\displaystyle {\frac {1}{(36+n)}}}. For a betting option with {\displaystyle p} numbers that define a win, the chance of winning a bet is {\displaystyle {\frac {p}{(36+n)}}}

For example, betting on “red”, there are 18 red numbers, {\displaystyle p=18}, the chance of winning is {\displaystyle {\frac {18}{(36+n)}}}.

The payout given by the casino for a win is based on the roulette wheel having 36 outcomes and the payout for a bet is given by {\displaystyle {\frac {36}{p}}} .

For example, betting on 1-12 there are 12 numbers that define a win, {\displaystyle p=12}, the payout is {\displaystyle {\frac {36}{12}}=3}, so the better wins 3 times their bet.

The average return on a player’s bet is given by {\displaystyle {\frac {p}{(36+n)}}\times {\frac {36}{p}}={\frac {36}{(36+n)}}}

For {\displaystyle n>0} the average return is always lower than 1 so on average a player will lose money. With 1 green number {\displaystyle n=1} the average return is {\displaystyle {\frac {36}{37}}}, that is, after a bet the player will on average have {\displaystyle {\frac {36}{37}}} of their original bet returned to them. With 2 green numbers {\displaystyle n=2} the average return is {\displaystyle {\frac {36}{38}}}.

This shows that the expected return is independent of the choice of bet.

## Called (or call) bets or announced bets

Although most often named “call bets” technically these bets are more accurately referred to as “announced bets”. The legal distinction between a “call bet” and an “announced bet” is that a “call bet” is a bet called by the player without him placing any money on the table to cover the cost of the bet. In many jurisdictions (most notably the United Kingdom) this is considered gambling on credit and is illegal in some jurisdictions around the world. An “announced bet” is a bet called by the player for which he immediately places enough money to cover the amount of the bet on the table, prior to the outcome of the spin or hand in progress being known.

There are different number series in roulette that have special names attached to them. Most commonly these bets are known as “the French bets” and each covers a section of the wheel. For the sake of accuracy, zero spiel, although explained below, is not a French bet, it is more accurately “the German bet”. Players at a table may bet a set amount per series (or multiples of that amount). The series are based on the way certain numbers lie next to each other on the roulette wheel. Not all casinos offer these bets, and some may offer additional bets or variations on these.

### Voisins du zéro (*neighbors of zero)*

This is a name, more accurately “grands voisins du zéro”, for the 17 numbers that lie between 22 and 25 on the wheel, including 22 and 25 themselves. The series is 22-18-29-7-28-12-35-3-26-0-32-15-19-4-21-2-25 (on a single-zero wheel).

Nine chips or multiples thereof are bet. Two chips are placed on the 0-2-3 trio; one on the 4-7 split; one on 12-15; one on 18-21; one on 19-22; two on the 25-26-28-29 corner; and one on 32-35.

### Jeu zéro (*zero game*)

Zero game, also known as zero spiel (*Spiel* is German for game or play), is the name for the numbers closest to zero. All numbers in the zero game are included in the voisins, but are placed differently. The numbers bet on are 12-35-3-26-0-32-15.

The bet consists of four chips or multiples thereof. Three chips are bet on splits and one chip straight-up: one chip on 0-3 split, one on 12-15 split, one on 32-35 split and one straight-up on number 26.

This type of bet is popular in Germany and many European casinos. It is also offered as a 5-chip bet in many Eastern European casinos. As a 5-chip bet, it is known as “zero spiel naca” and includes, in addition to the chips placed as noted above, a straight-up on number 19.

### Le tiers du cylindre (*third of the wheel*)

This is the name for the 12 numbers that lie on the opposite side of the wheel between 27 and 33, including 27 and 33 themselves. On a single-zero wheel, the series is 27-13-36-11-30-8-23-10-5-24-16-33. The full name (although very rarely used, most players refer to it as “tiers”) for this bet is “le tiers du cylindre” (translated from French into English meaning one third of the wheel) because it covers 12 numbers (placed as 6 splits), which is as close to ^{1}⁄_{3} of the wheel as one can get.

Very popular in British casinos, tiers bets outnumber voisins and orphelins bets by a massive margin.

Six chips or multiples thereof are bet. One chip is placed on each of the following splits: 5-8; 10-11; 13-16; 23-24; 27-30; 33-36.

The tiers bet is also called the “small series” and in some casinos (most notably in South Africa) “series 5-8”.

A variant known as “tiers 5-8-10-11” has an additional chip placed straight up on 5, 8, 10 and 11; and so is a 10-piece bet. In some places the variant is called “gioco Ferrari” with a straight up on 8, 11, 23 and 30; the bet is marked with a red G on the racetrack.

### Orphelins (*orphans*)

These numbers make up the two slices of the wheel outside the tiers and voisins. They contain a total of 8 numbers, comprising 17-34-6 and 1-20-14-31-9.

Five chips or multiples thereof are bet on four splits and a straight-up: one chip is placed straight-up on 1 and one chip on each of the splits: 6-9; 14-17; 17-20 and 31-34.

### … and the neighbors

A number may be backed along with the two numbers on the either side of it in a 5-chip bet. For example, “0 and the neighbors” is a 5-chip bet with one piece straight-up on 3, 26, 0, 32 and 15. Neighbors bets are often put on in combinations, for example “1, 9, 14 and the neighbors” is a 15-chip bet covering 18, 22, 33, 16 with one chip; 9, 31, 20, 1 with two chips and 14 with three chips.

Any of the above bets may be combined, e.g. “orphelins by 1 and zero and the neighbors by 1”. The “…and the neighbors” is often assumed by the croupier.

### Final bets

Another bet offered on the single-zero game is “final”, “finale” or “finals”.

Final 4, for example, is a 4-chip bet and consists of one chip placed on each of the numbers ending in 4, that is 4, 14, 24 and 34. Final 7 is a 3-chip bet, one chip each on 7, 17 and 27. Final bets from final 0 (zero) to final 6 cost four chips. Final bets 7, 8 and 9 cost three chips.

Some casinos also offer split-final bets, for example final 5-8 would be a 4-chip bet, one chip each on the splits 5-8, 15-18, 25-28 and one on 35.

### Full completes/maximums

A complete bet places all of the inside bets on a certain number. Full complete bets are most often bet by high rollers as *maximum bets*.

The maximum amount allowed to be wagered on a single bet in European roulette is based on a progressive betting model. If the casino allows a maximum bet of $1000 on a 35-to-1 straight-up, then on each 17-to-1 split connected to that straight-up, $2000 may be wagered. Each 8-to-1 corner that covers four numbers) may have $4000 wagered on it. Each 11-to-1 street that covers three numbers may have $3000 wagered on it. Each 5-to-1 six-line may have $6000 wagered on it. Each $1000 incremental bet would be represented by a marker that is used to specifically identify the player and the amount bet.

For instance, if a patron wished to place a full complete bet on 17, the player would call “17 to the maximum”. This bet would require a total of 40 chips, or $40,000. To manually place the same wager, the player would need to bet:

Bet type | Number(s) bet on | Chips | Amount waged |
---|---|---|---|

Straight-up | 17 | 1 | $1,000 |

Split | 14-17 | 2 | $2,000 |

Split | 16-17 | 2 | $2,000 |

Split | 17-18 | 2 | $2,000 |

Split | 17-20 | 2 | $2,000 |

Street | 16-17-18 | 3 | $3,000 |

Corner | 13-14-16-17 | 4 | $4,000 |

Corner | 14-15-17-18 | 4 | $4,000 |

Corner | 16-17-19-20 | 4 | $4,000 |

Corner | 17-18-20-21 | 4 | $4,000 |

Six line | 13-14-15-16-17-18 | 6 | $6,000 |

Six line | 16-17-18-19-20-21 | 6 | $6,000 |

Total | 40 | $40,000 |

The player calls his bet to the croupier (most often after the ball has been spun) and places enough chips to cover the bet on the table within reach of the croupier. The croupier will immediately announce the bet (repeat what the player has just said), ensure that the correct monetary amount has been given while simultaneously placing a matching marker on the number on the table and the amount wagered.

The payout for this bet if the chosen number wins is 392 chips, in the case of a $1000 straight-up maximum, $40,000 bet, a payout of $392,000. The player’s wagered 40 chips, as with all winning bets in roulette, are still his property and in the absence of a request to the contrary are left up to possibly win again on the next spin.

Based on the location of the numbers on the layout, the number of chips required to “complete” a number can be determined.

- Zero costs 17 chips to complete and pays 235 chips.
- Number 1 and number 3 each cost 27 chips and pay 297 chips.
- Number 2 is a 36-chip bet and pays 396 chips.
- 1st column numbers 4 to 31 and 3rd column numbers 6 to 33, cost 30 chips each to complete. The payout for a win on these 30-chip bets is 294 chips.
- 2nd column numbers 5 to 32 cost 40 chips each to complete. The payout for a win on these numbers is 392 chips.
- Numbers 34 and 36 each cost 18 chips and pay 198 chips.
- Number 35 is a 24-chip bet which pays 264 chips.

Most typically (Mayfair casinos in London and other top-class European casinos) with these *maximum* or *full complete* bets, nothing (except the aforementioned maximum button) is ever placed on the layout even in the case of a win. Experienced gaming staff, and the type of customers playing such bets, are fully aware of the payouts and so the croupier simply makes up the correct payout, announces its value to the table inspector (floor person in the U.S.) and the customer, and then passes it to the customer, but only after a verbal authorization from the inspector has been received.

Also typically at this level of play (house rules allowing) the experienced croupier caters to the needs of the customer and will most often add the customer’s winning bet to the payout, as the type of player playing these bets very rarely bets the same number two spins in succession. For example, the winning 40-chip / $40,000 bet on “17 to the maximum” pays 392 chips / $392,000. The experienced croupier would pay the player 432 chips / $432,000, that is 392 + 40, with the announcement that the payout “is with your bet down”.

There are also several methods to determine the payout when a number adjacent to a chosen number is the winner; for example, player bets 40 chips on “23 to the maximum” and number 26 is the winning number. The most notable method is known as the “station” system or method. When paying in stations, the dealer counts the number of ways or stations that the winning number hits the complete bet. In the example above, 26 hits 4 stations – 2 different corners, 1 split and 1 six-line. The dealer takes the number 4, multiplies it by 30 and adds the remaining 8 to the payout: 4 × 30 = 120, 120 + 8 = 128. If calculated as stations, they would just multiply 4 by 36, making 144 with the players bet down.

In some casinos, a player may bet full complete for less than the table straight-up maximum; for example, “number 17 full complete by $25” would cost $1000, that is 40 chips each at $25 value.

## Betting strategies and tactic

Over the years, many people have tried to beat the casino, and turn roulette—a game designed to turn a profit for the house—into one on which the player expects to win. Most of the time this comes down to the use of betting systems, strategies which say that the house edge can be beaten by simply employing a special pattern of bets, often relying on the “Gambler’s fallacy”, the idea that past results are any guide to the future (for example, if a roulette wheel has come up 10 times in a row on red, that red on the next spin is any more or less likely than if the last spin was black).

All betting systems that rely on patterns, when employed on casino edge games will result, on average, in the player losing money. In practice, players employing betting systems may win, and may indeed win very large sums of money, but the losses (which, depending on the design of the betting system, may occur quite rarely) will outweigh the wins. Certain systems, such as the Martingale, described below, are extremely risky, because the worst-case scenario (which is mathematically certain to happen, at some point) may see the player chasing losses with ever-bigger bets until he runs out of money.

The American mathematician Patrick Billingsley said that no betting system can convert a subfair game into a profitable enterprise. At least in the 1930s, some professional gamblers were able to consistently gain an edge in roulette by seeking out rigged wheels (not difficult to find at that time) and betting opposite the largest bets.

### Prediction methods

Whereas betting systems are essentially an attempt to beat the fact that a geometric series with initial value of 0.95 (American roulette) or 0.97 (European roulette) will inevitably over time tend to zero, engineers instead attempt to overcome the house edge through predicting the mechanical performance of the wheel, most notably by Joseph Jagger at Monte Carlo in 1873. These schemes work by determining that the ball is more likely to fall at certain numbers, and if sufficiently good will raise the return of the game above 100%, defeating the betting system problem.

Edward O. Thorp (the developer of card counting and an early hedge-fund pioneer) and Claude Shannon (a mathematician and electronic engineer best known for his contributions to information theory) built the first wearable computer to predict the landing of the ball in 1961. This system worked by timing the ball and wheel, and using the information obtained to calculate the most likely octant where the ball would fall. Ironically, this technique works best with an unbiased wheel though it could still be countered quite easily by simply closing the table for betting before beginning the spin.

In 1982, several casinos in Britain began to lose large sums of money at their roulette tables to teams of gamblers from the USA. Upon investigation by the police, it was discovered they were using a legal system of biased wheel-section betting. As a result of this, the British roulette wheel manufacturer John Huxley manufactured a roulette wheel to counteract the problem.

The new wheel, designed by George Melas, was called “low profile” because the pockets had been drastically reduced in depth, and various other design modifications caused the ball to descend in a gradual approach to the pocket area. In 1986, when a professional gambling team headed by Billy Walters won $3.8 million using the system on an old wheel at the Golden Nugget in Atlantic City, every casino in the world took notice, and within one year had switched to the new low-profile wheel.

### Specific betting systems[edit]

The numerous even-money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a martingale betting strategy, wherein the gambler doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet. The problem with this strategy is that, remembering that past results do not affect the future, it is possible for the player to lose so many times in a row, that the player, doubling and redoubling his bets, either runs out of money or hits the table limit. A large financial loss is certain in the long term if the player continued to employ this strategy. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence. Regardless of the specific progression, no such strategy can statistically overcome the casino’s advantage, since the expected value of each allowed bet is negative.

### Labouchère system

The Labouchère System is a progression betting strategy like the martingale but does not require the gambler to risk his stake as quickly with dramatic double-ups. The Labouchere System involves using a series of numbers in a line to determine the bet amount, following a win or a loss. Typically, the player adds the numbers at the front and end of the line to determine the size of the next bet. When he wins, he crosses out numbers and continues working on the smaller line. If he loses, then he adds his previous bet to the end of the line and continues to work on the longer line. This is a much more flexible progression betting system and there is much room for the player to design his initial line to his own playing preference.

This system is one that is designed so that when the player has won over a third of his bets (less than the expected 18/38), he will win. Whereas the martingale will cause ruin in the event of a long sequence of successive losses, the Labouchère system will cause bet size to grow quickly even where a losing sequence is broken by wins. This occurs because as the player loses, the average bet size in the line increases.

As with all other betting systems, the average value of this system is negative.

### D’Alembert system

The system, also called *montant et demontant* (from French, meaning upwards and downwards), is often called a pyramid system. It is based on a mathematical equilibrium theory devised by a French mathematician of the same name. Like the martingale, this system is mainly applied to the even-money outside bets, and is favored by players who want to keep the amount of their bets and losses to a minimum. The betting progression is very simple: After each loss, you add one unit to the next bet, and after each win, one unit is deducted from the next bet. Starting with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. If this is followed by a win, the next bet would be 1 units.

This betting system relies on the gambler’s fallacy—that the player is more likely to lose following a win, and more likely to win following a loss.

### Other systems

There are numerous other betting systems that rely on this fallacy, or that attempt to follow ‘streaks’ (looking for patterns in randomness), varying bet size accordingly.

Many betting systems are sold online and purport to enable the player to ‘beat’ the odds. One such system was advertised by Jason Gillon of Rotherham, UK, who claimed you could ‘earn £200 daily’ by following his betting system, described as a ‘loophole’. As the system was advertised in the UK press, it was subject to Advertising Standards Authority regulation, and following a complaint, it was ruled by the ASA that Mr. Gillon had failed to support his claims you could earn £200 daily, and that he had failed to show that there was any loophole.

## Real-life roulette exploits

- In the summer of 1891 at the Monte Carlo casino, a part-time swindler and petty crook from London named Charles Wells broke the bank at each table he played over a period of several days. Breaking the bank meant he won all the available money in the table bank that day, and a black cloth would be placed over the table until the bank was replenished.
- In the 1960s and early ‘70s, Dr. Richard Jarecki won about $1.2 million at dozens of European casinos. He claimed that he was using a mathematical system designed on a powerful computer. In reality, he simply observed more than 10,000 spins of each Roulette wheel to determine flaws in the wheels. Eventually the casinos realized that flaws in the wheels could be exploited, and replaced older wheels. The manufacture of roulette wheels has improved over time.
- In 2004, Ashley Revell of London sold all of his possessions, clothing included, and placed his entire net worth of US$135,300 on red at the Plaza Hotel in Las Vegas. The ball landed on “Red 7” and Revell walked away with $270,600.

## In literature

- The 1866 novella, titled The Gambler, by the famous Russian writer Fyodor Dostoyevsky has a prime focus of the game as a major theme throughout the story. At the point of his life that he wrote this, gambling was at its peak for him. The novella is insightful about the game itself, and has technical descriptions of how he played the wheel and explains each move the main character does while playing the game.
- In the 1937 comedic short story “All’s Well with Bingo”, by British writer P. G. Wodehouse, the main character Bingo Little plays roulette at the Monte Carlo casino, betting on black. When his wife Rosie, who does not want him to gamble, comes by the table, Bingo cannot claim his winnings or else Rosie will see he is gambling. He has no choice but to let it all ride. Fortunately, black keeps coming up. Eventually, Rosie leaves, and Bingo is able to take his winnings. The story also references the Martingale betting strategy and the “en prison” rule.

- Players should not collect their winnings and betting chips until all bets have been paid. This is to avoid confusion and minimize the chance for players to steal other players’ chips.
- Players must not touch chips after the dealer gives the hand signal or announces “no more bets”. Players are not allowed to remove, change or add bets past this point.
- When the dealer has placed the
*dolly*(the plastic marker used to mark the winning number) it is strictly prohibited to touch any chips on a winning bet. - Dealers are not allowed to take cash from a player’s hand. To purchase chips with cash, place it on the table. This provides a better view of the transaction for casino surveillance.
- The use of electronic equipment at the table, such as mobile phones and cameras, is prohibited in most jurisdictions.
- The only items allowed in front of a player are chips, money, drinks, and cigarettes. Bulky items such as wallets and purses or bags must not be placed on the table.

## Common etiquette practices

- Players should place chips on the board rather than tossing them. Tossed chips may displace other bets or roll down to the “chipping machine”. If the player cannot reach to place a bet themselves, they should announce the bet to the dealer. This is treated as any other call bet.
- Changes for cash or color chips are supposed to be done in between spins. If the dealer has time, they will make changes during the spin, but they will most likely prioritize call bets before changes.
- All call bets are considered courtesy bets and are only placed if the dealer has time to change and place the bets. The bet is considered taken only if the dealer and the inspector dealer has repeated the bet. If the dealer does not take the bet, they will announce “no bet”. To argue with the dealer about which bets have been taken is considered extremely impolite and will most likely render a warning from the inspector dealer or pit boss.
- Most casinos ban food at the table. Drinking rules vary.

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