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61-518: Blackjack (formerly black jack or vingt-un ) is a casino banking game . It is the most widely played casino banking game in the world. It uses decks of 52 cards and descends from a global family of casino banking games known as " twenty-one ". This family of card games also includes the European games vingt-et-un and pontoon , and the Russian game Ochko  [ ru ] . The game

122-402: A blackjack, under the condition that they still get paid if the dealer also has a blackjack. Insurance bets lose money in the long run. The dealer has a blackjack less than one-third of the time. In some games, players can also take insurance when a 10-valued card shows, but the dealer has an ace in the hole less than one-tenth of the time. The insurance bet is susceptible to advantage play. It

183-429: A card), "stand" (end their turn and stop without taking a card), "double" (double their wager, take a single card, and stand), "split" (if the two cards have the same value, separate them to make two hands), or "surrender" (give up half of their bet and retire from the game). Number cards count as their number, the jack, queen, and king ("face cards" or "pictures") count as 10, and aces count as either 1 or 11 according to

244-453: A certain number of hands, such as four hands (for example, "resplit to 4"). 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 resplitting aces or allowing the player to hit split aces. Games allowing aces to be resplit are not uncommon, but those allowing the player to hit split aces are extremely rare. Allowing

305-471: A commission, known as a " rake ". The luck factor in a casino game is quantified using standard deviations (SD). The standard deviation of a simple game like roulette can be calculated using the binomial distribution . In the binomial distribution, SD = n p q {\displaystyle {\sqrt {npq}}} , where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes

366-417: A dealer blackjack will result in the loss of the split and double bets; the only exception is with a pair of aces 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, when 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

427-461: A higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning are 18/38 and his chances of losing 1 unit are 20/38. The player's expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one "zero" and therefore

488-414: 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

549-461: A predictable long-term advantage to the casino, or "house", while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish ) in a casino game are referred to as advantage players . The players' disadvantage

610-520: A result of 1 unit for a win, and 0 units for a loss, rather than −1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 × 10 ∗ 18 / 38 ∗ 20 / 38 {\displaystyle {\sqrt {10*18/38*20/38}}} = 3.16 units. After 10 rounds,

671-426: 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 object of the game is to win money by creating card totals higher than those of the dealer's hand but not exceeding 21, or by stopping at a total in the hope that the dealer will bust. On their turn, players choose to "hit" (take

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732-421: A small mirror or electronic sensor used to peek securely at the hole card. In European casinos, "no hole card" games are prevalent; the dealer's second card is not drawn until the players have played their hands. Dealers deal the cards 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

793-472: A table or through the purchase of paper tickets or cards, such as keno or bingo . Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, that involves random numbers. Casinos may also offer other types of gaming, such as hosting poker games or tournaments where players compete against each other. Games commonly found at casinos include table games, gaming machines and random number games. In

854-444: A table. The dealer deals from their left ("first base") to their far right ("third base"). Each box gets an initial hand of two cards visible to the people playing on it. The dealer's hand gets its first card face-up and, in "hole card" games, immediately gets a second card face-down (the hole card), which the dealer peeks at but only reveals when it makes the dealer's hand a blackjack. Hole card games are sometimes played on tables with

915-491: A time and do not require the involvement of casino employees. Tables games, such as blackjack or craps , involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. Random number games are based on the selection of random numbers, either from a computerized random number generator or from other gaming equipment. Random number games may be played at

976-702: Is a comparing card game where players compete against the dealer, rather than each other. Blackjack's immediate precursor was the English version of twenty-one called vingt-un , a game of unknown provenance. The first written reference is found in a book by the Spanish author Miguel de Cervantes . Cervantes was a gambler , and the protagonists of his " Rinconete y Cortadillo ", from Novelas Ejemplares , are card cheats in Seville . They are proficient at cheating at veintiuno (Spanish for "twenty-one") and state that

1037-421: Is a result of the casino not paying winning wagers according to the game's "true odds", which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, the true odds would be 6 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that

1098-404: 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%. All things being equal, using fewer decks decreases the house edge. This mainly reflects an increased likelihood of player blackjack, since if the player draws a ten on their first card,

1159-412: Is advantageous to make an insurance bet whenever the hole card has more than a one in three chance of being a ten. Card counting techniques can identify such situations. 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 the percentage change. For example, if an edge of 10% is reduced to 9%, it

1220-424: Is allowed. Insurance is a side bet that the dealer has a blackjack. The dealer asks for insurance bets before the first player plays. Insurance bets of up to half the player's current bet are placed on the "insurance bar" above the player's cards. If the dealer has a blackjack, insurance pays 2 to 1. In most casinos, the dealer looks at the down card and pays off or takes the insurance bet immediately. In other casinos,

1281-429: Is at the front of the betting box controls the position, and the dealer consults the controlling player for playing decisions; the other bettors "play behind". A player can usually control or bet in as many boxes as desired at a single table, but an individual cannot play on more than one table at a time or place multiple bets within a single box. In many U.S. casinos, players are limited to playing one to three positions at

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1342-495: Is based on a player's point total and the dealer's visible card. Players can sometimes improve on this decision by considering the composition of their hand, not just the point total. For example, players should ordinarily stand when holding 12 against a dealer 4. But 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: Even when basic and composition-dependent strategies lead to different actions,

1403-418: Is consequently known as "late" surrender. The alternative, "early" surrender, gives the 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. 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

1464-416: Is necessary to complete the task. In games that have a skill element, such as blackjack or Spanish 21 , the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting ), on the first hand of the shoe (the container that holds the cards). The set of optimal plays for all possible hands is known as " basic strategy " and is highly dependent on

1525-449: Is not a blackjack, even one with a value of 21. Wins are paid out at even money, except for player blackjacks, which are traditionally paid out at 3 to 2 odds. Many casinos today pay blackjacks at less than 3:2. This is common in single-deck blackjack games. Blackjack games usually offer a side bet called insurance , which may be placed when the dealer's face-up card is an ace. Additional side bets, such as "Dealer Match" which pays when

1586-478: Is reduced by one percentage point, not reduced by ten percent. Blackjack rules are generally set by regulations that establish permissible rule variations at the casino's discretion. Blackjack comes with a "house edge"; the casino's statistical advantage is built into the game. Most of the house's edge comes from the fact that the player loses when both the player and dealer bust. Blackjack players using basic strategy lose on average less than 1% of their action over

1647-433: Is sometimes seen in "blackjack-like" games, such as in some charity casinos. Each blackjack game has a basic strategy, the optimal method of playing any hand. When using basic strategy, the long-term house advantage (the expected loss of the player) is minimized. An example of a basic strategy is shown in the table below, which applies to a game with the following specifications: Key: Most basic strategy decisions are

1708-422: Is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win. It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as a percentage of turnover, and the variance tells them how much they need in

1769-980: The United States , 'table game' is the term used for games of chance such as blackjack , craps , roulette , and baccarat that are played against the casino and operated by one or more live croupiers , as opposed to those played on a mechanical device like a slot machine or against other players instead of the casino, such as standard poker . Table games are popularly played in casinos and involve some form of legal gambling , but they are also played privately under varying house rules. The term has significance in that some jurisdictions permit casinos to have only slots and no table games. In some states, this law has resulted in casinos employing electronic table games, such as roulette , blackjack , and craps . Table games found in casinos include: Gaming machines found in casinos include: Random numbers games found in casinos include: Casino games typically provide

1830-450: The " Reno rule", doubling down is only permitted on hard totals of 9, 10, or 11 (under a similar European rule, only 10 or 11). The 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

1891-557: The 1770s and 1780s, but the first rules appeared in Britain in 1800 under the name of vingt-un . Twenty-One, still known then as vingt-un , appeared in the United States in the early 1800s. The first American rules were an 1825 reprint of the 1800 English rules. English vingt-un later developed into an American variant in its own right which was renamed blackjack around 1899. According to popular myth, when vingt-un ('twenty-one')

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1952-533: The UK, the Gambling Commission (GC) now requires that all RTP (Return to Player) values be clearly displayed for both online and land-based casino games. This regulation ensures greater transparency, giving players the information they need to make more informed choices about the games they play. In games where players are not competing against the house, such as poker , the casino usually earns money via

2013-401: The casino against dealers who steal chips or players who cheat. Recordings can also identify advantage players . When a player's hand signal disagrees with their words, the hand signal takes precedence. A hand can "hit" as often as desired until the total is 21 or more. Players must stand on a total of 21. After a bust or a stand, play proceeds to the next hand clockwise around the table. After

2074-453: 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. A player total of 21 on the first two cards is a "natural" or "blackjack", and the player wins immediately unless the dealer also has one, in which case the hand ties. In the case of a tie ("push" or "standoff"), bets are returned without adjustment. A blackjack beats any hand that

2135-485: The difference in expected reward is small, and it becomes smaller with more decks. Using a composition-dependent strategy rather than a 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. Casino game There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as slot machines and pachinko , are usually played by one player at

2196-406: The expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss. The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase. As

2257-589: The foundation of future efforts to beat blackjack. Ed Thorp used Baldwin's hand calculations to verify the basic strategy and later published (in 1963) Beat the Dealer . At a blackjack table, the dealer faces five to nine playing positions from behind a semicircular table. Between one and eight standard 52-card decks are shuffled together. To start each round, players place bets in the "betting box" at each position. In jurisdictions allowing back betting, up to three players can be at each position. The player whose bet

2318-430: The house advantage (ignoring the en prison rule) is equal to 1/37 = 2.7%. The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges of up to 25%, slot machines having up to 15%. The calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation

2379-408: The last hand is played, the dealer reveals the hole card and stands or draws according to the game's rules. 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. If the dealer shows an ace, an "insurance" bet

2440-408: The long run, giving blackjack one of the lowest edges in the casino. The house edge for games where blackjack pays 6 to 5 instead of 3 to 2 increases by about 1.4%. Player deviations from basic strategy also increase the house edge. 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

2501-670: The mineral name was transferred by prospectors to the top bonus hand. He could not find any historical evidence for a special bonus for having the combination of an ace and a black jack. 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 , the first mathematically sound optimal blackjack strategy. This paper became

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2562-435: 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 a 1:1 payout for a blackjack. The rule that bets on tied hands are lost rather than pushed is catastrophic to the player. Though rarely used in standard blackjack, it

2623-507: The name stuck even after the ten-to-one bonus was withdrawn. French card historian Thierry Depaulis debunks this story, showing that prospectors during the Klondike Gold Rush (1896–99) gave the name blackjack to the game of American vingt-un , the bonus being the usual ace and any 10-point card. Since blackjack also refers to the mineral zincblende , which was often associated with gold or silver deposits, he suggests that

2684-403: 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. 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

2745-401: The number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see that the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This

2806-560: 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. "Rinconete y Cortadillo" was written between 1601 and 1602, implying that ventiuno was played in Castile since the beginning of the 17th century or earlier. Later references to this game are found in France and Spain. The first record of the game in France occurs in 1888 and in Britain during

2867-405: The payoff waits until the end of the play. In face-down games, if a player has more than one hand, they can look at all their hands before deciding. This is the only condition where a player can look at multiple hands. Players with blackjack can also take insurance. When this happens, it is called 'even money,' as the player is giving up their 3:2 payout for a 1:1 payout when taking insurance with

2928-502: The player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager. The house edge, or vigorish, is defined as the casino profit expressed as a percentage of the player's original bet. (In games such as blackjack or Spanish 21 , the final bet may be several times the original bet, if the player doubles and splits.) In American roulette , there are two "zeroes" (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to

2989-481: 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 surrendering, 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

3050-432: The player to hit hands resulting from split aces reduces the house edge by about 0.13%; allowing resplitting of aces reduces the house edge by about 0.03%. Note that a ten-value card dealt on a split ace (or vice versa) will not be counted as a blackjack but as a soft 21. 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%. Under

3111-409: The player's cards match the dealer's up card, are also sometimes available. After the initial two cards, the player has up to five options: "hit", "stand", "double down", "split", or "surrender". Each option has a corresponding hand signal. Hand signals help the " eye in the sky " make a video recording of the table, which resolves disputes and identifies dealer mistakes. It is also used to protect

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3172-444: The player's choice. If the total exceeds 21 points, it busts, and all bets on it immediately lose. After the boxes have finished playing, the dealer's hand is resolved by drawing cards until the hand achieves a total of 17 or higher. If the dealer has a total of 17 including an ace valued as 11 (a "soft 17"), some games require the dealer to stand while other games require another draw. The dealer never doubles, splits, or surrenders. If

3233-421: The player's expected loss. The Reno rule increases the house edge by around 0.1%, and its European version by around 0.2%. In most non-U.S. casinos, a "no hole card" game is played, meaning that the dealer does not draw nor consult their second card until after all players have finished making decisions. With no hole card, it is rarely the correct basic strategy to double or split against a dealer ten or ace, since

3294-421: The same effect on basic strategy and the house edge as reverting to a hole card game. 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

3355-435: The same for all blackjack games. Rule variations call for changes in only a few situations. For example, to use the table above on a game with the stand-on-soft-17 rule (which favors the player, and is typically found only at higher-limit tables today) only 6 cells would need to be changed: hit on 11 vs. A, hit on 15 vs. A, stand on 17 vs. A, stand on A,7 vs. 2, stand on A,8 vs. 6, and split on 8,8 vs. A. Regardless of

3416-589: The specific rule variations, taking insurance or "even money" is never the correct play under a basic strategy. Estimates of the house edge for blackjack games quoted by casinos and gaming regulators are based on the assumption that the players follow basic strategy. Most blackjack games have a house edge of between 0.5% and 1%, placing blackjack among the cheapest casino table games for the player. Casino promotions such as complimentary matchplay vouchers or 2:1 blackjack payouts allow players to acquire an advantage without deviating from basic strategy. The basic strategy

3477-441: The specific rules and even the number of decks used. Traditionally, many casinos were reluctant to disclose the house edge of their slot games, making it difficult for players to assess the true pay out potential. However, this practice is slowly changing, as more online casinos are beginning to provide this information, and independent research, such as that conducted by Michael Shackleford , has also shed light on these figures. In

3538-495: The subsequent probability of drawing an ace is higher with fewer decks. It also reflects the decreased likelihood of a blackjack–blackjack push in a game with fewer decks. Casinos generally compensate by tightening other rules in games with fewer decks, 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, restrict resplitting, require higher minimum bets, and pay

3599-477: 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. 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

3660-493: The way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so they outsource their requirements to experts in the gaming analysis field. Shoe (cards) Too Many Requests If you report this error to the Wikimedia System Administrators, please include

3721-466: Was introduced into the United States (in the early 1800s, during the First World War, or in the 1930s, depending on the source), 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

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