What Are The Odds Of Winning Blackjack?

Blackjack is a very popular card game played worldwide, particularly in casinos.

Although the rules are simple - get closer to 21 than the dealer without going over 21 - there's a fascinating amount of depth to it.

To find out about the history of blackjack, how to use Basic Blackjack Strategy to optimise your play, card counting and more, make sure to check out this How To Play Blackjack Guide.

This article will focus on some of the probabilities involved in blackjack, from how likely you are to bust if you’re dealt another card to the likelihood of winning a hand. 

You’ll also find out how blackjack compares to sports betting, in terms of the bookmaker or casino margin, and why you might sometimes be better to wager on blackjack rather than sports when completing Matched Betting or casino offers, if both are an option. 

It's worth mentioning that you don’t need to understand any of this to get the best possible return from blackjack.

Outside of using advanced systems like card counting, following Basic Blackjack Strategy reduces the casino’s edge as much as possible to give you the best long-term results. 

At the same time, having some insight into the workings of blackjack, and how likely certain outcomes are, can help you understand why Basic Strategy works. 

This can give you a greater enjoyment of the game and give you more confidence when playing blackjack. 

Basic Blackjack Strategy

One of the interesting features of blackjack that sets it apart from many other casino games is that it involves skill as well as luck.

You have to decide how to play the hand you’re dealt, and your choices affect your long-term returns. 

The good news is that, over the years, an optimum strategy for playing blackjack has been developed. This is known as Basic Blackjack Strategy.

To make things even easier, you can use a Blackjack Calculator to tell you exactly how to play for any situation.

Following Basic Strategy takes all the guesswork out of playing blackjack since there will always be a single correct way to play your hand, no matter what upcard the dealer is showing

This maximises the Return To Player (RTP) of blackjack, which is around 99.5% assuming you always use the correct strategy. This is a very high RTP for a casino game.

Odds and Probability

The terms odds and probability are often used interchangeably. However, like many English words, they both have a range of meanings depending on context.

In terms of the title of this article, the word ‘odds’ will mostly be understood to be the same as probability, so it could equally have read “What is the probability of winning blackjack?” This is a fairly informal but commonly used meaning of the word 'odds', and different to the word's use in betting.

Later on, we’ll also have a look at how probabilities in blackjack relate to actual betting odds, but first, let’s look at the difference between probability and betting odds.

Probability

Probability is how likely something is to happen.

Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

This can either be left as a fraction or evaluated as a number, which will always be between 0 and 1. Multiplying by 100 converts this into a percentage.

To show how this works we can calculate the likelihood of different totals when rolling two fair dice. The diagram below shows the probabilities of rolling all possible totals from 2 to 12.

There are 36 different possible totals when rolling two dice, so we’ll always be dividing by 36 to work out the probabilities. 

Since there's only one possible way to roll 12 with two dice (each die needs to land on a 6), the probability of this outcome is 1 in 36 (1/36 or 2.8%). 

The most likely total when rolling two dice is 7. This is because there are 6 different ways to roll a 7, which is more than for any other total. The probability of rolling a 7 is therefore 6 in 36 (6/36 or 16.7%)

Here are some other probabilities that can be worked out in the same way:

• The probability of rolling a double is 6/36 or 1/6.
• The probability of rolling at least one of any particular number is 11/36.

Looking at all different possible outcomes and counting up how many 'desirable' outcomes there are can be a useful way to work out probabilities. 

The same principle can be used to work out some probabilities in blackjack, as we'll see later.

Odds

In betting, odds are used to show the ratio of winnings to stake. The three main types of betting odds are fractional, decimal, and American. 

In the UK, fractional odds are usually used for betting.

Fractional odds are calculated by dividing the potential winnings by the stake.

For example, if you bet on Bournemouth to win at odds of 5 to 1 (5/1), you'll make £5 profit for every £1 staked if they win. 

In Europe, as well as in Matched Betting, decimal odds tend to be used.

An easy way to convert from fractional to decimal odds is to divide the first number by the second number, then add 1. For fractional odds of 5/1:

Decimal odds = (5 / 1) + 1 = 5 + 1 = 6.

You can find out more about betting odds here.

The Probability of a Net Win

If you play blackjack using perfect Basic Strategy, you'll achieve an average Return To Player (RTP) of around 99.5%.

This means that for every £100 wagered, you'll get £99.50 back on average, losing just 50p.

Due to variance, you're unlikely to lose exactly 50p from wagering £100. 

Sometimes you'll end up in profit and sometimes you'll lose money, but your average long-term loss will be 50p per £100 wagered. 

This means that when playing with Basic Strategy, you'll almost (but not quite) break even over time. Due to that 0.5% casino edge, the longer you play, the more you'll lose on average. However, it’s possible to turn the tables on the casino by taking advantage of casino offers to give yourself the edge.

Since you pretty much break even over time when playing blackjack it's tempting to assume that the chances of winning a hand must be slightly less than 50%. 

However, the situation is a little more complicated for a few reasons:

• Splitting or doubling affects how much you stake on a given hand, and your potential profit or loss. You could win one of your split hands and lose the other one, for example.
  
• If you're dealt a blackjack / natural and the dealer doesn't also have a blackjack, your profit will be 1.5 times your stake, rather than equal to your stake.
  

• If you and the dealer tie, the wager is settled as a push and your stake is returned for no profit or loss.
• If allowed by the rules of the blackjack variant you’re playing, you might sometimes surrender and win half your stake.

A net win is where you make an overall profit from a hand of blackjack. 

This takes into account all money staked on the hand after doubling and splitting and all money returned in winnings.

Calculating the probabilities of a net win, push, or loss is complicated, but ambling expert Michael Shackleford, also known as the Wizard of Odds, has worked them out and presented them here.

The mathematical technique used to calculate these probabilities is called combinatorial analysis. 

This basically goes through all possible scenarios to work out how likely you are to end up in profit, break even, or lose money overall on a hand of blackjack. 

Here's a table showing the probabilities:

If your hand results in a push you make no profit or loss, so it’s interesting to look at the probabilities ignoring pushes (i.e. when you break even after the wager is settled).

Here are the probabilities without including push results:

You can see this mentioned in this discussion on the Wizard of Odds site.

To work out the Win probability in the second table you can divide the first table’s Win probability by the sum of the Win and Loss percentages, then multiply by 100:

Win Probability (excluding push) = (42.43 / (42.43 + 49.09)) x 100

Win Probability (excluding push) = (42.43 / 91.52) x 100 = 46.36%

Loss Probability (excluding push) = 100% - 46.36% = 53.64%

As you can see, the probability of a win is significantly lower than 50%, even though your actual long-term probability of ending up in profit is very close to 50%.

This is largely because some of those 46.36% of wins will be paid out at 1.5 times your stake, when you win with a natural / blackjack. 

The probability of being dealt a blackjack depends on the number of decks used, but is around 4.75%. 

Again, this information can be found here. 

Doubling and splitting also affects the probability of a net win or loss. 

The Probability of Going Bust

In blackjack, the aim is to beat the dealer.  Here are two ways to achieve this:

• Scoring more points than the dealer without going over 21. Scoring 21 or less and the dealer scoring over 21

• Drawing cards with a total value over 21 means you go bust. 

One situation where you can easily work out the likelihood of going bust is if you’re drawing one more card to a hard hand.

 A hard hand is any hand that doesn’t contain a flexible ace (an ace that can count as either 1 or 11 in that hand).

 You can read more about hard and soft blackjack hands and flexible aces here. 

To simplify the maths, the probabilities below were worked out assuming the dealer is using an infinite deck, where the proportion of each different value of cards is always the same. 

For example, there are four aces in a deck of 52 cards, so aces make up 4/52 of a deck. This will always be the same proportion if you assume the deck is infinite.

Real-world casinos obviously don't use infinite decks (they tend to use a much more reasonable 4 to 8 decks).

The effect of this is that the proportion of different cards in the deck, known as the deck composition, changes as cards are dealt. 

As a result, the probability that your hand busts if you have a certain total also changes.

Nevertheless, these probabilities give a reasonable guide as to how likely you are to bust depending on the total value of your hand.

The same method used to calculate dice probabilities earlier is used again - divide the number of 'desirable' outcomes by the total possible number of outcomes.

If you have a hard total of 11 or lower (for example a 6 and a 5), you can't bust by drawing one extra card.

The highest value cards are all worth 10, so if you're dealt one, you won't bust and your hand will be worth the highest possible total of 21.

If you were dealt an ace, you’d score this as 1 point to take your total to 12, rather than choosing to bust by adding 11 points.

At the other end of the table, if you're foolish enough to hit when you have a hard total of 21 (for example a 6, 7, and 8), your hand is certain to bust.

If you have a hard 14 (for example a Queen and a 4), your hand will bust if you're dealt an 8, 9, or 10 value card.

Four out of every 52 cards is an 8, four are 9s, and 16 are 10 value cards (the 10s, jacks, queens, and kings).

This means that 24 out of 52 cards (24/52) will lead to you busting, which is a probability of 24/52 or 46.2%.

Explaining Basic Blackjack Strategy 

If you’re dealt a hard 16, there’s a 62.5% chance that you’ll bust if you take another card, so standing might appear to be the best choice. However, you also need to consider the dealer’s card.

If your hand is worth 16 points, the dealer will beat you if they end up with 17, 18, 19, 20, or 21 points, which can happy in many different ways. 

As you can see from this blackjack strategy chart, you should only stand on a hard 16 if the value of the dealer’s upcard is lower than 7.

If the dealer’s card has a value over 7, or an ace, you should hit. If you have a hard 16 and are allowed to surrender, you should do this if the dealer has a 9, 10 value card or ace.

If the dealer has a 10-value card like a Queen, for example, they’ll beat your 16 with just one more card if they draw a 7, 8, 9, 10, Jack, Queen, King, or Ace (this assumes the dealer doesn’t peek to see if they have blackjack before you play). 

This means that 32 out of every 52 cards drawn will lead to the dealer beating your 16 by drawing one card, which is a probability of 61.5%. If the dealer was only allowed to draw one more card, you would be better off standing, since there’s a 62.5% chance of busting if you hit, and only a 61.5% chance that the dealer will beat you with that card. 

However, the dealer isn’t restricted to drawing just one more card. For example, they would beat you with two more cards by drawing a 2 followed by either a 5, 6, 7, 8 or 9, or a 3 followed by 4, 5, 6, 7, or 8. 

There are many other ways that the dealer could beat your 16 by drawing more than one additional card, so the probability they’ll beat your 16 if you stand will be much higher than 62.5%.

For this reason, your best option if you find yourself with a hard 16 against a dealer’s 10-value card is to hit, or surrender if the rules allow it. 

A great tool for analysing blackjack hands is the Wizard Of Odds Blackjack Hand Calculator, which can be found here:

https://wizardofodds.com/games/blackjack/hand-calculator/

Here are the settings that correspond to an online blackjack game called Premium Blackjack:

Hard 16 Against Queen

Entering a Queen for the dealer and a hard 16 for the player, then clicking ‘Calculate’ shows the Expected Values of standing, hitting, and doubling:

The Expected Values are all very negative since the dealer has one of the two best cards (an ace being the other one) and a hard 16 is the worst possible starting hand for the player.

This is because impossible to beat the dealer with a 16 unless they bust and you’re very likely to bust yourself if you take another. 

The Expected Value of hitting is -0.570817, which means that on average you’ll lose 57.08% of your stake if you hit, due to your big disadvantage.

However, standing is even worse, losing you 57.66% of your stake, on average. For this reason, you’re slightly better off if you hit, which makes the best of a bad situation. 

Although it’s interesting to see why you should hit in this scenario, in practice it’s much easier to use Outplayed’s Blackjack Calculator.

This has Basic Blackjack Strategy built into it and does all the hard work for you, telling you exactly how you should play. 

In this case, you can see that hitting is the best option if you have a hard 16 against a dealer’s Queen. 

Soft 18 Against 2

Soft 18 is probably one of the most misplayed blackjack hands. It’s not obvious how you should play this total against the dealer’s upcard, no matter what it is. 

There are also three different choices you should make, depending on the dealer’s card. 

First, we’ll look at how you should play if the dealer has a 2 against your soft 18. Again, we’ll use the Blackjack Hand Calculator:

As you can see from the positive expected values, a soft 18 is an advantageous hand, and you’ll end up making a profit in the long term when you’re dealt this against the dealer’s 2 no matter whether you stand, double, or hit.

However, you’re slightly better off if you stand in this case, as it has the highest expected value. 

The Blackjack Calculator confirms this:

Soft 18 Against 9

If you’re up against a dealer’s 9 with your soft 18, you no longer have the upper hand, since there are lots of ways for the dealer to beat you with one or more additional cards starting from a 9.

Because of this, the expected values are negative for all three possible choices:

The clear winner here is to hit since this has the least negative expected value, which loses you the smallest amount of money on average over time.

Entering these cards into the Blackjack Calculator confirms that this is the best decision:

Soft 18 Against 3

If you’re dealt a soft 18 and the dealer has 3, the positive expected values show that you have a slight advantage and will win the hand more than half the time.

In this situation, your best choice is to double. 

Depending on the blackjack variant you’re playing, you might not be able to double.

As you can see from the Blackjack Hand Calculator above, standing is best if you aren’t allowed to double. 

Outplayed’s Blackjack Calculator confirms that you should double if you’re allowed to, or stand otherwise:

You can see how complicated soft 18 is to play from these Basic Blackjack Strategy charts:

Just for completeness, here are the Basic Blackjack Strategy charts for pairs:

Betting Odds and Blackjack

When betting on a sporting event, for example betting on Brighton to beat Liverpool, a bookmaker will give you certain odds. These show how much profit you’ll make if your bet wins. 

For example, if Brighton are at odds of 3/1 (4.0 in decimal), you’ll make £30 profit from a £10 bet on Brighton if they win. 

Betting odds are related to how likely a bet is to win - higher odds are used for less likely outcomes, which means that although your bet is less likely to win, you’ll make more profit if it does. 

Despite this link between betting odds and the likelihood of a bet winning, there’s an important difference between betting odds and probability.

Bookmakers factor in a margin to their odds by making their odds ‘unfair’ (lowering them compared to fair odds). This ensures that they profit from their betting markets in the long term.  

If bookmakers offered fair odds, the implied probability of these odds would be the same as the actual probability of the outcome occurring.

The implied probability is calculated by dividing 1 by the decimal odds, then multiplying by 100 if you want this as a percentage. 

For the Brighton bet above, this is:

Implied Probability = (1 / 4) x 100 = 25%

Normally in betting, the probability of an outcome is lower than the implied probability, which is how bookmakers make a profit over time

Bookmakers estimate the actual probability of an event occurring, then calculate the fair odds by dividing 1 by this probability.

They then reduce this to create their actual odds, building a profit margin in the betting market. 

On occasion, bookmakers misprice their odds so they’re higher than the fair odds. It’s possible to take advantage of these mispriced odds using value betting strategies.

The reason for mentioning all of this is to compare betting odds to playing blackjack.

When wagering on blackjack you aren’t given odds in the same way as you are when you bet on sports.

This time, the casino’s edge comes about due to the Return To Player of blackjack being below 100% (it’s normally around 99.5% if you use Basic Strategy).

This means you’ll lose 50p per £100 staked on average. 

Another way to put this is that the expected value (EV) of wagering £100 on blackjack is -£0.50. In general, the EV is -0.50% of your stake.

To relate this to a sports bet, let’s look at betting on a coin toss. This is a bet that’s offered by some bookmakers, for example in cricket.

A fair coin has a 50% chance of landing on either heads or tails. Fair odds for a coin toss are 1/1 (2.0 in decimal). 

Bookmakers typically offer odds of around 1.9 for either heads or tails. This means you’ll make £90 profit if your bet wins but lose £100 if it loses. The EV can be calculated as follows:

EV = (0.5 x £90) + (0.5 x -£100) = £45 - £50 = -£5

This is ten times worse than the EV of -£0.50 that you get from wagering £100 on blackjack. 

To get the same expected value on a coin toss you’d need odds of 1.99. This would give you a £99 profit on a winning bet and a £100 loss on a losing bet. The EV is:

EV = (0.5 x £99) + (0.5 x -£100) = £49.50 - £50 = -£0.50

Due to the very high RTP of blackjack (assuming you always use Basic Strategy), you’ll lose far less money in the long term than you will when gambling on sports. 

This is due to the much smaller margin that the casino has with blackjack compared to sports bets. 

Another way to compare blackjack to betting odds is to look at a bet placed at evens (1/1 or 2.0 in decimal). The implied probability for this bet is 50%.

To achieve an EV of -£0.50 on a £100 bet you’d need the actual probability of the outcome to be 49.75%:

EV = (0.4975 x £100) + (0.5025 x -£100) = £49.75 - £50.25 = -£0.50

Real bookmaker odds have implied probabilities that are nowhere near this close to the actual probabilities of an outcome, so this again goes to illustrate how much better blackjack is compared to gambling on sports when looking at long-term losses. 

Going further, we can draw parallels between blackjack wagering and Matched Betting and see what sort of back and lay odds you’d need on a qualifying cash bet to get the same 50p loss per £100 staked. 

For this, we can use a Matched Betting Calculator. To achieve a qualifying loss of 50p from a £100 bet, you’d need to get an incredibly close match between back and lay odds of something like back odds of 2 and lay odds of 2.01:

Back odds of 4 and lay odds of 4.02 give the same qualifying loss:

Let’s imagine you’re doing an offer where you need to wager £100. You’re allowed to either place it on a sports bet or wager it on blackjack (assuming blackjack counts 100% towards wagering). 

There are advantages and disadvantages to placing a sports bet compared to wagering on blackjack.

Advantages of Backing and Laying a Sports Bet

• Assuming you can find a very close match quickly, this may be quicker than wagering £100 with £1 stakes on blackjack. This is especially true if you use an online odds matching tool. Increasing the blackjack stake would speed up the process but you’d be much more likely to lose more money if you were unlucky. 

• You have a known qualifying loss.

Advantages of Wagering a £100 Bonus on Blackjack

• Your average loss of 50p is very small. To achieve a 50p qualifying loss on your sports bet, comparable to the average loss from wagering on blackjack, extremely close back and lay odds would be needed. These are generally difficult to find, even using an odds matcher, and are bad for your account health. 

• There’s no need to have money in a betting exchange to cover the liability of your bet. 

Wagering on Blackjack for Casino Offers

When completing worthwhile casino offers (those with a positive expected value), wagering on blackjack is often the best choice due to its very high Return To Player (RTP).

This reduces your average losses when wagering your own money, increasing your long-term profits.

It’s important to carefully check bonus terms to ensure blackjack is eligible for the offer, and also check the wagering contributions. 

You’ll sometimes find casino offers where blackjack doesn’t contribute 100% towards wagering, and this can be as low as 10% in some cases. 

If you needed to wager £100 in total and blackjack only contributed 10% towards wagering, you’d need to stake a total of £1,000 to complete wagering. 

However, in cases where blackjack is eligible and counts 100% towards wagering, it’s a great choice. 

If you’re interested in trying out casino offers, it’s well worth contacting Outplayed’s Customer Support team to ask them about a Diamond trial. This includes both casino and Matched Betting offers. 

With Outplayed’s Diamond membership, you’ll find many high-quality guides for profitable sign-up and reload casino offers. Many of these allow you to wager on blackjack. 

The Offers Team always check bonus terms carefully, so you can be confident that the slot or game recommended, whether blackjack or otherwise, will be a good choice for the offer. 

Conclusion

Whether you’re gambling recreationally or doing worthwhile casino offers, understanding some of the probabilities involved in blackjack can give you an appreciation of why it’s best to play according to Basic Blackjack Strategy. 

Having some insight into blackjack’s inner workings can also give you a greater enjoyment of the game. 

The optimum way to play blackjack is often counter-intuitive, so seeing yourself why you should play in a certain way can give you more confidence in your play. 

You can find out how to use blackjack, roulette, or online slots to make long-term profits from casinos at outplayed.com.