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Introduction

The North American game of Blackjack, also known as 21, has been one of the most popular casino games of the last hundred years and has spread throughout the world. In the 21st century it has been overtaken in popularity by Slots (slot machine games), but it remains one of the most popular casino card games and is available in almost all casinos both on and offline.

Blackjack dealers play under fixed rules, determined by the house. A good thing to keep in mind is that the dealer is the last person to act on their hand. If one of the players at the table busts, they will lose their wager even if the dealer busts afterwards, which gives the house an advantage over players. Keeping It Simple – Blackjack Rules Explained Depending on the variant you’re playing, between 4 and 8 decks of cards are used. Unlike Poker, you compete against the dealer in Blackjack and not against. Blackjack is one of the most popular casino card games. It is played around the globe in live casinos, as well as online. If you are interested in getting in to blackjack put don’t know the rules you will find that it’s easy to learn how to play blackjack. Following are the basic rules of this popular card game. Blackjack Rules: Learn how to play 21 card game. After this introduction to the game, it is time to get down to business and explain how to play blackjack if you’ve never had a chance to play this hugely popular game. The good news is that blackjack rules are very easy to learn as far as the play is concerned.

Blackjack is a casino banked game, meaning that players compete against the house rather than each other. The objective is to get a hand total of closer to 21 than the dealer without going over 21 (busting).

At the start of a Blackjack game, the players and the dealer receive two cards each. The players' cards are normally dealt face up, while the dealer has one face down (called the hole card) and one face up. The best possible Blackjack hand is an opening deal of an ace with any ten-point card.

The house advantage of this game is derived from several rules that favour the dealer. The most significant of these is that the player must act before the dealer, allowing the player to bust and lose their bet before the dealer plays.

Players should be aware that there is another card game called Black Jack in the UK which is an entirely different card game, effectively the same as Crazy Eights.

Note. Gambling can be dangerously addictive. You can find information and advice on our Responsible Gambling page.

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Dedicated to providing accurate information about online gambling and the legal aspects involved since 2015, John Isaac's team at online-gambling.com have produced a plethora of online blackjack resources for players.

Equipment

Blackjack is played with a standard international deck of cards with the Jokers removed, leaving 52 cards. Originally the game was played with a single deck. However, as a counter measure to card counting, casinos introduced multi-deck games, based on the false assumption that if there were more cards in play it would be harder for the card counter to keep track of them all. As a result, Blackjack is now usually offered in either single deck, double deck, 4 deck, 6 deck or 8 deck variants. It should be noted that there are exceptions in online casinos where far larger numbers of decks can be used than would be practical to manage offline.

Aside from the cards, the game requires a table, chips, a discard tray, cut card and a shoe.

After the dealer has shuffled a player will be selected at random and asked to take the cut card – a coloured plastic card matching the playing cards in size – and place it at a random position within stack of cards. The dealer will then move the cards above the cut card to the back of the stack. This technique is intended to demonstrate to the players that the dealer cannot have rigged the deck. The cut card is then reinserted into the stack of cards by the dealer at a pre-defined position and when this card is reached this indicates the final deal of the game before the cards are shuffled.

Where multiple decks are used, after the shuffle the cards will be placed into a dispenser called a shoe. This piece of equipment has two purposes: to hold large stacks of cards in multi-deck games and make the practice of hole carding (cheating by catching a glimpse of the dealer’s hole card) more difficult. In fact hole carding is not illegal in the vast majority of jurisdictions. If the dealer is poorly trained or sloppy enough to fail to protect their down card from being seen by a player at the table this is not the player's fault and the player is not obliged to look away to prevent themselves seeing the down card. If however the player uses any form of device, for instance a metal lighter to observe the reflection in, or an accomplice off table signals the information to them, this is cheating. Hole carding is only legal where the player can see the card naturally from one of the player positions at the table.

Card Values

When playing Blackjack the numeral cards 2 to 10 have their face values, Jacks, Queens and Kings are valued at 10, and Aces can have a value of either 1 or 11. The Ace is always valued at 11 unless that would result in the hand going over 21, in which case it is valued as 1.

Any hand with an Ace valued as 11 is called a ‘soft’ hand. All other hands are ‘hard’ hands.

A starting hand of a 10 valued card and an Ace is called a Blackjack or natural and beats all hands other than another Blackjack. If both the player and dealer have Blackjack, the result is a push (tie): neither the player nor the bank wins and the bet is returned to the player.

Order of Play and Playing Options

Each player sitting at the table places their desired bet in the betting circle directly in front of them. In most casinos if there are untaken betting circles, the players sitting at the table can choose to play more than one hand at a time. The minimum and maximum bet size varies from casino to casino, generally with a ratio of 40 to 100 between them. For example with a $25 minimum bet the maximum will usually be somewhere from $1000 to $2500. Once the bets are placed the dealer will move their hand across the table from their left to their right signalling that no further bets can be placed. The dealer then deals cards one at a time clockwise around the table, from the dealer's left to the dealer's right: first a card face up to each betting circle that has a bet in it, then a card face up to the dealer, and then a second card face up to each betting circle with a bet and finally a second card face down to the dealer.

In many places the dealer's first card is initially dealt face down. The dealer's second card is used to flip the first card face up and then slid underneath the first card. The exact dealing protocol varies from place to place as determined by the casino management.

If the dealer has a 10 or an Ace face up players are offered the option to place an Insurance bet. Insurance is a side bet on whether or not the dealer has a Blackjack, unrelated to the final outcome of the round. If a player chooses to take insurance they place an additional bet equal to half of their original bet. This insurance bet wins if the dealer has Blackjack.

The dealer now checks their down card to see if they have Blackjack. If they have Blackjack they expose their down card. The round is concluded and all players lose their original bet unless they also have Blackjack. If a player and the dealer each have Blackjack the result is a push and the player's bet is returned. Any insurance bets are paid out at 2:1.

If the dealer does not have Blackjack any insurance bets are lost and any players who have Blackjack are paid. It is then the turn of the remaining players to take their actions. Starting with the player sitting furthest to dealer's left they have the following options:

Stand – If the player is happy with the total they’ve been dealt they can stand, taking no further action and passing to the next player. The player can take this action after any of the other player actions as long as their hand total is not more than 21. The hand signal to Stand is waving a flat hand over the cards.

Hit – If the player wishes to take another card they signal to the dealer to by scratching the felt beside their hand or pointing to their hand. A single card is then played face up onto their hand. If the hand total is less than 21 the player can choose to Hit again or Stand. If the total is 21 the hand automatically stands. If the total is over 21 the hand is bust, the player’s bet is taken by the house and the turn to act passes to the next player.

Double Down – If the player considers they have a favourable hand, generally a total of 9, 10 or 11, they can choose to 'Double Down'. To do this they place a second wager equal to their first beside their first wager. A player who doubles down receives exactly one more card face up and is then forced to stand regardless of the total. This option is only available on the player's two-card starting hand. Some casinos will restrict which starting hand totals can be doubled.

Split – If the player’s first two cards are of matching rank they can choose to place an additional bet equal to their original bet and split the cards into two hands. Where the player chooses to do this the cards are separated and an additional card is dealt to complete each hand. If either hand receives a second card of matching rank the player may be offered the option to split again, though this depends on the rules in the casino. Generally the player is allowed a maximum of 4 hands after which no further splits are allowed. The split hands are played one at a time in the order in which they were dealt, from the dealer's left to the dealer's right. The player has all the usual options: stand, hit or double down. Some casinos restrict the card ranks that can be split and may also restrict the option to Double after splitting a pair.

A player who splits Aces is usually only allowed to receive a single additional card on each hand. Normally players are allowed to split two non-matching 10-value cards, for example a King and a Jack. However, some casinos restrict the splitting of ten value cards to pairs of the same rank (two Jacks for instance). It should be noted in any case that splitting 10's is almost always a poor play for the player. If Aces are split and the player draws a Ten or if Tens are split and the player draws an Ace, the resulting hand does not count as a Blackjack but only as an ordinary 21. In this case the player's two-card 21 will push (tie with) dealer's 21 in three or more cards.

Surrender – Some casinos allow a player to surrender, taking back half their bet and giving up their hand. Surrender must be the player's first and only action on the hand. In the most usual version, known as Late Surrender, it is after the dealer has checked the hole card and does not have a Blackjack. It has become increasingly rare for casinos to offer the surrender option.

After all players have completed their actions the dealer plays their hand according to fixed rules. First they will reveal their down card. The dealer will then continue to take cards until they have a total of 17 or higher. The rules regarding Soft 17 (a total of 17 with an Ace counted as 11 such as A+6) vary from casino to casino. Some require the dealer to stand while others require additional cards to be taken until a total of hard 17 or 18+ is reached. This rule will be clearly printed on the felt of the table.
If the dealer busts all non-busted player hands are automatically winners.

Payouts

If the player and dealer have equal unbusted totals the hand is considered a push and the player’s bet is returned.

If a player wins a hand they are paid out at 1:1 on the total bet wagered on that hand. For example if the player wagered $10 and then doubled down placing a further bet of $10 on the hand and won, they would be paid a total of $40, their $20 bet back and $20 winnings.

If the player has Blackjack they are paid at 3:2, so that a wager of $10 the player would be paid a total of $25, their $10 bet back plus $15 winnings.

If the player has placed the Insurance bet and the dealer has Blackjack, the player’s hand loses but the Insurance bet is paid out at 2:1. So if the player had bet $10 on the hand and $5 on the Insurance bet, they would lose the $10 and be paid a total of $15 – their $5 Insurance bet returned and $10 winnings. This effectively results in a push overall for the hand.

Variants

Deal

In some casinos the players' initial two-card hands are dealt face down. All additional cards dealt to the player are given face up. The initial cards are revealed by the player if the hand goes bust, or if the player wishes to split a pair. Otherwise the dealer reveals the cards at the end of the round when it is time to settle the bets. This style of game is rare nowadays: casinos don't like to allow players to touch the cards, because of the risk of card marking.

In European style games only the dealer’s face up card is dealt the start of the round. Dealer's second card is dealt after all players have acted, and the dealer checks for Blackjack at this point. Player Blackjacks are paid at the end of the round if the dealer does not have Blackjack. If the dealer has Blackjack the rules regarding Doubled and Split hands vary from casino to casino. Some casinos will take both bets while others will only take the initial bet and return the other.

Blackjack payout

It should be noted that some casinos have started to offer a reduced payout on Blackjack, most commonly 6:5. This is very bad for the player, increasing the House Edge significantly. Any game offering a reduced payout on Blackjack should be avoided by players.

Splits

The maximum number of hands that can be created by splitting depends on the rules in the casino: some only allow one split.

When splitting 10 value cards, not all casinos will allow players to split non-matching 10 cards. For instance, in some casinos you could split two Jacks but could not split a King and a Jack. Also, some casinos will limit which card ranks can be split.

House rules will dictate whether the player is allowed to Double after splitting, and whether a player who splits Aces is allowed to receive more than one additional card on a hand.

Surrender

Not all casinos offer the Surrender option.

A few casinos may offer Early Surrender in which the player can take back half of their bet and give up their hand before the dealer checks for Blackjack. This is very rare nowadays

In European style games there is normally no Surrender option. If Surrender were offered it would of course have to be Early Surrender.

Five Card Charlie

The side rule is rarely offered. When it is in effect, a player who collects a hand of five cards (two cards plus three hits) without going bust is immediately paid even money, irrespective of the dealer's hand.

Home game blackjack

Blackjack can be played at home, rather than in a casino. In this case a fancy Blackjack table is not needed: just at least one pack of cards and something to bet with - cash, chips or maybe matches. Unless the players have agreed in advance that the host should deal throughout, to ensure a fair game the participants should take turns to be the dealer. The turn to deal can pass to the next player in clockwise order after every hand or every five hands or whatever the players agree. If playing with a single deck of cards, it is desirable to re-shuffle the cards after every hand.

Swedish Pub Blackjack

Nightclubs and pubs in Sweden often offer a Blackjack variant that is less favourable to the players. All the essential rules are the same as in the casino version unless the player and dealer have an equal total of 17, 18 or 19. In the casino version the player's stake is returned in these situations, but in Swedish pubs the house wins.

Although pub stakes may vary, they are often much lower than in casinos with a minimum stake of 20 or 40 Krona and a maximum of 60 Krona (about US$7) for each hand.

Optimal Strategy

Basic Strategy table for one of the more commonly available rule combinations (6 decks, Resplit to 4 hands, Dealer Stands on Soft 17, Late Surrender, Double After Split).

First and foremost, as a general rule the player should never take Insurance. Unless using an advanced and mathematically proven strategy that will alert the player to the rare situations in which Insurance is worthwhile, it should be avoided as a bad bet for the player.

Next, it should be understood that every possible combination of player hands and dealer up card has a mathematically correct play. These can be summarized in what is known as a Basic Strategy table. However, certain plays in the table need to be modified according to the specific combination of rules in force. To be sure of playing correctly, it is necessary to generate a Basic Strategy table for the specific rules of the game being played. Various tools are available online to do this. We would recommend this Blackjack Basic Strategy Calculator.

It should be noted that even playing perfect Basic Strategy for the rule set in play, the player will still usually be at a disadvantage.

Card Counting

Card Counting provides the player a mathematically provable opportunity to gain an advantage over the house. It must be understood that this does not guarantee that the player will win. Just as a regular player may win though good luck despite playing at a disadvantage, it is perfectly possible for the Card Counter to lose through an extended period of bad luck even though playing with a small advantage over the House.

The basic premise of Card Counting is that mathematically speaking, low cards on average are beneficial to the dealer while high cards favour the player. There are many subtle reasons for this but the most significant are:

• A player who receives a Blackjack (a ten value card and an Ace – two high cards) is paid one and a half times their bet. The dealer however only receives the player’s bet when dealt a Blackjack.
• While the player can stop taking additional cards at any time, rules require the dealer to continue drawing cards until they reach a total of 17. The player can choose whether or not to take an additional card on a total of 16 whereas the dealer has to take one. In this situation small cards are less likely to cause the dealer to bust are thus favour the dealer, while big cards cause the dealer to bust more often and favour the player.
• The majority of situations where it is correct of the player to double are starting hands that would be made very strong by the addition of a ten value card or an Ace. Therefore, doubling becomes more favourable when there are more ten value cards and Aces left in the deck.

So the Card Counter looks for times when there are more high cards left to be played than a regular deck would have. Rather than trying to remember each card that has been played, the Card Counter will usually use a ratio system that offsets cards that are good for the player against cards that are good for the dealer.

The most commonly used Card Counting system is the HiLo count, which values cards as follows:

To keep track the player starts at zero, adds one to the total every time a low card is played and subtracts one from the total when a high card is played. This is called the ‘Running Count’. It may seem counter-intuitive to subtract one for high value cards that are good for the player, but a high card that has been played is one less high card that is left to be played. Where the Running Count is positive the player knows that there are more player favourable cards remaining to be played.

When kept correctly the Running Count will start at 0 and, if all the cards were to be played out, would end at 0. This is because there are an equal number of high cards and low cards. The HiLo count is therefore referred to as a ‘Balanced Counting System’.

Card Counting systems are generally not impeded by the addition of multiple decks to the game. At any rate multiple decks do not make it significantly more difficult for the Card Counter to keep track of the Running Count, since the Card Counter only needs to keep track of a single number, the Running Count. However many decks are used, the count begins at zero and would end at zero if there were no cards left, so no changes need to be made to the counting process.

Where multiple decks do make a difference is in how much impact a positive Running Count has to the player advantage. If the Running Count is +10 and there are two decks remaining to play, this means there are an extra 5 player favourable cards in each deck. If there are 5 decks remaining to be played there are only 2 extra player favourable cards in each deck. The higher the concentration of extra player favourable cards the stronger the player’s advantage. To estimate the strength of the player advantage the Running count therefore needs to be divided by the number of decks remaining to be played. This figure is called the True Count.

With the True Count the player has a consistent measure of how many extra player favourable cards are contained within the cards remaining to be dealt. The player can use this information to vary their bet and playing strategy. Deviations from Basic Strategy are far less important than placing big bets when the True Count is high and low bets (or preferably nothing) when the True count is low or negative.

It is important to note that sizing your bet correctly is critical to your long term success as a card counter. This requires substantial additional knowledge that is beyond the scope of this article. Instead we refer interested readers to the books listed below for an insight into this complex aspect of card counting.

While Card Counting is legal in most jurisdictions, for obvious reasons casinos do not like players that can consistently beat them. They therefore employ counter measures and any players they identify as Card Counters will be asked to leave the casino. The most common method used to identify Card Counters is to watch for a large bet spread (difference between the minimum and maximum bet a player uses) and to see whether large bets correlate with player favourable counts. Card Counters have developed several methods to help them avoid detection. The two most common are:

• Wonging / Back Counting. Named after Blackjack author Stanford Wong, this is the practice of watching the cards being played and only sitting down to play when there is a player favourable count. This practice reduces the bet spread the player uses as they only place bets in player favourable situations but casinos are now well aware of this strategy and watch out for players hanging around a table and not playing. The method is still useful, but not without its problems.
• Team Play. This involves several trained Card Counters working together. Most commonly there would be several 'Spotters' sitting at different tables keeping track of the count and either back counting or playing minimum bets. When a table reaches a positive count the Spotter would signal to the 'Big Player' who would come over and bet big during the player favourable count. This allows both players to make very little variation in their bets. Casinos are aware of this strategy and watch for groups of players working together.

There are several variations on team play designed to be employed in different situations and to different effects. These are covered more fully in the reading resources detailed below.

Successful Card Counting is generally only profitable in land based casinos, not in online games. The strategy relies on the game having a 'memory' in that cards are dealt from the cards remaining after previous rounds have been played. Online Blackjack games are dealt by computer and normally use a random number generator to shuffle the whole deck after every round of play. Games of this sort are not countable.

There are some Live Blackjack games online, which are played over a video feed with a human dealer. These could technically be counted but there are several significant disadvantages that make this difficult or not worth the player's time:

1. Games of this type are very slow to play. A slow game means less money made.
2. The games generally offer poor 'penetration'. This means that the decks are shuffled early, not allowing enough cards to be dealt out for many player favourable situations to develop. (The most favourable situations for the player tend to occur further into the shoe.)
3. The casino's software records every player bet and all the cards dealt. This makes it relatively easy for a casino to employ software to track the count and watch for players raising their bet or only playing when the count is favourable.

For the above reasons Card Counting has not become commonplace online.

Recommended Books

There is a great deal more to card counting successfully than we can reasonable cover here. Many books have been written on this subject and we will recommend some of the better ones below:

Donald Schlesinger: Blackjack Attack – One of the foremost mathematicians in the Blackjack field, Schlesinger successfully compares the strength of various counting systems in different conditions.

Arnold Snyder: Blackbelt in Blackjack – One of the most easily accessible authors on the subject of Blackjack, Snyder still provides everything you need to know to start on your journey.

Rick Blaine: Blackjack Blueprint – A good book covering everything from Basic Strategy, through several counting systems and on to advanced techniques and team play.

Bryce Carlson: Blackjack for Blood – Discussion of various card counting systems and strategies to avoid being detected. Includes discussion of some strategies that unlike card counting, may not be legal. As such we would strongly advise user caution and research before engaging some of the strategies discussed.

Ian Andersen: Burning the Tables in Las Vegas – One of the best discussions of how to play successfully long term without being detected.

Olaf Vancura and Ken Fuchs: Knockout Blackjack – Credited as being the first published unbalanced counting system (system that did not require a True Count conversion).

Ken Uston: Million Dollar Blackjack – An old book now but written by a man famous for popularising the concepts of team play. This book covers several counting systems alongside some advanced techniques.

Kevin Blackwood: Play Blackjack Like the Pros – This book covers Basic Strategy, a variety of counting systems, money management and team play.

Stanford Wong: Professional Blackjack – One of the definitive books on the topic, the act of waiting for a favourable deck before sitting down to play is to this day referred to as ‘Wonging’.

Nathaniel Tilton: The Blackjack Life – A autobiographical account of a small number of players implementing modernised team play strategies. Very useful insight into how team play can still be effective.

Eliot Jacobson: The Blackjack Zone – A lot of space is devoted to how to become a better player and debunking myths surrounding gambling, but this book also has a good treatment of the basics of card counting.

Peter Griffin: The Theory of Blackjack – Peter Griffin was one of the most widely respected gambling mathematicians of all time. This book is maths heavy but very informative.

There are other good books on this subject but the above are the ones we feel any player should ensure they are familiar with before considering trying to win money by Card Counting.

Sites for blackjack rules, information and analysis

Here are some other useful websites with rules and information about Blackjack (21).

ThePogg.com provides a Blackjack Guide with rules, advice and casino reviews. The Basic Strategy section includes a comprehensive calculator that can generate the optimal basic strategy for almost any rule combination alongside a fairness calculator to check your results.

BlackjackInfo.com was formerly run by Kenneth R Smith but has now been acquired by an affiliate advertisement network. The forums on this site still contain a wealth of information and discussion on the various aspects of card counting.

Blackjack in Color is an unusual free Web-based Blackjack book providing an analysis of Blackjack and Card Counting illustrated by 139 charts. The author Norm Wattenberger also publishes the Blackjack Scams site, which points out some short-cuts that will more likely cost you money than make a profit, runs Blackjack The Forum and publishes Casino Verite Blackjack Card Counting training software..

Wizard of Odds has a large Blackjack section with information on the game, its variants and strategy. They provide a trainer with which you can practice card counting.

James Yates has written a page Blackjack Solved, which explains Harvey Dubner's Blackjack card counting system.

The Wikipedia Blackjack page needs little explanation. A well detailed and referenced information source on Blackjack.

One of the most interesting aspects of blackjack is the
probability math involved. It’s more complicated than other
games. In fact, it’s easier for computer programs to calculate
blackjack probability by running billions of simulated hands
than it is to calculate the massive number of possible outcomes.

This page takes a look at how blackjack probability works. It
also includes sections on the odds in various blackjack
situations you might encounter.

An Introduction to Probability

Probability is the branch of mathematics that deals with the
likelihood of events. When a meteorologist estimates a 50%
chance of rain on Tuesday, there’s more than meteorology at
work. There’s also math.

Probability is also the branch of math that governs gambling.
After all, what is gambling besides placing bets on various
events? When you can analyze the payoff of the bet in relation
to the odds of winning, you can determine whether or not a bet
is a long term winner or loser.

The Probability Formula

The basic formula for probability is simple. You divide the
number of ways something can happen by the total possible number
of events.

Here are three examples.

You want to determine the probability of getting heads when
you flip a coin. You only have one way of getting heads, but
there are two possible outcomes—heads or tails. So the
probability of getting heads is 1/2.

You want to determine the probability of rolling a 6 on a
standard die. You have one possible way of rolling a six, but
there are six possible results. Your probability of rolling a
six is 1/6.

You want to determine the probability of drawing the ace of
spades out of a deck of cards. There’s only one ace of spades in
a deck of cards, but there are 52 cards total. Your probability
of drawing the ace of spades is 1/52.

A probability is always a number between 0 and 1. An event
with a probability of 0 will never happen. An event with a
probability of 1 will always happen.

Here are three more examples.

You want to know the probability of rolling a seven on a
single die. There is no seven, so there are zero ways for this
to happen out of six possible results. 0/6 = 0.

You want to know the probability of drawing a joker out of a
deck of cards with no joker in it. There are zero jokers and 52
possible cards to draw. 0/52 = 0.

You have a two headed coin. Your probability of getting heads
is 100%. You have two possible outcomes, and both of them are
heads, which is 2/2 = 1.

A fraction is just one way of expressing a probability,
though. You can also express fractions as a decimal or a
percentage. So 1/2 is the same as 0.5 and 50%.

You probably remember how to convert a fraction into a
decimal or a percentage from junior high school math, though.

Expressing a Probability in Odds Format

The more interesting and useful way to express probability is
in odds format. When you’re expressing a probability as odds,
you compare the number of ways it can’t happen with the number
of ways it can happen.

Here are a couple of examples of this.

You want to express your chances of rolling a six on a six
sided die in odds format. There are five ways to get something
other than a six, and only one way to get a six, so the odds are
5 to 1.

You want to express the odds of drawing an ace of spades out
a deck of cards. 51 of those cards are something else, but one
of those cards is the ace, so the odds are 51 to 1.

Odds become useful when you compare them with payouts on
bets. True odds are when a bet pays off at the same rate as its
probability.

Here’s an example of true odds:

You and your buddy are playing a simple gambling game you
made up. He bets a dollar on every roll of a single die, and he
gets to guess a number. If he’s right, you pay him $5. If he’s
wrong, he pays you $1.

Since the odds of him winning are 5 to 1, and the payoff is
also 5 to 1, you’re playing a game with true odds. In the long
run, you’ll both break even. In the short run, of course,
anything can happen.

Probability and Expected Value

One of the truisms about probability is that the greater the
number of trials, the closer you’ll get to the expected results.

If you changed the equation slightly, you could play this
game at a profit. Suppose you only paid him $4 every time he
won. You’d have him at an advantage, wouldn’t you?

• He’d win an average of $4 once every six rolls
• But he’d lose an average of $5 on every six rolls
• This gives him a net loss of $1 for every six rolls.

You can reduce that to how much he expects to lose on every
single roll by dividing $1 by 6. You’ll get 16.67 cents.

On the other hand, if you paid him $7 every time he won, he’d
have an advantage over you. He’d still lose more often than he’d
win. But his winnings would be large enough to compensate for
those 5 losses and then some.

The difference between the payout odds on a bet and the true
odds is where every casino in the world makes its money. The
only bet in the casino which offers a true odds payout is the
odds bet in craps, and you have to make a bet at a disadvantage
before you can place that bet.

Here’s an actual example of how odds work in a casino. A
roulette wheel has 38 numbers on it. Your odds of picking the
correct number are therefore 37 to 1. A bet on a single number
in roulette only pays off at 35 to 1.

You can also look at the odds of multiple events occurring.
The operative words in these situations are “and” and “or”.

• If you want to know the probability of A happening AND
  of B happening, you multiply the probabilities.
• If you want to know the probability of A happening OR of
  B happening, you add the probabilities together.

Here are some examples of how that works.

You want to know the probability that you’ll draw an ace of
spades AND then draw the jack of spades. The probability of
drawing the ace of spades is 1/52. The probability of then
drawing the jack of spades is 1/51. (That’s not a typo—you
already drew the ace of spades, so you only have 51 cards left
in the deck.)

The probability of drawing those 2 cards in that order is
1/52 X 1/51, or 1/2652.

You want to know the probability that you’ll get a blackjack.
That’s easily calculated, but it varies based on how many decks
are being used. For this example, we’ll use one deck.

To get a blackjack, you need either an ace-ten combination,
or a ten-ace combination. Order doesn’t matter, because either
will have the same chance of happening.

Your probability of getting an ace on your first card is
4/52. You have four aces in the deck, and you have 52 total
cards. That reduces down to 1/13.

Your probability of getting a ten on your second card is
16/51. There are 16 cards in the deck with a value of ten; four
each of a jack, queen, king, and ten.

So your probability of being dealt an ace and then a 10 is
1/13 X 16/51, or 16/663.

The probability of being dealt a 10 and then an ace is also
16/663.

You want to know if one or the other is going to happen, so
you add the two probabilities together.

16/663 + 16/663 = 32/663.

That translates to approximately 0.0483, or 4.83%. That’s
about 5%, which is about 1 in 20.

You’re playing in a single deck blackjack game, and you’ve
seen 4 hands against the dealer. In all 4 of those hands, no ace
or 10 has appeared. You’ve seen a total of 24 cards.

What is your probability of getting a blackjack now?

Your probability of getting an ace is now 4/28, or 1/7.
(There are only 28 cards left in the deck.)

Your probability of getting a 10 is now 16/27.

Your probability of getting an ace and then a 10 is 1/7 X
16/27, or 16/189.

Again, you could get a blackjack by getting an ace and a ten
or by getting a ten and then an ace, so you add the two
probabilities together.

16/189 + 16/189 = 32/189

Your chance of getting a blackjack is now 16.9%.

This last example demonstrates why counting cards works. The
deck has a memory of sorts. If you track the ratio of aces and
tens to the low cards in the deck, you can tell when you’re more
likely to be dealt a blackjack.

Since that hand pays out at 3 to 2 instead of even money,
you’ll raise your bet in these situations.

The House Edge

The house edge is a related concept. It’s a calculation of
your expected value in relation to the amount of your bet.

Here’s an example.

Expected value is just the average amount of money you’ll win
or lose on a bet over a huge number of trials.

Using a simple example from earlier, let’s suppose you are a
12 year old entrepreneur, and you open a small casino on the
street corner. You allow your customers to roll a six sided die
and guess which result they’ll get. They have to bet a dollar,
and they get a $4 win if they’re right with their guess.

Over every six trials, the probability is that you’ll win
five bets and lose one bet. You win $5 and lose $4 for a net win
of $1 for every 6 bets.

The expected value of that $1 bet, for the customer, is about
84 cents. The expected value of each of those bets–for you–is
$1.16.

That’s how the casino does the math on all its casino games,
and the casino makes sure that the house edge is always in their
favor.

With blackjack, calculating this house edge is harder. After
all, you have to keep up with the expected value for every
situation and then add those together. Luckily, this is easy
enough to do with a computer. We’d hate to have to work it out
with a pencil and paper, though.

What does the house edge for blackjack amount to, then?

It depends on the game and the rules variations in place. It
also depends on the quality of your decisions. If you play
perfectly in every situation—making the move with the highest
possible expected value—then the house edge is usually between
0.5% and 1%.

If you just guess at what the correct play is in every
situation, you can add between 2% and 4% to that number. Even
for the gambler who ignores basic strategy, blackjack is one of
the best games in the casino.

Dealer Rules Of Blackjack

Expected Hourly Loss and/or Win

You can use this information to estimate how much money
you’re liable to lose or win per hour in the casino. Of course,
this expected hourly win or loss rate is an average over a long
period of time. Over any small number of sessions, your results
will vary wildly from the expectation.

Here’s an example of how that calculation works.

• You are a perfect basic strategy player in a game with a
  0.5% house edge.
• You’re playing for $100 per hand, and you’re averaging
  50 hands per hour.
• You’re putting $5,000 into action each hour ($100 x 50).
• 0.5% of $5,000 is $25.
• You’re expected (mathematically) to lose $25 per hour.

Here’s another example that assumes you’re a skilled card
counter.

• You’re able to count cards well enough to get a 1% edge
  over the casino.
• You’re playing the same 50 hands per hour at $100 per
  hand.
• Again, you’re putting $5,000 into action each hour ($100
  x $50).
• 1% of $5,000 is $50.
• Now, instead of losing $25/hour, you’re winning $50 per
  hour.

Effects of Different Rules on the House Edge

The conditions under which you play blackjack affect the
house edge. For example, the more decks in play, the higher the
house edge. If the dealer hits a soft 17 instead of standing,
the house edge goes up. Getting paid 6 to 5 instead of 3 to 2
for a blackjack also increases the house edge.

Luckily, we know the effect each of these changes has on the
house edge. Using this information, we can make educated
decisions about which games to play and which games to avoid.

Here’s a table with some of the effects of various rule
conditions.

These are just some examples. There are multiple rules
variations you can find, some of which are so dramatic that the
game gets a different name entirely. Examples include Spanish 21
and Double Exposure.

The composition of the deck affects the house edge, too. We
touched on this earlier when discussing how card counting works.
But we can go into more detail here.

Every card that is removed from the deck moves the house edge
up or down on the subsequent hands. This might not make sense
initially, but think about it. If you removed all the aces from
the deck, it would be impossible to get a 3 to 2 payout on a
blackjack. That would increase the house edge significantly,
wouldn’t it?

Here’s the effect on the house edge when you remove a card of
a certain rank from the deck.

These percentages are based on a single deck. If you’re
playing in a game with multiple decks, the effect of the removal
of each card is diluted by the number of decks in play.

Looking at these numbers is telling, especially when you
compare these percentages with the values given to the cards
when counting. The low cards (2-6) have the most dramatic effect
on the house edge. That’s why almost all counting systems assign
a value to each of them. The middle cards (7-9) have a much
smaller effect. Then the high cards, aces and tens, also have a
large effect.

The most important cards are the aces and the fives. Each of
those cards is worth over 0.5% to the house edge. That’s why the
simplest card counting system, the ace-five count, only tracks
those two ranks. They’re that powerful.

Blackjack Rules Explained Rules

You can also look at the probability that a dealer will bust
based on her up card. This provides some insight into how basic
strategy decisions work.

Perceptive readers will notice a big jump in the probability
of a dealer busting between the numbers six and seven. They’ll
also notice a similar division on most basic strategy charts.
Players generally stand more often when the dealer has a six or
lower showing. That’s because the dealer has a significantly
greater chance of going bust.

Summary and Further Reading

Blackjack Rules Printable

Odds and probability in blackjack is a subject with endless
ramifications. The most important concepts to understand are how
to calculate probability, how to understand expected value, and
how to quantify the house edge. Understanding the underlying
probabilities in the game makes learning basic strategy and card
counting techniques easier.