Blackjack

The Rules
Blackjack can be played with one to eight ordinary decks of cards. Cards of rank 2 through 10 are scored according to their face value. All face cards are 10 points. Aces are semi-wild and can be worth either 1 or 11 points. The highest hand in blackjack is an ace and any 10-point card and is called a blackjack. A winning blackjack pays 3:2. If both player and dealer have a blackjack the bet is a push. Aside from a blackjack a winning hand pays even money. The player wins if his hand has more points than the dealer, without going over 21. Thus a 21-point hand is the highest and is why the game is sometimes called 21. If either the player or dealer go over 21 it is called a break or bust and automatically loses. If both the player and dealer bust the player loses, where lies the house advantage. If the player and dealer tie the bet is a push.
A round of blackjack begins with each player placing a bet in the circle or logo directly in front of him. Then the dealer will give each player and himself two cards. Player cards are usually dealt face up. One dealer card is dealt face up (the up card) and the other face down (the hole card). If the dealer has a ten or an ace as the up card it is possible he has a blackjack in which case all player hands will lose except with another blackjack. In the U.S. the dealer will check for blackjack immediately if one is possible and will collect all losing bets immediately if he does have a blackjack.

In the event the dealer has an ace as the up card he will allow the players to insure their hands against a blackjack. This is much like any insurance policy in which you are betting something bad will happen. The insurance bet in blackjack pays 2:1 if the dealer has a blackjack. If the dealer has an ace showing and a player has a blackjack the dealer may ask "even money?" This is because if the player has a blackjack the net result of both the blackjack and the insurance bet will be an even money win regardless of whether the dealer has a blackjack. After all players have had a chance to accept or decline insurance the dealer will check the hole card.

After it has been established that the dealer does not have a blackjack the players in turn may play their hands. The following options are available. After it has been established that the dealer does not have a blackjack the player in turn may play their hands. The following options are available.

Stand: If the player is satisfied with his hand as-is he may stand pat. To signify you wish to stand wave your hand as if to wave the dealer away. In a single deck game tuck your cards face down under your bet.

Hit: If the player wishes to take another card he may continue to do so until he either stands or busts. To signify you wish to hit tap the table with your finger. In a single deck game scrape your cards lightly against the felt.

Double: If the player feels he needs one and only one more card then he may double his bet and be dealt one more card, good or bad. This option is only offered on the first two cards, and sometimes on the first two cards after splitting. To signify you wish to double place another wager next to your original wager of equal value. In single deck place your cards face up by your bet.

Split: If the player's first two cards are of equal point value he may split them into two hands. In this event each card is the first card of a new hand. The player must also make another wager of equal value to the first for the second hand. The player may usually resplit up to 2 or 3 times if another splitting opportunity arises. Doubling after splitting is usually but not always allowed. To signify you wish to split put the additional wager next to the original wager. In single deck place your cards face up by your bet.

Surrender: Finally some casinos offer the player the option to surrender on the first two cards. If the player does not like their prospects he may forfeit half the bet as well as his cards. This option is generally only offered after the dealer checks for blackjack, known as "late surrender."

After all players have played their hands, from the dealer's left to right, the dealer will play his hand. The dealer has no free will but must always play by certain house rules. Usually the rule is that the dealer must hit until he reaches a score of 17 or more. Some casinos stipulate that if the dealer has a soft 17, consisting of an ace and any number of cards totaling 6, he must also hit. If the dealer busts all players that did not bust automatically win.

The Basic Strategy
The most important thing to know about blackjack is the basic strategy. This strategy is simply the best way to play every possible situation, without any knowledge of the distribution of the rest of the cards in the deck. Following is the basic strategy for four of more decks when the dealer stands on soft 17. Links are also provided to more basic strategy charts for other rules. However the most common game is the multiple deck game (4 or more decks) where the dealer stands on soft 17. If you only memorize one table I would suggest the one below. It can be played effectively under any rules.
To use the basic strategy look up your hand along the left vertical edge and the dealer's up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. Rule variations can have an effect on some borderline situations. The most flexible rules are the number of decks, whether the dealer hits or stands on a soft 17, and whether doubling is allowed after splitting.

Key to table:
H
Hit
S
Stand
D
Double if allowed, otherwise hit
Ds
Double if allowed, otherwise stand
P
Split
H/P
Split if allowed to double after a split, otherwise hit
H/R
Surrender if allowed, otherwise hit
Some obvious situations have been left out to keep the chart as small as possible. I have more basic strategy charts for other numbers of decks, as well as European blackjack.

1 deck
2 decks
4 or more decks
European blackjack
The best way, I have found, to memorize the basic strategy is notice patterns and to try to understand why you should play every situation as the chart says. Then make flash cards and go over and over them until you know it cold. Do not deal out cards to yourself because the soft totals and the pairs will not occur often enough to test your knowledge.

Many people do not believe in the basic strategy because they once took the advice of someone who knew it and then lost the hand. Let me make something perfectly clear, you will not win every hand with the basic strategy! In fact you won't even win half your hands. However I can personally testify that while you will have short term ups and downs over the long run you will roughly break even using it.

Insurance
Do not take insurance, even if you have a blackjack. Card counters can get away with making smart insurance bets when the deck is rich in tens but the non-counting player should always decline it. The following table shows the house edge on the insurance bet depending on the number of decks used.
House Edge on Insurance
Number
of Decks House
Edge
1 5.882%
2 6.796%
4 7.246%
6 7.395%
8 7.470%

Surrender
Sometimes in a 6 or 8 deck game the player has the option to surrender. To be specific the player may forfeit half their bet to be excused from playing out their hand. Obviously this option should only be taken in the worst hands when the net return is less than 50%. In late surrender (the only kind I have ever seen) the player may only opt to surrender after the dealer checks for a blackjack. The following table is a basic guide for when to surrender (Y=yes, N=no).
Basic Surrender Strategy
Player's
Hand Dealer's Card
9 10 A
15 N Y N
16 Y Y Y
Appendix 6 shows more details depending on exact card composition and the number of decks.

House Edge
See my Blackjack House Edge Calculator to determine the house edge under 360 possible rule combinations.
Rule Variations
Rule variations will have an effect on the player's expected return. The numbers below show the effect on the player's return under various rules and after taking into consideration proper basic strategy adjustments. These changes are relative to the following Atlantic City rules: 8 decks, dealer stands on soft 17, player may double on any first two cards, player can double after splitting, player may resplit to 4 hands.
Rule Variations
Rule Effect
Early surrender against ace +.39%
Early surrender against ten +.24%
Player may draw to split aces +.19%
Late surrender +.09%
Player may resplit aces +.08%
Late surrender against ten +.07%
Late surrender against ace +.00%
Resplit to only 2 hands -.01%
No-peek: ace showing -.01%
Player may double on 9-11 only -.09%
No-peek: ten showing -.10%
Player may not resplit -.10%
Player may not double after splitting -.14%
Player may double on 10,11 only -.18%
Dealer hits on soft 17 -.22%
Player loses 17 ties -1.87%
Player loses 17,18 ties -3.58%
Player loses 17-19 ties -5.30%
Player loses 17-20 ties -8.38%
Player loses 17-21 ties -8.86%
In European blackjack and in many online casinos the dealer does not check for a blackjack after dealing the cards. This is referred to as the "no-peek" rule, because the dealer doesn't peek to see if he has a blackjack. In this case, after the players have played their hands, if the dealer does have a blackjack, then the player loses the full amount bet, including the additional bet if the player doubled or split. This rule necessitates some adjustment in the basic strategy which is explained in more detail in my online casino appendix.

Bad Strategies
Three popular bad strategies encountered at the blackjack table are never bust, mimic the dealer, and always assume the dealer has a ten in the hole. All three of these are very bad strategies. Following are my specific comments on each of them, including the house edge under Atlantic City rules (dealer stands on soft 17, split up to 4 hands, double after split, double any two cards) of 0.43%.
Never bust: For my analysis of this strategy I assumed the player would never hit a hard 12 or more and based all other decisions on maximizing expected value under this assumption. This results in a house edge of 3.91%.

Mimic the dealer: For my analysis of this strategy I assumed the player would always hit 16 or less and stand on 17 or more. The player as well as dealer stood on soft 17. The player never doubled or split, since the dealer is not allowed to do so. This results in a house edge of 5.48%.

Assume ten in the hole: For this strategy I first figured out the optimal basic strategy under this assumption. If the dealer had an ace up I reverted to the proper basic strategy assumption of assuming the dealer did not have a ten. Then I went back and used this strategy under regular playing conditions. This results in a house edge of 10.03%.

Card Counting
Let me say loud and clear that card counting is hard and is not as rewarding as television and the movies make it out to be. If it were an easy way to make money everyone would be doing it.
If you do not know the basic strategy trying to count cards is highly ill-advised. Experienced card counters still play by the basic strategy the great majority of the time. There can be no short cut around learning the basic strategy, those who attempt card counting without a firm foundation in the basic strategy are making a big mistake.

To be a successful counter you have to be able to count down a deck fast and memorize large tables of numbers as well as make it look like you're just a casual player. Furthermore, with today's rules, a realistic advantage the counter will have is only 0.5% to 1.5%. You will not win money slowly and gradually but your bankroll will go up and down like a roller coaster in the short run. Only in the long run over hundreds of hours of playing can you count on winning.

The underlying principle behind card counting is that a deck rich is tens and aces is good for the player, a deck rich in small cards is good for the dealer. The reason for this is complicated but to give just two examples: (1) Blackjacks are more common in ten and ace rich decks, which benefit the player more than the dealer. (2) The probability of busting a stiff hand is greater. The dealer is forced to hit a stiff hand and the player is not.

To gauge the richness of the deck in good cards the player will keep track of the cards the are already played. Strategies vary but all assign a point value to each card. For example the Ken Uston's Plus/Minus strategy assigns a value of +1 to 3, 4, 5, 6 and 7, and -1 to tens and aces. Everything else is 0, or neutral. At the beginning of a deck or shoe the count is 0. Then the counter constantly adds and subtracts from the count according to the cards played. This running total is called the "running count." A positive count means that a disproportional number of small cards have already been played which means the deck is rich in large cards. To determine the "true count" divide the running count by the number of decks left to be played, or in some strategies the number of half decks. This will tell you the relative richness of the deck in good cards.

The true count is used in two ways, to determine how much to bet and how to play your hand. Unless it is obvious every situation has a line in which you should play one way if the count is above the line and another if below. For example a 12 against a 6 may dictate that you stand if the true count is +1 or greater and hit if the true count is less than +1. The counter will also bet more when the deck is rich in good cards.

A problem arises when it comes to treating aces. The player should bet more when the deck is rich in aces since they add to the probability of getting a blackjack. However, when it comes to playing your hand the number of aces left is not nearly as important as the number of tens, so it is desirable, but not necessary, to distinguish between tens and aces. Some card counting strategies keep a side count of aces. In the Hi-Opt I and Revere Plus/Minus aces are counted separately and only considered when making the wager. This is a more accurate and powerful way to play than assigning a negative value to aces and not keeping a side count, as some strategies do. Yet many people feel that for the beginner it is too confusing to keep two counts. A player is more likely to make mistakes keeping two counts and that costs money. The efficiency of a strategy that does not keep a side count of aces is only modestly less but you likely will gain more from fewer mistakes made. Different experts fall in various places in the spectrum in terms of what to recommend for the beginner. The Zen Count takes the middle ground and gives aces a value of -1 and tens -2. Personally I have tried both and would recommend against a count that requires a side count of aces to a person ready to take up card counting. The Uston Advanced Plus/Minus is a good strategy that does not involve an ace side count and can be found in the book Million Dollar Blackjack. How well you know a counting strategy is much more important that which strategy you know.

Legally speaking the player may play blackjack any way he wants without cheating or using a computer, and the casinos may do anything from making conditions unfavorable to barring in an effort to stop anyone who they deem has an advantage over the game. Much of the challenge of card counting is avoiding suspicion that you are anything but a normal non-counting player. The most obvious indication that somebody is counting is that they make a substantial increase in bet size after a lot of small cards leave the table. Although the greater the factor by which you can increase your bet the greater your odds of winning, more than doubling your last bet is a fast way to arouse "heat" from the dealer and pit boss. Usually when casinos do realize you are counting they will either shuffle the cards whenever you increase your bet, essentially removing any advantage, or ask you to leave.

This is only scraping the surface of the subject of card counting. To learn more see my book review section for suggestions on good blackjack books.

Appendices
Appendix 1: Total dependent expected return table for an infinite deck.
Appendix 2: This appendix is a probability table of the dealer's final hand given the dealer's up-card, assuming the dealer does not have a blackjack.
Appendix 3a: Composition dependent exceptions to single deck basic strategy where the dealer stands on soft 17.
Appendix 3b: Composition dependent exceptions to double deck basic strategy where the dealer stands on soft 17.
Appendix 3c: Composition dependent exceptions to single deck basic strategy where the dealer hits a soft 17.
Appendix 4: Details on the standard deviation in blackjack.
Appendix 5: This table shows the player's expected return given their first two cards and the dealer's up card, assuming basic strategy is followed.
Appendix 6: Fine points of when to surrender.
Appendix 7: Standard deviation of blackjack.
Methodology
I use both combinatorial pure math and random simulations to study blackjack. My basic strategies are the product of a combinatorial program I have worked very hard on. Expected returns for specific sets of rules are usually the product of random simulation. For some rule variations and for checking my own work I use Stanford Wong's Blackjack Edge software and his books Professional Blackjack and Basic Blackjack.