Blackjack

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Blackjack, also known as 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 an element of skill and decision making that is involved, and the publicity that surrounds the practice of card counting, in which players can win money by making betting and strategy decisions based on the cards that have been dealt. Casinos strongly frown upon card counting, but it is a difficult skill to master and few players are successful at it.

Rules

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 any given person's hand are added with 2 through 10 having face value, Ace having value 1 or 11, and King, Jack, and Queen cards having the value 10. If the player and the dealer both have the same point value, this is known as a "push", and neither player wins the hand.

After initial bets are placed, the dealer deals out the cards (either from a single hand-held deck 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 Atlantic City casinos, 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), he is immediately paid 3:2 for his bet, unless the dealer also has a natural, which is a push. If the dealer has a natural, all players without a natual 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 "taking a hit") 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. 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. Once 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's discretion; it depends only on the point total that the dealer holds. If the dealer has less than 17, he draws another card, and continues to draw more cards until having 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). Las Vegas casinos typically stand; Reno and Atlantic City casinos typically hit.

If the first two cards form a total of 21, this is a special case known as "blackjack" or "natural". The player who gets blackjack receives a better payout of 3:2. However, if the dealer and the player both receive blackjack, then this is a push.

Special plays

Casinos often offer variations on the rules which add to the player's gambling opportunies during the course of play. The most common of these are:

  • Pair splitting. If the player has two identical cards, she may place an additional bet of equal value and play two hands instead of one, using each of the two cards as the start of a hand. Any two 10-count cards are considered a pair, and so may be split. In most casinos, if one splits a pair of Aces, one receives second card to each, but can make no further plays on either hand.
  • Doubling down. The player can double his bet and receive just one more card (forfeiting the opportunity to hit further). Some casinos only let players double down if their initial point total is 11 or 10 (or in some cases 9). Las Vegas casinos typically let a player double down with any two cards. A few casinos allow double-after-split, where a player who has split a pair into two hand receives a second card to each may then choose to double down on those two cards.
  • Surrender. This rule is rare, but some casinos allow a player who has a bad hand to give up the hand and get half her bet back.

Basic Strategy

As in most 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 just 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 deck 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 0.25%. 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.

(Should add a basic strategy table here for 1 deck? 4 decks?)

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 or certain events occurring on the next deal. 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 only wins even money, while the player is paid 3:2). When the deck has more small cards like 4s, 5s, and 6s; it is more likely that the player will be dealt a bad hand and bust, favoring the dealer (likewise, they increase the chance of a dealer bust 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 10-counts and Aces to offer a positive expecation 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 as often as 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 like 4s and 5s, and rich in 10s, that may alter the odds in favor of standing.

Most card counting schemes assign a positive, negative, or zero point value to the each card in the deck. Normally, low value cards, such as a 2 or 3, are given a negative value, and 10s are given a positive value. The exact number assigned to the cards depend on the specific card counting method in use. The card counter keeps a running tally of the point values as they are dealt. In order 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).

If the tally is a 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, in order to avoid facing casino countermeasures.

Counting schemes which 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 level two counts, which assign point values of -2, -1, 0, +1, or +2 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. Aces can add the lowest possible value of 1 to a player's card total, which implies that they should have a negative point count; but for purposes of getting a blackjack, they are extremely valuable to have remaining in the deck. Most counting schemes give aces a positive count, recognizing that there is a compromise involved in this process. One scheme actually assigns a zero value to aces, and requires the counter to keep a separate side count of aces.

(Need references to Thorpe, Uston, Snyder, etc.)