# Blackjack - Probability

After all boxes have finished playing, the dealer's hand is resolved by drawing cards until the hand busts or achieves a value of 17 or higher a dealer total of 17 including an ace, or "soft 17", must be drawn to in some games and must stand in others. This is why the bet is described as "insurance", since it seems to protect your original bet against a dealer blackjack. To do this, you place a bet no more than one-half of your original bet on the insurance line. I was reading through some of your past Ask the Wizard columns and saw your calculation of the probability of a string of losses in the August 4, Column. An almost identical theme was shown in the Canadian film The Last Casino. Since that is "17 or more", the dealer stops with a final total of

## Introduction

An example of basic strategy is shown in the table below, and includes the following parameters: The bulk of basic strategy is common to all blackjack games, with most rule variations calling for changes in only a few situations. For example, if the above game used the hit on soft 17 rule, common in Las Vegas Strip casinos, only 6 cells of the table would need to be changed: A, surrender 15 or 17 vs.

A, double on A,7 vs. Also when playing basic strategy never take insurance or "even money. Estimates of the house edge for blackjack games quoted by casinos and gaming regulators are generally based on the assumption that the players follow basic strategy and do not systematically change their bet size.

Most blackjack games have a house edge of between 0. Casino promotions such as complimentary matchplay vouchers or 2: Basic strategy is based upon a player's point total and the dealer's visible card. Players may be able to improve on this decision by considering the precise composition of their hand, not just the point total. For example, players should ordinarily stand when holding 12 against a dealer 4. However, in a single deck game, players should hit if their 12 consists of a 10 and a 2.

The presence of a 10 in the player's hand has two consequences: However, even when basic and composition-dependent strategy lead to different actions, the difference in expected reward is small, and it becomes even smaller with more decks. Using a composition-dependent strategy rather than basic strategy in a single deck game reduces the house edge by 4 in 10,, which falls to 3 in , for a six-deck game. Blackjack has been a high-profile target for advantage players since the s.

Advantage play is the attempt to win more using skills such as memory, computation, and observation. These techniques, while generally legal, can be powerful enough to give the player a long-term edge in the game, making them an undesirable customer for the casino and potentially leading to ejection or blacklisting if they are detected.

The main techniques of advantage play in blackjack are as follows:. During the course of a blackjack shoe, the dealer exposes the dealt cards. Careful accounting of the exposed cards allows a player to make inferences about the cards which remain to be dealt. These inferences can be used in the following ways:. A card counting system assigns a point score to each rank of card e. When a card is exposed, a counter adds the score of that card to a running total, the 'count'. A card counter uses this count to make betting and playing decisions according to a table which they have learned.

The count starts at 0 for a freshly shuffled deck for "balanced" counting systems. Unbalanced counts are often started at a value which depends on the number of decks used in the game.

Blackjack's house edge is usually between 0. Card counting is most rewarding near the end of a complete shoe when as few as possible cards remain. Single-deck games are therefore particularly susceptible to card counting. As a result, casinos are more likely to insist that players do not reveal their cards to one another in single-deck games. In games with more decks of cards, casinos limit penetration by ending the shoe and reshuffling when one or more decks remain undealt.

Casinos also sometimes use a shuffling machine to reintroduce the exhausted cards every time a deck has been played. Card counting is legal and is not considered cheating as long as the counter isn't using an external device, [12]: Sometimes a casino might ban a card counter from the property. The use of external devices to help counting cards is illegal in all US states that license blackjack card games. Techniques other than card counting can swing the advantage of casino blackjack toward the player.

All such techniques are based on the value of the cards to the player and the casino as originally conceived by Edward O.

Shuffle tracking requires excellent eyesight and powers of visual estimation but is more difficult to detect since the player's actions are largely unrelated to the composition of the cards in the shoe.

Arnold Snyder's articles in Blackjack Forum magazine brought shuffle tracking to the general public. His book, The Shuffle Tracker's Cookbook, mathematically analyzed the player edge available from shuffle tracking based on the actual size of the tracked slug.

Patterson also developed and published a shuffle-tracking method for tracking favorable clumps of cards and cutting them into play and tracking unfavorable clumps of cards and cutting them out of play. The player can also gain an advantage by identifying cards from distinctive wear markings on their backs, or by hole carding observing during the dealing process the front of a card dealt face down. These methods are generally legal although their status in particular jurisdictions may vary.

Many blackjack tables offer a side bet on various outcomes including: The side wager is typically placed in a designated area next to the box for the main wager.

A player wishing to wager on a side bet is usually required to place a wager on blackjack. Some games require that the blackjack wager should equal or exceed any side bet wager. A non-controlling player of a blackjack hand is usually permitted to place a side bet regardless of whether the controlling player does so.

The house edge for side bets is generally far higher than for the blackjack game itself. Nonetheless side bets can be susceptible to card counting. A side count, designed specifically for a particular side bet, can improve the player edge. Only a few side bets, like "Lucky Ladies", offer a sufficient win rate to justify the effort of advantage play. In team play it is common for team members to be dedicated toward counting only a sidebet using a specialized count.

Blackjack can be played in tournament form. Players start with an equal numbers of chips; the goal is to finish among the top chip-holders. Depending on the number of competitors, tournaments may be held over several rounds, with one or two players qualifying from each table after a set number of deals to meet the qualifiers from the other tables in the next round.

Another tournament format, Elimination Blackjack , drops the lowest-stacked player from the table at pre-determined points in the tournament. Good strategy for blackjack tournaments can differ from non-tournament strategy because of the added dimension of choosing the amount to be wagered. As in poker tournaments, players pay the casino an initial entry fee to participate in a tournament, and re-buys are sometimes permitted.

Some casinos, as well as general betting outlets, provide blackjack among a selection of casino-style games at electronic consoles. Video blackjack game rules are generally more favorable to the house; e. Video and online blackjack games deal each coup from a fresh shoe, rendering card counting much less effective. Blackjack is a member of a large family of traditional card games played recreationally all around the world. Most of these games have not been adapted for casino play.

Furthermore, the casino game development industry is very active in producing blackjack variants, most of which are ultimately not adopted for widespread use in casinos. The following are the prominent twenty-one themed comparing card games which have been adapted or invented for use in casinos and have become established in the gambling industry.

Twenty-one or "Siebzehn und Vier" German: An ace can only count as eleven, but two aces count as a blackjack. It is mostly played in private circles and barracks. In addition to the different rules, the dealer plays their hand after the players have played their hands. Do you need help memorizing the rules of blackjack as a player and a dealer? Learn how to memorize blackjack strategy, the values of different cards and the different rules for blackjack dealers in our Master Your Memory course.

Are you ready to deal the cards? Before you deal cards to the players, several things need to be done. Once your cards are shuffled, make sure all players have placed their bets. Remember, players are allowed to have basic strategy cards at the table. Deal the player on your left first, then move left to right down the remaining players. Finish by dealing yourself one card face down.

Deal another card to each player, this time with the card facing up. Finally, deal your final card. This time, it should face upwards. If your card is an ace, you need to ask the players if they want to purchase insurance.

Players that did buy insurance receive their original bets back. Starting from your left, all of the players play their hand in turn. Players can stand, in which case you move on to the next player. They can also hit, in which case you deal them a new card face up.

You can collect their bet and move on to the next player. If they have blackjack on their first hand, pay back their bet with a 3: The dealer cannot give you cash for the chips at the table. To do that, you must take the chips to the casino cashier. If you have a lot of low denomination chips in front of you at the table, you should trade them for the equivalent higher value chips instead.

In between hands, just tell the dealer you want to "color up", and he will have you push your chips into the middle of the table. He will count them down, and give you a smaller stack of chips that amount to the same value. This makes them easier to carry for you, and for the dealer it maintains his supply of smaller chips. Now you can take those chips to another table for more play, or head to the casino cashier where you can exchange them for cash.

So, if you have made it this far, congratulations. You should have a good idea of what to expect when you sit down at a blackjack table in the casino. What we have not talked about is how to actually make the best decisions while playing the game. That is a whole subject all its own.

To have the best chance of winning, you should learn and practice "basic strategy", which is the mathematically best way to play each hand against each possible dealer upcard. For a free chart that shows the right play in every case, visit our Blackjack Basic Strategy Engine. If you are looking to play from the comfort of your home, you can visit our online blackjack or live dealer blackjack sections for further resources.

Hopefully I've covered just about everything you need. But if you have other questions, feel free to post a reply at the bottom of the page. Our free blackjack game lets you play at your pace, and the Strategy Coach provides instant feedback on the best strategy. To find the best strategy, use our most popular resource: The Blackjack Strategy Engine provides free strategy charts that are optimized for your exact rules. If you prefer a plastic card that you can take to the table with you, we have those too: Blackjack Basic Strategy Cards.

The original version of this explanation of the rules of blackjack has a very long history here at BlackjackInfo. I created and published it here sometime in It was widely copied by other sites, and it has appeared without my permission on literally hundreds of sites over the years.

When I relaunched BlackjackInfo with a new mobile-friendly design in , I took the opportunity to write this all-new version. Hmmm seems I have been making some bad calls for years now, I thought splitting tens against anything but an ace or 10 was a good move: If a player decides to stand on 15 for whatever reason and the dealer has 16, must the dealer still draw another card since it is less than 17?

Is there any significance in blackjack when you have a black jack paired with a black ace, same suit? The question came up on the multiple choice question on Millionaire. I guessed 16 but the answer was 32??? In playing 21 with one deck off cards aND two people playing, in playing Blackjack with one deck of cards and two people playing what is the most black jack show up.

Ken, This may not be the most appropriate page to post this, but let me explain the situation. I aspire to hopefully gather a group of trustworthy guys together to form a blackjack team. Team play is complicated and far more involved than a group of friends pooling resources. There is not much published on team play. The following book may be helpful.

The strategy does not change, but the player is worse off by around 0. As the dealer I get up to Can the dealer chose to stay and take the chips bet from player on the left.

But pay the player on the right? His rules are fixed. He must hit until he has 17 or higher, and then he must stand. Even if all the players at the table have 18, the dealer must stand if he ends up with a Most casinos now deal games with an extra rule about soft This is covered in detail in the article above.

I have a question. I signed up on an online casino and I was getting ready to play blackjack for real money and I asked the live chat help person how many decks were being used and she said 24 decks.

Casinos, both online and land-based, can deal the game pretty much any way they like, including increasing the number of decks to a ridiculous 24! Fortunately, once you get to 8 decks, the game does not get much worse for the player by adding even more decks.

Eight decks is the most typically seen in brick-and-mortar casinos, but in most jurisdictions, land-based or online, there is no legal requirement for any specific number of decks. Is there any standard in the way a dealer deals from the deck? You are describing a CSM continuous shuffle machine , where after each hand the dealer immediately puts the used cards back into the shuffler.

As you note, this eliminates the ability to count cards, or to even observe a useful bias. Since used cards can return into play immediately, the penetration is effectively zero.

These machines have spread widely. The only recourse is to see if your casino also still offers regular games either hand-shuffled, or machine-shuffled but with a normal discard tray. If not, voice your discontent and look elsewhere. Should I be able to ask a casino to provide a copy of their rules? I assume you are talking about online casinos. I didnt catch it at first but sure enough when I drew another card I busted. This particular game would not count both my Aces as one.

Is this ever done at a casino? Who knows what else they are doing wrong! To answer your question, no, this is never done at any casino I have visited. Is this a good bet? What is the house percentage? Yes, there are outstanding opportunities afforded by some sidebets under some circumstances, but if you are able to figure out how to beat them, you no longer need to ask about them.

So, the answer to that question is always no. I read the following in the Casino Verite Software: Can you help me with this? There you can find: This works because of the unbalanced nature of the count. Or do I need to count them equally? Treat them independently, and reassess after each drawn card changes the hand. Here are some examples: You will draw each of those hands about once every hands or so.

As to whether or not to double, 9,3 is a hard 12 and should certainly never be doubled. Also against a dealer 4 in some 1 and 2 deck games. See the Strategy Engine for accurate advice for any game. I assume you are asking about accessing the charts on your smartphone in the casino.

I do not recommend that. In the US, there are laws prohibiting the use of devices in gambling. Most of these laws are based on the Nevada version, which is written in a way that it could be interpreted to mean even something as harmless as looking up a strategy.

If you want access to the strategy in the casino, get a plastic card instead. The shoe game will be easier for a visually impaired player, because both the other players and the dealer have full access to the needed information about the hands.

I have played at the table on many occasions with blind players, and the dealer has always assisted by verbally providing the details of the hand.

Awesome page, One question.. Is this a standard rule? Need to be sure which is the standard and which is the exceptionâ€¦ Thanks. I have seen the behavior you describe in online casinos, but I have never seen it dealt that way in any land-based casino. There, the dealer always deals a card to the first split hand, finishes that hand, and then deals a card to the second split hand and begins it.

I was in Cancun in a casino and in one hand I had 2 Aces against dealer King. I split the 2 Aces and I,ve got Queens on both aces but the dealer draw a card that was an Ace and said that he won since he had blackjack and I only had Blackjack is 21 in the first two cards, and it beats a total of 21, even the case of splitting and getting two hands that look like blackjack. They are just 21s.

But when the dealer does not take a hole card and all bets are subject to losing to a potential dealer blackjack , you should not double or split against a dealer ten or ace because of this. Hi, can please anyone help me with an answer. Do casinos now change the deck of cards after every game or not? Because I heard lot of people saying that now it is impossible to memorise cards that are still in the game. But I am not sure if this is due to change or because casino use so many decks at once I read above that there are 8 decks in the game.

I think what you are trying to describe are continuous shuffle machines CSMs , which allow the dealer to put the discards back into the machine immediately instead of waiting until the shuffled shoe is completed. The use of a CSM does eliminate the ability to count cards. Fortunately, there are still plenty of games available in most areas that do not use CSMs.

The difference is that you must draw a card to your total of 9, whether you double or not. Standing is not an option. With A8 instead, you already have a completed solid hand of Basic strategy will reduce the house edge, but not eliminate it. In typical games, your long-run expectation will be to lose around half a percent of your total action. Yes, tipping the dealer is common. If a dealer is pleasant, I like to tip a small amount on the hand after I get blackjack, but even then I skip some hands.

It was a cool list. Despite the title, it covered many unusual rule variations. Understand the rules here, and then visit the Strategy Engine to see the appropriate plays. Practice with the Trainer. Are you asking about a rule that pays you for having 5 cards and not busting?

The free Windows software at this site will analyze these rules for you, including optimal strategy and the effect on the game. Free BJ Combinatorial Software. Tell me about the best place to sit at a table in Vegas. I have heard that you do not want to be on the end. If you are a basic strategy player, it makes no difference where you sit.

If you are a card counter, you can see an extra few cards before you play your hand by sitting at the end, which helps a small bit. For that reason, many players avoid it. When the dealer has a 2 through 6 up, they must draw another card except A6 depending on the table rules.

As a result, the dealer busts more often with those upcards. This is why standing on player totals of is the best play against the small dealer upcards.

As for 12v2 and 12v3, those are just exceptions you have to remember. No, pairs and soft hands are completely different. Use the Strategy Engine to see how to play any situation.

Any thoughts on this difference? It is likely that you saw players doubling A7v2, not just hitting it. Hitting would simply be a mistake, as it is the third best way to play the hand. The choice of whether to stand or double with A7v2 is a close one. In fact, correct basic strategy for that hand depends on whether the dealer hits or stands on soft 17s. The strategy engine takes all this into account when creating an accurate strategy chart for you.

In S17 games, you should stand. In H17 games, you should double. Except in single deck. Can a person win under those rules? I quit playing there. I generally play at the Indian Casinos in Calif.