Blackjack

A game of Blackjack with a blackjack hand of 21.

Blackjack, also known as Twenty-one, Vingt-et-un (French for "twenty-one"), or Pontoon, is the most widely played casino banking game in the world.[1] The standard game is played with one or more Anglo-American decks containing 52 cards. The basic rules of the game involve adding the value of an initial two card hand in hopes of being dealt a value of twenty-one. If a value of less than twenty-one is dealt, the player may choose to be dealt single cards until they either reach a value of twenty one, reach a value they feel comfortable to play, or reach a value that exceeds twenty-one. The winner holds a hand with a value of, or nearest to, twenty-one without exceeding it. The game is played in many variations at casinos with different table rules. Much of blackjack's popularity is due to the mix of chance, skill, and the publicity that surrounds card counting (varying one's wager and playing strategy to take advantage of knowledge of the cards yet to be dealt). The casino game should not be confused with the British card game Black Jack.

Contents

History

Blackjack's precursor was Twenty-one, a game of unknown origin. The first written reference is found in a book by Miguel de Cervantes, who is most famous for writing Don Quixote, among other works. Cervantes was a gambler himself, and the main characters of his tale "Rinconete y Cortadillo", from "Novelas Ejemplares", are a couple of cheaters working in Seville. They are proficient at cheating at "ventiuna" (Spanish for twenty-one), and state that the object of the game is to reach 21 points without busting and that the Ace values 1 or 11. The game is played with the Spanish Baraja, which is without eights, nines and tens. This short story was written between 1601 and 1602, so the game was played in Castilia since the beginning of the 17th Century or earlier. Later references to this game are found in France and Spain.[2]

When 21 was introduced in the United States it was not popular, so gambling houses tried offering various bonus payouts to get the players to the tables. 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 bonus payout was soon abolished. In the modern game, a "natural" or "blackjack" is simply an ace plus a ten-value card.

Rules of play against a casino

In Blackjack at a casino, the dealer faces one to seven players from behind an arc-shaped table. Each player plays his hand independently against the dealer. At the beginning of each round, the player places a bet in the "betting box" and receives an initial hand of two cards. The object of the game is to get a higher card totaling than the dealer's hand, but without going over 21, which is called “busting” or “breaking." Cards with a number 2 to 10 printed on them count as that value; the jack, queen, and king (also known as "face cards") count as 10; the ace card can be either 1 or 11 according to the player's best interest. The player goes first and plays his hand by taking additional cards if he desires. If he goes over 21 points, he "busts" and automatically loses the hand and his bet. Then the dealer plays his or her hand. If the dealer busts, he loses to all remaining players who have cards whose values are equal to or below 21. If neither busts, the higher hand total wins. If a player ties with the dealer, the hand is a "push", also known as a "standoff", and the player's bet is returned (this means player does not lose his bet, but wins nothing either; this rule does apply in the US as well as in European casinos). It is possible for the dealer to lose to some players but still beat other players in the same round.

Example of a Blackjack game. The top half of the picture shows the beginning of the round, with bets placed and an initial two cards for each player. The bottom half shows the end of the round, with the associated losses or payoffs.

Cards are dealt in three ways, either from one or two hand-held decks, from a box (known as a "shoe") containing four to eight decks, or from a shuffling machine. When dealt by hand, the player's two initial cards are usually face-down, while the dealer has one face-up card called the "upcard" and one face-down card called the "hole card." (In European blackjack, the dealer's hole card is not actually dealt until the players all play their hands.) When dealt from a shoe, all player cards are normally dealt face-up, with minor exceptions. It shouldn't matter to the non-expert player whether his cards are dealt face-down or face-up since the dealer must play according to predetermined rules. If the dealer has less than 17, he must hit. If the dealer has 17 or more, he must stand (take no more cards), unless it is a "soft 17" (a hand that includes an ace valued as "11," for example a hand consisting of Ace+6, or Ace+2+4). With a soft 17, the dealer follows the casino rules printed on the blackjack table, either to "hit soft 17" or to "stand on all 17's."

The best possible hand is a "blackjack" or "natural", or an initial two-card total of 21 (an ace and a ten-value card). A blackjack beats all other hands, including hands of 21 achieved with 3 or more cards. Blackjack vs. blackjack is a push. When the dealer's upcard is an ace, the player is usually allowed to make a side bet called "insurance," of up to half his wager, which pays 2:1 if the dealer gets a blackjack, and is forfeited otherwise.

The minimum and maximum bets are posted on the table. The payoff on most bets is 1:1, meaning that the player wins the same amount as he or she bets. The traditional payoff for a player blackjack is 3:2, meaning that the casino pays $3 for each $2 originally bet, but many casinos today pay less at some tables.[3]

Player decisions

After receiving his initial two cards, the player has four standard options: he can "hit," "stand," "double down," or "split a pair." Each option requires the use of a hand signal. At some casinos or tables, the player may have a fifth option, called a "surrender."

signal: (handheld) Scrape cards against table. (face up) Touch finger to table or wave hand toward himself or herself.
signal: (handheld) Slide cards under chips. (face up) Wave hand horizontally.
signal: Place additional chips next to (not on top of) the original bet. Point with one finger.
signal: Place additional chips next to the original bet outside the betting box. Point with two fingers spread into a V formation.

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 recording provides a means of resolving disputes or identifying mistakes, and is also used to protect the casino against dealers who steal chips or players who cheat. It may also be used by the casino to identify advantage players whose activities, while legal, make them undesirable customers.

Each player may normally "hit" as many times as desired so long as the total in his hand is not above hard-20. On achieving 21 (including soft 21), a player is normally required to stand; busting is an irrevocable loss and the player's wager is immediately forefeited to the house. After a bust or a stand, play proceeds to the next player clockwise around the table. When the last player has finished, the dealer then reveals the hole card and stands or draws further cards according to the rules of the game. After the dealer's final outcome is established, any bets remaining on the table associated with losing hands are forefeited, and winners are paid out.

Rule variations and their consequences for the house edge

While the basic rules of casino blackjack are generally determined by law or regulation, certain variations are allowed at the discretion of the casino. The key game rules 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[4].

As with all casino games, blackjack incorporates a "house advantage" or "house edge". The primary house advantage in blackjack comes from the fact that if the player busts he loses, regardless of whether the dealer subsequently busts. Nonetheless, a blackjack player using basic strategy will lose less than 1% of his 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 in general 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 player draws a ten on his 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. When offering single deck blackjack games, casinos are more likely to disallow doubling on soft hands or after splitting, to restrict resplitting, 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 0.66%

Late/early surrender

Surrender, for those games that allow it, is usually first permitted only after the dealer has checked the hole card for blackjack and is therefore referred to as "late" surrender. The alternative, "early" surrender, gives the option for the player to surrender before the dealer checks for blackjack or in a no-hole-card game. Early surrender was originally the norm in Atlantic City casinos but is much more favourable to the player than late surrender, and has largely disappeared. Nonetheless early surrender games can still be found in several countries. Most medium-strength hands should be surrendered against a dealer Ace if the hole card has not been checked.

While it is tempting 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 25% 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 player splits a pair, and the initial cards dealt to a split hand creates a new pair, most games allow the player to split the new pair (or "resplit"). The player places a further wager and the dealer separates the pair 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"). It is common for resplitting to be specifically prohibited in the case of aces, but allowed for other denominations.

Hit/resplit split aces

After splitting aces, one 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. Allowing the player to hit hands resulting from split aces reduces the house edge by about 0.13%; allowing resplitting of aces reduces house edge by about 0.03%. While games allowing aces to be resplit are not uncommon, those allowing the player to hit split aces are extremely rare.

Double after split

After a player has split a pair, most casinos allow doubling down on the new two-card hands. "Double after split" decreases the house edge by about 0.12%.

Double on 9/10/11 or 10/11 only

This rule,often called the Reno rule, restricts the player to doubling down only on an initial player total of 10 or 11 (sometimes 9, 10, or 11 - more common in Europe). It prevents doubling on soft hands such as soft 17 (ace-6), and is unfavorable for the player. It increases the house advantage by between 0.09% (8 decks) and 0.15% (1 deck) for the 9-11 rule, and between 0.17% (8 decks) and 0.26% (single deck) for the 10-11 rule. These numbers can vary due to interaction with other rules.

No hole-card

In most non-U.S. casinos, a 'no hole card' game is played, meaning that the dealer does not draw nor consult his 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 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.

In some places, such as some casinos in Australia and New Zealand, if the dealer is later found to have blackjack, the player loses only his original bet but not any additional bets (doubles or splits). This has the same basic strategy as the hole card game, and the same advantage.

Altered payout for blackjack

In many casinos, usually at tables with the lowest table minimums and single-deck games, a blackjack pays only 6:5 or even 1:1 instead of the usual 3:2. 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 blackjacks generally pay 1:1 payout for blackjack, and this is a key reason why it has never approached the table version in terms of popularity (as well as the fact that cards are shuffled after every deal, which renders counting schemes much less effective). The 6:5 rule is most commonly employed on table blackjack at single deck games, where they help the house to compensate for low house edge intrinsic in using one deck only.[3]

Dealer wins ties

Allowing the dealer to win all push hands 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.

Insurance

If the dealer's upcard is an ace, the player is offered the option of taking insurance before the dealer checks his or her 'hole card'.

Insurance is a side bet of up to half the original bet placed on a special portion of the table usually marked "Insurance Pays 2 to 1". This side bet is offered only 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 a blackjack and almost certainly results in a loss for the player. (Thus,the expression, "ace in the hole"). It is attractive (although not necessarily wise) for the player to insure against this possibility by making an "insurance" bet, which pays 2-to-1 if the dealer has a blackjack, in which case the "insurance proceeds" will make up for the concomitant loss on the original bet. The insurance bet is lost if the dealer does not have blackjack, although the player can still win or lose on the original bet.

Insurance is a poor bet for the player unless he is counting cards because, in an infinite deck, 4/13 of the cards have a value of ten (10, J, Q, or K) and 9/13 therefore are not, so the theoretical return for an infinite deck game is 4/13 * 2 * bet - 9/13 * bet = -1 /13 * bet, or -7.69%. In practice, the average house edge will be lower than this, because by eliminating even one non-ten card from the shoe (the dealer's ace), the dealer causes the proportion of the remaining cards that are valued at ten to be higher. Even so, the bet is generally to be avoided, as the house's average edge is still more than 7%.

A player who is counting cards can keep count of the remaining tens in the shoe and use it to make insurance bets only when he or she has an edge (e.g., when more than one third of the remaining cards are tens). In addition, in a multi-hand single deck game, it is possible for insurance to be a good bet if the player simply observes the other cards on the table - for an initial hand, if the dealer has an ace, then there are 51 cards left in the deck, of which 16 are tens. However, if there are as few as 2 players playing, and neither of their two initial cards is a ten, then 16 of 47 remaining cards are tens - better than 1 in 3, making the insurance bet a good one.[5]

When the player has blackjack and the dealer has an ace, the insurance bet may be offered as "even money", meaning that the player's blackjack is paid immediately at 1:1 before checking the dealer's hand. 'Even money' is only a slightly different bet; the difference being that the player must have sufficient funds to insure blackjack if even money is not offered. Taking even money is generally a poor choice, because one of the player's two cards is a ten, so the proportion of tens remaining in the deck is lower.

In casinos in which a hole card is dealt, a dealer who is showing a card with a value of ace or 10 may slide the corner of his hole card over a small mirror or electronic sensor on the tabletop in order to check whether he has a blackjack. This practice minimizes the risk of inadvertently revealing the hole card, which may give the sharp-eyed player a considerable advantage.

Side bets

Some casinos offer a side bet with their blackjack games. Examples include side bets based on getting three 7s, a three card poker-style bet, a pair, and many others.[6] For the side bet, the player will typically put up an additional wager alongside his or her main bet and can win or lose the side bet, regardless of the main game result. The house edge for side bets is usually much higher than for the main game.

Blackjack strategy

Basic strategy

The complete set of optimal decisions for a player regarding only the dealer's current exposed card and the point total of his own current hand is known as basic strategy. The basic strategy table below applies to the following ruleset:

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 H
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,8 A,9 S S S S S S S S S S
A,7 S 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 except stand on 16v10 if not first two cards.)

In most Las Vegas Strip casino games, the dealer must hit on soft 17. This rule change requires a slightly modified basic strategy table: double on 11 vs. A, double on A/7 vs. 2, double on A/8 vs. 6 and surrender 15, 17 or 8/8 vs. A.

Composition-dependent strategy

Basic strategy is based upon a player's point total and the dealer's visible card. A player may be able to improve on this decision by considering the precise composition of his hand, not just the point total. For example, a player should ordinarily stand when holding 12 against a dealer 4. However, in a single deck game, the player should hit if his 12 consists of a 10 and a 2. The presence of a 10 in the player's hand has two consequences:[7]

However, in situations in which basic and composition-dependent strategy lead to different actions, the difference in expected value between them is small. Additionally, as the number of decks used in a blackjack game rises, both the number of situations in which composition determines the correct strategy and the house edge improvement from using a composition-dependent strategy falls. Using a composition-dependent strategy only reduces house edge by 0.0031% in a six-deck game, less than one tenth the improvement in a single-deck game (0.0387%).[8]

Advantage play

Blackjack has been a pre-eminent target in casinos for several decades in the field of advantage play, which is the attempt to win more using "honest" skills such as memory, mental computation and observation. These techniques, while entirely 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 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 game, the dealer progressively exposes cards which are dealt to his own and the players' hands. Careful observation of the exposed cards allows a player to make inferences about the cards which remain to be dealt, and use these inferences in one of two ways:

A typical card-counting system applies a point score for each rank of card (e.g. 1 point for 2-6 , 0 points for 7-9 and -1 point for 10-A). Whenever a card is exposed, a counter adds the score of that card to his running total score, which is used to make betting and playing decisions according to a table which he has learned. The count starts at 0 for a freshly shuffled deck for "balanced" counting systems. Unbalanced counts are often started at a number which reflects the total number of decks.

Depending on the particular blackjack rules in a given casino, basic strategy reduces the house advantage to less than 1%.[9] Card-counting, if done correctly, can give the player an advantage, typically ranging from 0 to 2% over the house.[10]

Card-counting mentally is legal and is not considered cheating.[11] However, most casinos have the right to ban players, with or without cause, and card-counting is frequently a reason for banning a player. Usually, the casino will inform the player that he is no longer welcome to play blackjack at that casino and he or she may be banned from the property. Players must be careful not to signal the fact that they are counting, and the use of electronic or other counting devices is usually illegal.

See also: MIT Blackjack Team

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.[12] One technique, mainly applicable in multi-deck games, involves tracking groups of cards (aka slugs, clumps, 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. This technique, which is admittedly much more difficult than straight card-counting and requires excellent eyesight and powers of visual estimation, has the additional benefit of fooling casino employees who are monitoring the player's actions and the count, since the shuffle tracker could be, at times, betting and/or playing opposite to how a straightforward card-counter would.[13]

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. [14][15][16] Other legal methods of gaining a player advantage at blackjack include a wide variety of techniques for hole carding or gaining information about the next card to be dealt. In addition, match-play coupons give the skillful basic-strategy blackjack player an edge. And finally, a special promotion - such as 2:1 for a blackjack - can temporarily swing the advantage to the player.

Variants

Pontoon is an English variation of blackjack with significant rule and strategy differences. However, in Australia and Malaysia, Pontoon is an unlicensed version of the American game Spanish 21 played without a hole card; despite the name, it bears no relation to English Pontoon.

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).

21st-Century Blackjack (also known as "Vegas Style" Blackjack) is commonly found in many California card rooms. In this form of the game, a player bust does not always result in an automatic loss; there are a handful of situations where the player can still push if the dealer busts as well, provided that the dealer busts with a higher total.

Certain rule changes are employed to create new variant games. These changes, while attracting the novice player, actually increase the house edge in these games. Double Exposure Blackjack is a variant in which the dealer's cards are both face-up. This game increases house edge by paying even money on blackjacks and players losing ties. 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.

The French and German variant "Vingt-et-un" (Twenty-one) and "Siebzehn und Vier" (Seventeen and Four) don't include splitting. An ace can only count as eleven, but two aces count as a blackjack. This variant is seldom found in casinos but is more common in private circles and barracks.

Chinese Blackjack is played by many in Asia. It has no splitting of cards,and includes other card combination regulations. Kampung Blackjack is a Malaysian variant of the Chinese Blackjack

Another variant is Blackjack Switch, a version in which a player is dealt two hands and is allowed to switch cards. 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.

In Multiple Action Blackjack the player places between 2 or 3 bets on a single hand. The dealer then gets a hand for each bet the player places on a hand. This essentially doubles the number of hands a single dealer can play per hour. Splitting and doubling are still allowed.

Recently, thanks to the popularity of poker, Elimination Blackjack has gained a following. Elimination Blackjack is a tournament format of blackjack.

Many casinos offer optional side bets at standard blackjack tables. For example, one common side-bet is "Royal Match", in which the player is paid if his first two cards are in the same suit, and receives a higher payout if they are a suited queen and king (and a jackpot payout if both the player and the dealer have a suited queen-king hand). Another increasingly common variant is "21+3," in which the player's two cards and the dealer's up card form a three-card poker hand; players are paid 9 to 1 on a straight, flush or three of a kind. These side bets invariably offer worse odds than well-played blackjack.

In April 2007, a new version of blackjack, called "three card blackjack" was approved for play in the State of Washington and is played with one deck of 52 cards. In this version of the game, the players place an ante bet. The players and dealer are then dealt 3 cards each. The players make the best blackjack (21) hand they can using 2 or all 3 cards. If the player likes his hand he makes a play bet that is equivalent to the ante bet. The dealer must qualify with an 18 or better. If the dealer qualifies and the player beats the dealer, the player is paid 1-1 on both the ante and play bets. If the dealer does not qualify, the player is paid 1-1 on his ante bet and play bet pushes. There is no hitting and no busting. At the same time that the player makes the ante bet, he has the option of making an "ace plus" bet. If the player has one ace in his hand of 3 cards, he gets paid 1-1. An ace and a 10 or face card pays 3-1. An ace and two 10's or face cards is paid 5-1. Two aces pays 15-1. Three aces pays 100-1.

Blackjack Hall of Fame

In 2002, professional gamblers around the world were invited to nominate great blackjack players for admission into the Blackjack Hall of Fame. Seven members were inducted in 2002, with new people inducted every year after. The Hall of Fame is at the Barona Casino in San Diego. Members include Edward O. Thorp, author of the 1960s book Beat the Dealer which proved that the game could be beaten with a combination of basic strategy and card counting; Ken Uston, who popularized the concept of team play; Arnold Snyder, author and editor of the Blackjack Forum trade journal; Stanford Wong, author and popularizer of the "Wonging" technique of only playing at a positive count, and several others.

See also

Notes

  1. Scarne's New Complete Guide to Gambling, p. 342
  2. Fontbona, Marc (2008). Historia del Juego en España. De la Hispania romana a nuestros días. Barcelona: Flor del Viento Ediciones. ISBN 978-84-96495-30-2. http://www.loteriasyapuestas.es/index.php/mod.pags/mem.libros/libro.18/idpag.600008/relcategoria.271032. 
  3. 3.0 3.1 Taking a hit: New blackjack odds further tilt advantage toward the house by Jeff Haney, Las Vegas Sun, November 13, 2003.
  4. QFIT.com 100+ Blackjack variations
  5. Blackjack Insurance Exceptions
  6. Blackjack side bets -- analyzed by The Wizard of Odds
  7. "The Wizard of Odds". Fine points of basic strategy in single-deck blackjack. http://wizardofodds.com/blackjack/appendix3c.html. Retrieved December 8, 2006. 
  8. "The Wizard of Odds". Total Dependent and Composition Dependent Basic Strategy in Blackjack. http://wizardofodds.com/blackjack/appendix15.html. Retrieved December 19, 2006. 
  9. Rules & House Edge Table
  10. Theory of Blackjack, p. 5
  11. Theory of Blackjack, pp 6–7
  12. The Mathematics of Gambling
  13. Shuffle Tracking Counts
  14. The Gambling Times Guide to Blackjack; Gambling Times Incorporated, Hollywood, CA; © 1984; Page 110; ISBN 0-89746-015-4 Shuffle-Tracking An Easy Way to Start
  15. Break the Dealer; by Jerry L. Patterson and Eddie Olsen; Perigee Books; A Division of Penguin Putnam; © 1986; ISBN 0-399-51233-0 Shuffle-Tracking; Chapter 6, Page 83]
  16. Blackjack: A Winner's Handbook; by Jerry L. Patterson; Perigee Books; A Division of Penguin Putnam; © 1990; ISBN 0-399-51598-4 Shuffle-Tracking; Chapter 4, Page 51]

Sources

Regulation in the United Kingdom

External links

Blackjack calculators