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Blackjack standard deviation details 5: Infinite deck expected return by player hand and dealer upcard 6: Fine points of when to surrender 7: Effect of card removal 8: Analysis of blackjack side bets 9: Composition-dependent expected returns for 1 to 8 decks Continuous shuffling machine vs.
Value and strategy for and bonuses Risk of ruin statistics Probabilities in the first four cards Value of each initial player card House edge using total-dependent vs.
Basic strategy when dealer exposes both cards The Ace-Five card counting method Basic strategy exceptions for three to six cards Blackjack splitting strategy when a back-player is betting Blackjack doubling strategy when doubling after splitting aces is allowed The dealer never doubles, splits, or surrenders.
If the dealer busts, all remaining player hands win. 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 Wins are paid out at 1: Many casinos today pay blackjacks at less than 3: After receiving an initial two cards, the player has up to four standard options: Each option has a corresponding hand signal.
Some games give the player a fifth option, "surrender". 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. Each hand may normally "hit" as many times as desired so long as the total is not above hard 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.
Insurance is a side bet that the dealer has blackjack and is treated independently of the main wager. 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".
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. 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 profitable bet.
This is an elementary example of the family of advantage play techniques known as card counting. The rules of casino blackjack are generally determined by law or regulation, which establishes certain rule variations allowed at the discretion of the 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 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 loss rate of players who deviate from basic strategy through ignorance is generally expected to be greater. 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.
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 aces against a dealer 10, where it is still correct to split.
In all other cases, a stand, hit or surrender is called for. The no hole card rule adds approximately 0. An example of basic strategy is shown in the table below, and includes the following parameters: 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: A, surrender 15 or 17 vs.
A, double on A,7 vs. 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. Casino promotions such as complimentary matchplay vouchers or 2: 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.
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,, which falls to 3 in , for a six-deck game.
Blackjack has been a high-profile target for advantage players since the s. 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:. 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:.
A card counting system assigns a point score to each rank of card e. 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.
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 is not using an external device, : 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.
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.
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.
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. Many blackjack tables offer a side bet on various outcomes including: 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 can be played in tournament form.