Blackjack Probabilities Chart

Every professional blackjack player uses strategy to improve their odds of winning when they play blackjack. Basic strategy can help you reduce the house edge to as little as 0.5%. In contrast, making your own decisions or simply not sticking to basic strategy can increase the house edge to around 2%. The exact playing decisions and house edge depend on the playing rules in effect at the table. To generate a strategy chart, go to the Wizard of Odds Blackjack Strategy Calculator. Use the pull-down menus to specify the playing conditions: number of decks, whether the dealer stands or hits soft 17 (the latter is more common), whether doubling.

One of the most appealing aspects of blackjack is that there’s some element of skill involved. With many casino games, you are entirely reliant on luck, but with blackjack your actions affect the outcomes of hands.

Blackjack is still a game of chance; it’s just that luck isn’t the only factor that determines whether or not you win or lose.

What this means in practice is that you can actually improve your chances of winning. More accurately, in fact, it means that you can decrease your chances of losing.

Every decision you make, such as whether to hit or to stand, will have a direct impact on the result of a hand.

If you consistently make the correct decisions, you can reduce the house edge to a level where the casino’s advantage is almost obsolete.

On this page we explain how basic blackjack strategy can help you make correct decisions each and every time you play.

We explain how it works, how to use it, and we provide a sample strategy chart. We also look at a few blackjack strategies that don’t work.

How Blackjack Strategy Works

You have some information to work with every time you have a decision to make at the blackjack table. You know what cards you have, and you can see one of the dealer’s cards. Based on this information, it’s possible to work out the probabilities of what could happen next.

This is because there’s a fixed number of cards in the decks, and a fixed probability for each of those cards being dealt.

This is done by comparing the probabilities of all the possible combinations of cards that could be dealt, and determining how these combinations would impact the final outcome of the hand.

Once you know how the different actions you can take will affect your chances of winning, you can then choose the optimal one. There’s always a correct mathematical decision to make, and taking it enables you to keep the house edge to the absolute minimum.

That is essentially the whole point of blackjack strategy.

The problem with basic blackjack strategy is that it’s not always easy to establish the correct decision accurately. There are some complicated mathematical calculations required.

Unless you’re a genius, there’s a very small chance of you being able to make those calculations every time you play a hand. Thankfully, you don’t have to make any calculations.

These rules tell you exactly what action you should take in any given situation, based on the cards in your hand and the exposed dealer card.

By following them, you can apply basic blackjack strategy without using any math at all. All you have to do is learn the rules.

Given that there are hundreds of different situations you can find yourself in at the blackjack table, learning the rules for what to do in each one isn’t necessarily easy.

It might be pretty obvious that you should stand if you have 20 and the dealer is showing an eight, but situations such as having 12 when the dealer is showing a three are perhaps not so clear.

If you want to apply basic blackjack strategy perfectly, then you need to know what to do in every possible situation. This is where the use of strategy charts comes in handy.

A blackjack strategy chart is a matrix that shows all the possible combinations of your hand and the dealer’s exposed card. It shows the action you should take when facing each combination.

These charts are based on the correct rules for employing basic strategy, so if you do what the chart says, you’ll be making the right decision every time.

The following is an example of how a strategy chart looks. Along the top you have the dealer’s card, and down the side is your hand. Each individual cell shows what action you should take for the relevant combination.

The chart includes a key for the action each symbol in the cells represents.

You’ll notice that some of the actions are dependent on certain rules. For example, splitting is the right decision in some situations only if you are allowed to double after a split. This is because there are variants of blackjack where some of the rules are different.

The perfect strategy will vary depending on the exact rules of the blackjack variant you are playing. The chart shown above is the correct strategy for playing an eight deck game where the dealer stands on soft 17.

A few decisions would be slightly different if you were playing another game. These differences are, however, very marginal. If you follow the above chart for any variant, you will still play close to perfect hand.

Therefore, you stand a much better chance of winning more hands than you lose during a single session.

There are a few blackjack strategies that, for some reason, are popular among players even though they don’t work. These are as follows:

• Mimic the Dealer
• Never Bust
• Assume a Ten
• Progressive Betting

Mimic the dealer is a simple strategy where you simply act in the same way as a dealer would in any situation. You would never split, double, or surrender, because these options aren’t available to the dealer.

Basically, you would just hit on less than 17 and stand on 17 or higher, regardless of the dealer’s exposed card. This isn’t a good strategy at all, because splitting and doubling can be very advantageous to the player in the right situations.

Never bust is an equally simple strategy.

You just never hit if there’s a risk of going bust, so you always stand on 12 or higher. While this might seem like a safe approach, it actually increases the house edge.

A ten strategy works on the basis that you assume the next card will always be a ten, and that the dealer’s unexposed is a ten. Players often work on this assumption due to the fact that cards valued at ten make up around 30% of the deck (remember jacks, queens, and kings are all valued at ten).

However, 70% of the cards aren’t valued at ten, so you are still more likely not to get a ten. As such, this strategy doesn’t really work and increases the house edge.

Progressive betting is increasing or decreasing your bet size based on the result of your previous bet. This is a strategy that can be used in any form of betting, and there are several different progressive betting systems in existence.

They don’t have any effect on the house edge, because your chances of winning or losing a hand don’t change based on how much you bet.

They can also be very dangerous, particularly when aligned with systems such as the Martingale where you keep increasing your stake after a loss. One bad run can result in the loss of your entire bankroll.

If players’ priority is to win and to improve with every single blackjack game, then they need to put effort and time into achieving it. There are many other things that gamblers need to take into account and focus on prior to playing and during the game. To make the best possible decisions every time, players should prepare themselves beforehand.

For instance, it is recommended for them to have a look at every possible hand they can get and what their best choice will be in such cases. Knowing how to proceed in the difficult situations when players have a hand 14, 15, or 16 is crucial as the total value of any of the hands is significantly high which means that the chance of players busting increases.

Blackjack Probability Chart

Whenever players’ hand total value is above 14, they are already in an unfavourable situation. Such cases require a good strategy and it is necessary for gamblers to think them through beforehand. Preparation and knowledge are compulsory if one wants to make the best possible decision.

Of course, as already mentioned, several other factors play a crucial role such as money management, discipline, decent bankroll and not to forget a bit of luck. Whenever players have the chance to turn the tables in their favour, they should take full advantage of the situation.

Important Things To Consider When Having Hand 14, 15 or 16

When players are unfortunate enough to get a hand 14, 15, or 16, they need to be very careful and stick to the strategy they have chosen. These are situations in which players are already one step from going bust regardless of the dealer’s upcard. However, this doesn’t mean that they should ignore its value, players need to always bear in mind that it is necessary for them to make their moves based on the dealer’s upcard.

Also, how players proceed in such situations shows their level of competence and knowledge to the rest of the players on the table. Since gamblers are already in an unfavourable situation, winning the hand shouldn’t be their priority. Instead, they should try to make the best move which is the move that will leave them with the smallest possible amount of money loss.

These are some of the trickiest hands in blackjack and as such, they are frequently misplayed. Part of the confusion results from the discrepancies in strategy charts. The optimal playing decisions vary depending on many different factors. These include how many decks are in play at the table, whether or not the dealer must hit soft seventeen, and whether players have the chance to late surrender.

All of these factors must be taken into account before you grab a basic strategy chart to take with you at the blackjack tables. What is optimal for hard totals 14 through 16 in a single-deck game may no longer be correct in multiple-deck variations.

What are Breaking Hands

The term breaking hands is commonly used in blackjack which places it among the important phrases players need to get familiar with. Gamblers have a breaking hand when they get their first two cards and they total 12 or above. The reason for this is that almost every single card will cause players to go bust (i.e. break their hand) as their total value will go over 21. Also, it can be referred to the dealer’s position as ‘breaking’ if their upcard is a 2 through 6.

The trouble with the so-called breaking hands 12 through hard 17 is that they invariably lose in the long term against all upcards of the dealer, including those that have higher bust rates for the house. Hard 14, 15, and 16 are particularly tough to approach because they lose more frequently than they win over the long haul.

The result is that the player ultimately ends up in the red with these totals no matter what playing decision they make. You probably think that’s bad. It is, but it gets worse since you will end up receiving horrible stiff underdogs approximately 40% of the time you spend at the blackjack tables.

What is a player to do with these hard totals then? The answer is simple – trust in basic strategy and approach such underdog hands courageously by making the correct playing decisions. And by ‘correct’ we do not necessarily mean the ones that would secure a winning outcome.

The moves basic strategy recommends for these three hard hands are considered optimal because they reduce your negative expectation, i.e. you will end up losing less money with these stiffs over the long haul. In other words, you are on the defence rather than adopting an offensive approach. In some cases, the strategy plays help you escape a highly disadvantageous situation and increase your winning chances.

Breaking Hands’ Situations

As the name hints, breaking hands is the situation when either the player or the dealer is in a very weak position. Such cases are extremely hard to cope with and the only way to have a chance of not going bust is to follow the basic strategy. Breaking hands are the reason why so many people lose in the long run as well. Thus, if players manage to learn how to deal with them, they will significantly improve their performance at the table.

The bottom line is that once gamblers have such breaking hands, the chances that they will go bust and lose are very high. However, if they use basic strategy, they will be able to improve their hand once in a while.

The move hitting here plays a crucial role and players should take their time to observe when they should hit and when this task should be left to the dealer. In cases where players have a breaking hand and the dealer’s position is standing, then they should hit. Otherwise, they risk losing the hand.

When Players Have Hand 14, 15 or 16

It will be best to have a look at all of these cases at once where players have a hand totalling 14, 15, and 16 as the strategy that needs to be used is the same. It is worth mentioning that the same goes for the situations when players have a hard 13 against different combinations of the dealer’s upcard.

Let’s first elaborate on the recommended strategy plays for hard 14. These are the easiest to remember since there are no discrepancies in the strategy based on decks and dealer rules. Hard 14 is always a stand when the dealer exposes small cards 2 through 6. The player must hit their hard 14 against all other upcards, namely 7 through ace.

When dealt A-3, you have a soft 14. This is a much better situation to be in since it is impossible to break this hand with a one-card draw. You have an advantage against a dealer who starts with weak small cards 4 through 6.

In single-deck S17 blackjack, you must double on soft 14 versus the dealer’s 4, 5, and 6. When playing with two to eight decks, you should double on A-3 only when the dealer has a 5 or a 6 provided that the S17 dealer rule applies.

A pair of 7-7 also adds up to a total of 14. In shoe games, this pair must be split when the dealer has 2 through 7 and hit versus upcards 8 through ace. At single-deck tables, the pair should be surrendered against the dealer’s 10. The rest of the moves coincide with those for multi-deck blackjack.

The player is also in a tough spot when holding a hard 15. This is a bad hand, to begin with, no matter what value the dealer’s upcard is. However, things get trickier since the best plays are influenced by the dealer’s drawing rules and the number of decks.

We shall tackle the strategy differences in more depth in the surrender section of the article. Provided that late surrender is unavailable, you should stand on hard 15 against low-value cards 2 through 6 and hit versus 7 through ace. Undoubtedly, hitting a hard total of 15 is not the easiest decision to make at the blackjack table, especially against the dealer’s 10.

Nevertheless, it has to be done because it results in the lowest possible negative EV for the player. The main idea behind hitting 15 against a 10 is that it gives you a shot at improving your situation. The differences might appear negligible but in the long run, they are not.

Soft 15 (A-4) requires a different approach due to the flexibility the ace gives you. You should double down versus low cards 4 through 6 and hit against all other cards the dealer starts with.

The situation of the player worsens even more when they are dealt a hard 16, the worst total one could possibly obtain in blackjack. There are several ways to get this terrible hand including 8-8, Q-6, 9-7, and 3-5-8. The pair of 8-8 should be split against all dealer upcards in the vast majority of blackjack variations. We expand on the particulars of this pair further on in this guide.

The correct strategy moves for hard 16, assuming you cannot surrender are relatively easy to remember. You stand on 16 against 2 through 6 and hit versus 7 through ace. The same applies to multi-card totals that add up to 16, or at least if you follow total-dependent basic strategy. In the absence of late surrender, hitting is again more optimal because it gives you the chance to improve your total against the strong dealer.

Again, all three hands will end up losing over the course of thousands of rounds played. The optimal decision is the one that cuts down your long-term losses the most. The above moves are recommended under total-dependent strategy. If you want to take your game to the next level, you can switch to composition-dependent strategy.

The latter takes into account the exact composition of the cards your hand consists of. Composition-dependent strategy recommends you to stand on hard 16 versus a 10 when your hand contains three or more cards like K-3-3. Also, when the 16 results from splitting a pair, you should stand rather than hit under composition-dependent strategy.

The Option to Surrender

There is one alternative move players can make which leads to the least money losses. However, due to this fact many landbased casinos do not offer the option to surrender as they know that if players know when to take advantage of it, they can greatly benefit from it.

Many professional gamblers won’t play in a casino which doesn’t provide the option to surrender when playing blackjack. However, if players find themselves in such a situation and there is no surrender option, all they can do is act according to the above-mentioned strategy and hope for the best.

When this option is available, most casinos tend to offer late surrender. This allows players to give up on poor hands like hard 15 and hard 16 in exchange for half of their original wager. With late surrender, you can forfeit a bad hand after the dealer has checked for blackjack when starting with an ace or a ten-value card.

Late surrender is beneficial to players because it takes away around 0.07% from the house advantage. Most novice players are averse to surrendering as the name of the move itself evokes negative connotations. However, surrendering is a smart move when you are dealt negative-expectation hands like 15 or 16 versus strong dealer upcards like 10s and aces.

As a general rule of thumb, surrendering is recommended whenever you receive a hand whose expectation of winning is less than 50%. The main advantage of surrendering is that it saves you money when you find yourself at a disadvantage. Late surrender is a defensive play which also allows advantage players to temper the effect variance has on their blackjack bankrolls.

The correct late surrender plays depend on deck number and the dealer’s fixed standing rules. In single-deck blackjack, surrender is recommended when you have hard 16 versus the dealer’s ace or 10.

Provided that the dealer hits soft 17, it is also recommended to surrender hard 15 against an ace. You should forfeit paired 7s against the dealer’s 10 in single-deck S17 blackjack. If one deck is in play and the dealer must hit soft 17, surrendering is advisable against tens and aces when you have 7-7.

In double-deck H17 games, surrender is advisable when you hold hard 15 and hard 16 against the dealer’s ace and 10. Paired 8s should also be surrendered against the ace in double-deck H17 blackjack.

As for shoe-dealt games, basic strategy suggests surrendering hard 16 against strong upcards such as 9, 10, and ace. The approach toward hard 15 in multi-deck variations depends on the dealer’s fixed rules for drawing and standing. You surrender the 15 against the dealer’s 10 in S17 variations and against the 10 and the ace in H17 multi-deck blackjack.

Hard 16 Consisting of Paired 8s

If you have read CasinoGuardian’s blackjack guide carefully so far, you probably remember that the rule of thumb of basic strategists is to always split pairs of 8-8 rather than forfeiting them despite the fact this is still a hard total of 16. Some gambling authors recommend surrendering the pair of 8s versus high dealer upcards like 10, K, Q, and J.

Regrettably, this is a major mistake, and here is why. The dealer undoubtedly has an advantage over you when you hold 8-8 versus a ten-value card. He or she would arrive at standing totals 17 through 21 77% of the time on average.

Blackjack Probability Math

What adds insult to injury is that the dealer’s probability of busting when starting with a ten-value card is rather small at 23%. A pair of 8-8 will cost you money no matter how you approach it but splitting is recommended because it reduces your losses the most. With 8-8, you have a great opportunity to turn a terrible stiff 16 into two brand new hands starting with an 8 each. This improves your chances of forming a good hand and beating the dealer.

Assuming you play standard six-deck S17 blackjack where you can resplit to up to four hands and double down after you split, your 8-8 will lose against the dealer’s ten-value card 77 hands out of every one hundred hands and win 23 times out of every one hundred hands. However, your win rate improves to 38 hands out of every hundred rounds when you split your 8-8.

Let’s suppose you are flat betting £1 per hand for simplicity’s sake. If you merely hit the pair, you will lose £77 and win £23 every one hundred hands on average. This makes for an average net loss of £54 in the long run. Meanwhile, if you consistently split your 8-8 versus the dealer’s ten-value card, you will lose £62 and earn £38.

Your net losses drop to 2 x £24 = £48 per every one hundred hands in this case. This may not sound like a significant improvement but you are still losing £6 less compared to drawing or staying on your pair of 8-8. Meanwhile, if you choose to surrender this pair, as some gambling authors advocate, you will net losses of £50 per every one hundred rounds on average (you lose only half your original wager when surrendering).

Therefore, consistently surrendering your pair of 8s versus the dealer’s 10 turns out to be £2 more expensive than splitting over the long haul. At this point, it is pretty much obvious you are in a losing spot when holding 8-8 no matter how you decide to play it out.

The bottom line is you will save more money by splitting in the long run compared to surrendering or the other possible plays. The only consolation of blackjack players in such instances is that they have made the mathematically optimal decision when dealt a long-term loser like stiff 16.

You can compare the expectation of each basic strategy play with paired 8s and 7s against the dealer’s 10 upcard below. The calculations are courtesy of mathematician and gambling expert Michael Shackleford, known as the Wizard of Odds.

Poker Probabilities Chart

As with all rules, there are always exceptions, however. Paired 8s should always be split unless one is playing shoe games and double-deck blackjack where the dealer must hit soft 17. Under these playing conditions, the odds favour surrendering the pair of 8s rather than hitting when the dealer shows an ace.

Exceptions are also made for paired 7-7 in single-deck blackjack. When the dealer must stand on all 17s, you surrender the 7-7 against a 10. Provided that the dealer must hit soft 17, basic strategy recommends you to surrender this pair whenever you are up against a 10 and an ace.

Odds and Probabilities

Players need to know what their odds are in case they happen to have a total value of 14, 15, or 16 in their hand as this will help them make better decisions. The following odds are accurate proving that the game is played with more than one deck and that gamblers decide to hit. If they have a 14 hand, the chance that they will go bust is 46%, and if the total of their hand is 15 – 54%.

In cases when they get unfortunate and get a total of 16, their chances of going bust are 62%. The worse-case scenario is when players get 19 or 20 as this leaves them with more than 85% chance of going bust. The good news is basic strategists never draw to hard 19 and hard 20 so their chances of busting with these totals are practically nil. Logically, the higher the total of the cards in the players’ hand, the more they are likely to bust by taking a hit.

Blackjack Percentage Chart

Conclusion

Probability In Blackjack

Having to deal with a 14, 15, or 16 hand is a big challenge which requires a lot of preparation and a good strategy and even then, players’ success is not guaranteed and they can only hope that the odds will be in their favour.

However, if they follow a strategy or choose the option to surrender, any of these choices will lead to the least amount of money they will lose. Once players find themselves in a bad situation, they should consider how to get out of it with minimal money losses instead of how to win the hand as in many cases this only pushes them to certain doom.