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Blackjack, also known as vingt-et-un, or twenty-one, is one of the most popular casino card games in the world. Much of its popularity is due to the mix of chance with elements of skill and decision making, and the publicity that surrounds the practice of card counting, in which players can turn the odds of the game in their favor by making betting and strategy decisions based on the cards that have been dealt. Officially, casinos strongly frown upon card counting. However, because card counting is a difficult skill to master and few players are successful at it, unofficially casinos are happy to have the public believe that there is one casino game in which money can be earned over a long period of time.


In blackjack, the players bet against the house dealer rather than against each other. The goal of each player is to have a higher point total than the dealer without going over 21. The values of the cards in each hand are added with 2 through 10 having face value, Ace having value 1 or 11 (player's choice), and King, Jack, and Queen cards having the value 10. If the player's and the dealer's hands have the same point value, this is known as a "push", and neither player nor dealer wins the hand.

After initial bets are placed, the dealer deals the cards (either from one or two hand-held decks of cards, or more commonly from a shoe containing four or more decks): two cards to each player, including himself. One of the dealer's two cards is visible, the other hidden (the hidden card is known as the "hole card"; in European blackjack, the hole card is not actually dealt until the players all play their hands). The cards of the players are dealt either face up or face down, depending on local casino practice; face up is the most common. At this point, if any player has a "natural" 21 (an Ace with any 10-count card), often called a "Blackjack", he is immediately paid 3:2 (most of the time: see Basic Strategy below) for his bet, unless the dealer also has a natural, which is a push. If the dealer has a natural, all players without a natural lose immediately; they do not get a chance to further improve their hands.

If the dealer does not have a natural, then one by one the dealer gives each player the option of asking for more cards (called "hitting") or staying with his current total (called "standing" or "holding"). The player may continue to ask for more cards, one by one, until he has either gone over 21 ("a bust"), or he is satisfied with the cards that he has (a total of 21 always stands). In addition, depending on what cards the player holds, and depending on the rules in effect at the table, the player may have the option of performing certain special plays (described below). If the player busts (takes a hit that put him over 21), he immediately loses the bet.

After all the players have finished making their decisions, the dealer then reveals the hidden "hole" card and may or may not draw additional cards. The decision of whether to draw more cards is not up to the dealer; it depends only on the point total that the dealer holds. If the dealer has fewer than 17, he draws another card, and continues to draw more cards until reaching a value equal to or greater than 17. If the dealer busts, then all remaining players win. Bets are normally paid out at the odds of 1:1. Casino rules vary on whether the dealer takes a hit when holding a "soft" 17 (that is, a hand such as an Ace with a six, which can be counted as either 7 or 17). In Atlantic City, all dealers will stand on a soft 17. In other areas, this is up to the individual casino.

Special plays and variants

Casinos often offer options which add to the player's gambling opportunities during the course of play. The most common of these are:
Pair splitting
If the player has two identical-value cards, he may place an additional bet equal to the original bet and play two hands instead of one, using each of the two cards as the start of a hand. Any two 10-value cards are considered a pair, and so may be split. (However, this is not a good idea because it's too likely that low cards will fall on them, ruining both hands, whereas unsplit they form a solid total of 20). In most casinos, if one splits a pair of Aces, one receives a second card to each but can make no further plays on either hand. (Usually a good move, however, since Aces are powerful, but two Aces unsplit form a weak total of hard 12). If a player has split, and the next card dealt has the same value, many casinos allow him to split again, often up to a total of four hands.
Doubling down
The player can double his bet and receive just one more card (forfeiting the opportunity to hit further). Some casinos allow players to double down only if their initial point total is 11 or 10 (or, in some cases, 9).
A few casinos allow double-after-split, where a player who has split a pair into two hands and has received a second card to each may then choose to double down on those two cards. Doubling down, whether the cards are split or unsplit, is a good idea when (and only when) the player has an edge on the dealer in the hand, that is, the player should expect to win more often than lose if he takes just one more card. Therefore, this is usually done on a total of 10 or 11 when the dealer shows a weak card like a Four, Five or Six.
Some casinos allow a player who has a bad hand to give up the hand and get half his bet back. If the player is allowed to surrender before the dealer checks for blackjack, this is called early surrender.
If the dealer has, as his up-card, an Ace, the players are offered the option of insurance before the dealer views the hole card. This is a side-bet that pays back 2:1, the insurance wager needs to be exactly half the amount of one or more of the player's wagers. If the dealer has a natural, one wins on the insurance bet, but loses the original bet. This is considered a very poor option for the player—consequently, almost every casino offers it as an option.
Pair of Aces
Almost never in casinos, but in some private games without pair splitting, a pair of Aces (with no other cards) always wins, even over a natural.
Card maximum
In some places a maximum number of cards, often five, for both, dealer and players, is imposed. Therefore, in the worst case, one may have to stop with a value of just 11 (four Twos and one Three).
The game is played with a 32-card deck, i.e. without Twos, Threes, Fours, Fives and Sixes. The Jacks count 2, Queens 3 and Kings 4, so there are no cards of values 5 and 6. The above special plays usually do not apply, but another one is often used, where a hand of five pictures (and nothing else) counts like a natural. This variant is very rare in casinos, but quite popular in non-profit home gambling in some countries.

Basic strategy

As in all casino games, the house has a statistical advantage over the players that will play itself out in the long run. But because blackjack, unlike other games, has an element of player choice, players can actually reduce the casino advantage to a small percentage by playing what is known as basic strategy. This strategy determines when to hit and when to stand, and also determines when doubling down or splitting is the correct action. Basic strategy is based on the player's point total and the dealer's visible card. There are slight variations in basic strategy depending on the exact house rules and the number of decks used. Under the most favorable conditions (single deck, downtown Las Vegas rules), the house advantage over a basic strategy player can be as low as 0.16%. Indeed, casinos offering special rules like surrender and double-after-split may actually be offering a positive expectation to basic strategy players; they are counting on players making mistakes to make money.

The following rules are beneficial to the skilled player:
  1. Doubles are permitted on any two-card hand except a blackjack.
  2. Doubles are permitted after splitting.
  3. Early surrender; the ability to forfeit half your wager against a face or ace before the dealer checks for blackjack.
  4. Normal (aka "late") surrender.
  5. Resplitting Aces.
  6. Drawing more than one card against a split Ace.
  7. Five or more cards with the total still no more than 21 as an automatic win ("Charlies")
The following rules are detrimental to the skilled player:
  1. Less than 3:2 payout on blackjacks (as is the case with Las Vegas Strip single-deck blackjack, paying out 6:5)
  2. Splitting a maximum of once (to two hands)
  3. Double down restricted to certain totals, such as 9-11 or 10,11
  4. Aces may not be resplit
  5. No-Peek (European) blackjack—player loses splits and doubles to a dealer blackjack
  6. Player losing ties

Basic strategy tables

Your Hand Dealer's face-up card
2 3 4 5 6 7 8 9 10 A
Hard totals
17-21 S S S S S S S S S S
13-16 S S S S S H H H H H
12 H H S S S H H H H H
11 D D D D D D D D D H
10 D D D D D D D D H H
9 D D D D D H H H H H
5-8 H H H H H H H H H H
Soft totals
A,8-10 S S S S S S S S S S
A,7 S D D D D S S H H H
A,6 H D D D D H H H H H
A,4-5 H H D D D H H H H H
A,2-3 H H H D D H H H H H
10,10 S S S S S S S S S S
5,5 D D D D D D D D H H
4,4 H H H H H H H H H H
2,2 3,3 H H SP SP SP SP H H H H

The above is a basic strategy table for 1 deck, Las Vegas Strip rules. Key : S=Stand, H=Hit, D=Double, SP=Split.

Card counting

Unlike casino games such as roulette and craps, where the outcome of one play has no effect on any future play, a hand of blackjack depletes the deck of the cards used in that hand, and this can alter the probability of certain events occurring on the next deal. In proper statistics terms, this is known as the Law of Independent Trials - past event have no effect on future probabilities. Specifically, if the remaining cards have a higher proportion of 10-count cards and Aces than normal, it is more likely that a player will be dealt a natural, which is to the player's advantage (yes, it's also more likely for the dealer to get a natural—but the dealer wins only even money, while the player is paid 3:2). When the deck has more small cards such as 4s, 5s, and 6s, it is more likely that the player will be dealt a bad hand and bust, favoring the dealer (likewise, it increases the chance of a dealer busting as well, but when the player busts, the dealer wins even if he later busts himself).

Because the house advantage in blackjack is so small to begin with, it is quite common for a deck that happens to be "rich" in remaining 10 count cards and Aces to offer a positive expectation to the player on the next hand. By keeping track of the cards played, a player can take advantage of these situations by betting larger amounts when the deck is in his favor and smaller amounts when it is not. In the long run, the deck will be unfavorable to the player more often than it is favorable, but it is the amount bet under each condition that counts. The player can also use information about the deck's composition to alter strategy. For example, basic strategy calls for hitting a 16 when the dealer's upcard is a 10, but this is a very close play; one loses less by hitting than standing, but not by much. If it is known, however, that the deck is depleted of small cards such as 4s and 5s, and rich in 10s, that may alter the odds in favor of standing.

It is difficult for most people to remember what cards have already been dealt, particularly from a multiple deck shoe. Therefore, most card counting schemes assign a positive, negative, or zero point value to each card in the deck. Normally, low-value cards, such as a 2 or 3, are given a positive value, and 10s are given a negative value. The exact number assigned to the cards depends on the specific card-counting method. The card counter mentally keeps a running tally of the point values as they are dealt. To make the count an accurate representation of the percentage of "good" cards left in the deck, this running tally must normally be divided by a factor based on the counter's estimate of the number of undealt cards that are left (so-called unbalanced counts do not require this additional adjustment, because that is factored into the count). Highly skilled counters have an expectation of 1 to 1.6% gain; professional counters do exist, and number perhaps a few hundred. It is probably safe to say that the best counters earn in the very low six figures of US dollars, comparable with those in other mentally exacting fields.

If the tally is sufficiently high, the counter can increase his or her bet, and also may make modifications to basic strategy. All of these calculations must be accurate, at the same time that the dealer and other players may be talking to him, and it must be done in such a way that the casino does not notice that any counting is taking place, to avoid facing casino countermeasures. In practice, the vast majority of people who attempt to count cards lose money through errors; casinos who notice a counter will often check to see if the counter is good enough to have a positive expectation, and ignore them otherwise. This detection process is mistake-prone.

In addition, a card counter can play the Insurance bet if the count of faces is sufficiently high with potentially an advantage over the house; this bet is in general almost always disadvantageous.

Counting schemes that assign point values of –1, 0, or +1 are called level one counts and are considered the easiest to perform. Slightly greater accuracy, at the cost of increased difficulty and likelihood of making mistakes, involves the use of multi-level counts, which assign point values of –2, +2, or greater to the various cards. This greater range of point values adds to the complication of keeping an accurate tally in one's head.

A final complication in card counting involves the issue of how to treat aces. While playing out hands, Aces are slightly disadvantageous for the player, which implies that they should have a positive point count; but for purposes of getting a blackjack, they are extremely valuable when they remain in the deck. Most counting schemes give aces a negative count, recognizing that there is a compromise involved in this process. Some schemes actually assign a zero value to aces, and require the counter to keep a separate side count of aces.

The theory of card-counting, and the first counting scheme, was published in 1962 by American mathematician Edward O. Thorp in his book Beat the Dealer, which is now regarded as a classic in the gambling literature genre. Much of the specific detail in the work, however, is no longer up-to-date— end play, for example, has practically disappeared because the casinos no longer deal to the last card, in a (somewhat panicked, some say) response to the book. Also, the counting system described (10-count) is harder to use and less profitable than the point-count systems that have been developed afterwards.

The most commonly used system by most professionals (both players and surveillance) is Hi-Lo. It assigns -1 to 10's and Aces, +1 to 2 through 6. Higher level counts theoretically generate higher profits, but for most players, decreased playing speed and increased fatigue and error rates argue against their use. K-O, an unbalanced count (7's are also +1) developed by Ken Fuchs and Olaf Vancura (Knock Out Blackjack), is only modestly less effective than Hi-Lo, but is substantially less error-prone.

In the early days of card-counting, it is undoubted that a few players were hugely successful. Ken Uston recounts his early successes—and court battles with the casinos—in his book Ken Uston on Blackjack. In reality, Ken Uston, though perhaps the most famous card counter through his 60 Minutes television appearance and his books, was overall only a small winner. The most financially successful card counters have made their fortunes in other businesses. Ed Thorp, for example, runs a successful fund.

There have been several MIT Blackjack Teams, made up of MIT students who team up to use a combination of card counting and group play to attempt to beat the house.

Casino counter-measures

Casinos can counter card counting by using large quantities of decks in dealing
cards. "Shoes" consisting of 6 or 8 decks are common. Increasing the number of decks decreases the tendency of the count to vary widely, offering the card counter fewer opportunities to take advantage of a player-advantageous count.

Player advantage can also be decreased by more frequently shuffling the cards. The shallower the "penetration" (the proportion of the shoe consumed before reshuffling), the less opportunity there is for the count to vary.

However, for the casinos there is a downside to frequent shuffling: It reduces the amount of time that the noncounting players are playing and consequently losing money to the house. It has become common for casinos to use automatic shuffling machines to compensate for this. Some models of shuffling machines shuffle one set of cards while another is in play. Others, known as Continuous Shuffle Machines (CSMs) allow the dealer to simply return used cards to a single shoe to allow playing with no interruption. Because CSMs essentially force minimal penetration, they remove almost all possible advantage of traditional counting techniques. As a result, some blackjack players call for a boycott of tables using CSMs.

Many casual card counters make small mistakes that cost the advantage they gain by counting. Two or three mistakes per hour may give back all of the counter's advantage. Even if you can count perfectly when practicing at home, it is much more difficult in an actual casino. The loud, distracting environments of most casinos, and even the availability of complimentary alcoholic beverages, play roles as casino counter-measures.

Casinos also look out for known card counters, who may be banned from play depending on regulatory commission rules. They also look for suspicious actions such as a long series of small bets followed by large one. Monitoring player behavior to assist in this identification falls to on-floor casino personnel ("pit bosses") and central security personnel who may use video surveillance ("the eye in the sky") as well as computer analysis to try to spot playing behavior indicative of card counting; early counter-strategies featured the dealer learning to count the cards themselves to recognise the patterns in the players. In addition, many casinos employ the services of various agencies who claim to have a catalog of advantage players. If a player is found to be in the Griffin Book or Biometrica, he will almost certainly be stopped from play and asked to leave regardless of his table play. For successful card counters, therefore, skill at "cover" behavior to hide counting to avoid "drawing heat" and possibly being barred, may be just as important as playing skill.

The Nevada casinos ban only the truly skilled counters playing for medium or high stakes; other states' casinos lack the ability to bar players, and may alter the game's dynamic against card counters by raising the minimum or lowering the limit on a table with a suspected counter, or by reshuffling sooner than the normal end of the shoe if they think that the player is offering a large bet on a positive count. (In these states, only the state gaming regulatory commission has the ability to bar people from casinos. Nevada also maintains such a list, and these lists are often shared amongst the various casinos and state regulators.)

There have been some high-profile lawsuits involving whether the casino is allowed to bar card-counters. Essentially, card-counting, if done in your head and with no outside assistance with devices or additional people, is not illegal (they can't arrest anyone for working in his own head). Using an outside aid, though, is illegal. However, the casinos despise counters and, if permitted by their jurisdiction, may ban counters from their casinos; in Nevada, where the casinos are ruled to be private places, the only prerequisite to a ban is the full reading of the Trespass Act to ban a player for life. Some skilled counters try to disguise their identities and playing habits; however, some casinos have claimed that facial recognition software can often match a camouflaged face with a banned one. Whether this is true is unknown.

Most casinos now hire consulting firms to help them track card counters.

Finally, the simplest countermeasure the casinos use in order to thwart card counting is simply to offer an inferior blackjack payoff of 6:5 instead of the standard 3:2. 6:5 blackjack is over eight times worse mathematically for the player than in a typical game with a regular payoff, expert player and novice alike cannot beat the game as a practical matter. The casinos offer this game using a single deck, which attracts players who think this gives them an advantage, when in fact the benefit of a single deck is outweighed several times over by the short blackjack payoff.
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