Blackjack

The aim of the game

In blackjack each player plays against the dealer, not against the other players at the table. A hand wins if its total is closer to 21 than the dealer's without going over 21. The game is usually dealt from several 52-card decks shuffled together and placed in a shoe; the number of decks varies from one casino to another.

Card values

• Cards from 2 to 10 count at face value.
• Jacks, queens and kings count 10.
• An ace counts 1 or 11, whichever is better for the hand.

A hand in which an ace can count as 11 without going over 21 is called "soft" (for example A+6, worth 7 or 17); any other hand is "hard". A soft hand cannot bust with one more card, because the ace falls back to 1.

How a hand is played

After the players have placed their stakes, each receives two cards, and the dealer receives one card face up and one face down. In some casinos the dealer takes the second card only after the players have finished their hands.

An ace together with a ten-value card as the first two cards is a blackjack (also called a "natural"), which beats any other total of 21. A blackjack usually pays 3 to 2: a stake of 10 units wins 15. If the dealer also has blackjack, the hand is a push and the stake is returned. With an infinite deck, a player is dealt a blackjack in 4.73% of hands. Some tables pay less than 3 to 2 for a blackjack, which increases the house edge.

When the dealer's face-up card is an ace or a ten-value card, in many casinos the dealer checks at once for blackjack ("peeks"). If there is one, the hand ends and the players lose only their original stake (except those who also hold a blackjack).

The player's decisions

The player acts before the dealer and can choose to:

• stand: take no more cards;
• hit: take another card, and possibly more, until the player stops or goes over 21;
• double down: double the stake and receive exactly one more card; this is usually allowed only on the first two cards, and some casinos restrict it to certain totals;
• split: two cards of the same value are separated into two hands, each with a stake equal to the original one; how many splits are allowed and what may be done after them varies from casino to casino, and split aces usually receive one card each (an ace and a ten made this way count as 21, not as blackjack);
• surrender, where it is offered: give up the hand after the first two cards and get back half the stake.

When the dealer shows an ace, the casino usually allows insurance: a separate bet of up to half the original stake that the dealer has blackjack, paid 2 to 1. For that payout to be fair, one third of the remaining cards would have to be worth 10; in a full deck, however, only 16 of the 52 cards are worth 10, which is less than one third. Insurance is therefore a separate bet with an edge for the house, and the strategy below does not use it.

A player who goes over 21 loses at once, even if the dealer later busts as well. This rule is the main source of the house edge.

The dealer's rules

The dealer makes no decisions. The dealer draws cards until reaching at least 17 and then stops. Tables differ on "soft 17" (for example A+6): under the S17 rule the dealer stands on every 17, and under the H17 rule the dealer draws another card on a soft 17. The rule in force is usually printed on the table layout. When the dealer busts, every player still in the hand wins 1 to 1.

The table shows how often the dealer busts depending on the face-up card, under S17, for an infinite deck and given that the dealer does not hold blackjack.

With a 4, 5 or 6 showing, the dealer often reaches a total between 12 and 16, from which another card must be drawn, and a high card then takes the hand over 21. With a 7 or higher, or with an ace, the dealer starts closer to 17 and busts less often. Overall, before any card is seen, a dealer who plays the hand out busts in 28.16% of hands.

Basic strategy

Basic strategy is, for every combination of the player's hand and the dealer's face-up card, the decision with the best average result, that is, the smallest average loss. The tables below are computed by comparing the exact average result of every possible decision (stand, hit, double, split), under these rules:

• an infinite deck (every card has the same probability at every draw), a close approximation of a shoe with many decks;
• the dealer stands on soft 17 (S17);
• blackjack pays 3 to 2;
• the dealer peeks for blackjack;
• doubling is allowed on any two cards, including after a split;
• one split per hand; split aces receive one card each;
• no surrender.

Under other rules, a few cells change. Rows are the player's hand, columns the dealer's face-up card. Legend: S = stand, H = hit, D = double, P = split.

The tables describe the first decision, with two cards. When doubling is no longer allowed (for example after a third card), the hands marked D hit, with one exception: A+7 stands.

Hard hands

Apart from pairs, which have their own table, a hard total of 7 or less always hits, and one of 17 or more always stands.

Soft hands

Pairs

The logic of the tables follows the dealer table: against a weak face-up card (2–6), when the dealer busts often, the strategy stands and doubles more often; against a strong one (7–A), it hits. Some cells look surprising, for example 16 against a 10: there both decisions lose on average, and the table only shows the one that loses less.

The house edge

Under the rules above, with basic strategy applied without mistakes, the house edge is 0.57% of the initial stake. If the dealer hits soft 17 (H17), with the other rules unchanged and the strategy adjusted, the edge rises to 0.79%.

A player who mimics the dealer (hits to 17, never doubles or splits) faces a much larger house edge: 5.67%. Both sides then play by the same rule, but the player acts first: a player who busts has already lost, even if the dealer would have busted too. The 3 to 2 payout for a blackjack offsets only part of that asymmetry. Basic strategy narrows the gap through doubling, splitting and standing on low totals when the dealer shows a weak card, but it cannot remove it.

Even with basic strategy applied perfectly, the edge remains with the house. These figures are averages over a very large number of hands, relative to the initial stake; in the short term, results swing widely in both directions, as the article Variance and the law of large numbers shows.

The idea of card counting, described mathematically in the 1960s, rests on the fact that between two shuffles the cards left in the shoe shift the probabilities slightly from one hand to the next; the calculations on this page assume an infinite deck, in which that effect does not exist.

Terms

• House edge
• RTP
• Variance
• House edge and RTP