# 5 Blackjack Strategy Decisions Explained with Simple Math

When you play blackjack, you should either use a basic strategy card or make playing decisions based on memory from basic strategy. The only way to keep the house edge at the blackjack table as low as possible is to always use the best strategy.

It’s hard, if not impossible, to figure out the most profitable strategy without the use of basic strategy charts or cards. The good news is that you can pick up a basic strategy card in a casino gift shop or print one online.

Basic strategy has been developed using computers to determine the most profitable, or least unprofitable, play in every situation you can have while playing blackjack.

You can simply use basic strategy and not worry about why it works.

But if you’re like me, you’d like to get a better understanding of how and why it works.

I’ve put together this post that includes 5 blackjack strategy decisions explained with simple math to help you understand a little more about how the best strategy is determined.

This page doesn’t include every strategic decision, but by learning about the 5 strategies included, it can help you understand why other plays are right and wrong. You can use the things you learn here to see why other decisions are made and use the same techniques and reasoning to run your own scenarios.

Everything you read on this page is based on mathematical calculations. People have created computer programs to run every possibility for blackjack decisions in combination with the probabilities of the cards remaining in the deck or shoe.

I’ve purposely kept the mathematical end of the sections simple, because most people aren’t interested in complicated math computations, and some people don’t understand them.

If you want to know more than I include below about the math, you can recreate the calculations yourself or invest in computer software to help. I include the simple mathematical explanations below so that everyone who reads them can follow along and get a basic understanding of why certain strategic decisions are better than others.

## 1 – Why You Always Split Aces

The ability to split pairs in blackjack is one of the most powerful strategy decisions available to players. This is why the first three sections on this page deal with split decisions. Without the ability to split pairs, the house edge would be so high that the game wouldn’t be worth playing.

When you get an ace as your first card of a blackjack hand, it’s the most powerful card. The ability to count it as 1 or 11, along with the instant blackjack total when your second card is a 10, jack, queen, or king, makes it profitable on average every time you receive an ace. Even a second card of 9, 8, or 7 gives you a profitable soft total of 20, 19, or 18.

This means that when you receive an ace, 7 out of 13 possible cards instantly give you a profitable long term hand. That only leaves 6 cards that aren’t instantly good, and two of the other 6 possible cards aren’t bad.

When you match an ace with a 6 you have a soft 17, which I talk about later, and getting another ace gives you a profitable split opportunity.

Now let’s talk about why you always split aces. Some of the numbers you just read come into play here, but the simple answer is that it’s more profitable on average to split aces than do anything else with them.

The only other option to splitting is hitting, but it’s not a profitable play.

When your first two cards are aces you have a soft total of 12. Things could be worse, but any total of 12 is not good. With a soft total of 12, the cards you hope to see when you hit are 9, 8, 7, or 6. This represents only 4 out of 13 possible cards, leaving 9 cards that aren’t good for your hand.

If you split the aces you start two hands with an ace. This replaces a single hand of soft 12. What this means is you take an unprofitable hand and replace it with two profitable hands. This is why you always split aces.

But let’s dig into the actual numbers behind this decision a bit more.

With an ace as your first card, you can receive 1 of 13 different cards as your second.

Let’s look at each possibility:

**A A –** When you get another ace you split them again if the house rules allow it. If you can’t split them again you play with a soft 12 and hit.

**A 2 –** This is a soft 13, and you hit.

**A 3 –** A soft 14, which you hit.

**A 4** – Soft 15, which you hit.

**A 5** – Soft 16, which you hit.

**A 6** – Soft 17, which you hit.

**A 7** – Soft 18

**A 8** – Soft 19

**A 9** – Soft 20

**A 10** – Blackjack

**A J** – Blackjack

**A Q** – Blackjack

**A K** – Blackjack

Everything you do when making strategic blackjack decisions is based on expected value. Expected value can be positive or negative, and is based on the profitability of your hand if it’s run thousands of times. Some hands are profitable on average, and some are losers on average.

Any hand with a value of 18 or higher has positive expectation. And two card totals of 21, or blackjack, are profitable, and they pay more than even money. Most blackjack tables pay 3 to 2.

As a side note, never play at a blackjack table that pays worse than 3 to 2 on blackjacks.

This means that each of the two hands starting with an ace after you split have 7 cards, 7 thru king, that are profitable. That leaves only 6 cards that are questionable, and they’re not all unprofitable.

But simply seeing why over half of the possible cards are profitable, with the 4 natural blackjack hands paying extra, proves that the best play is to always split aces.

In addition to creating two hands starting with an ace, you get to place another bet in a profitable situation. This makes starting with two aces very profitable in the long run.

## 2 – Why You Always Split 8’s

I covered quite a bit about the reasoning behind splitting and how to determine is a strategy decision is profitable or not in the last section, so we can jump right into the simple math behind why splitting 8’s is always correct.

If you don’t split 8’s, you have a hard 16. This is the worst starting hand in blackjack. With a hard 16, the negative expectation is higher than any other starting hand.

This fact alone makes splitting 8’s the best play.

When you have a hard 16 and stand, you lose on any hand where the dealer doesn’t bust. Because the dealer always hits until they have 17 and always stands on 18 or above, the only way you can win with 16 is when they bust.

At some tables the dealer stands on a soft 17, and at others they stand on a soft 17. It’s more profitable to hit on a soft 17 than stand on one, so it’s better for you to play at a table where the dealer stands on a soft 17.

If you hit on a hard 16, any card of 6 or higher make you bust. This means 8 cards make you bust and only 5 cards help your hand.

More than half the available cards make you an automatic loser.

Now let’s look at what happens when you split your 8’s.

You have to make another bet, but you then start with two hands with a hard 8. Let’s look at each possible outcome starting with an 8.

**8 A** – Gives you a soft 19.

**8 2** – Gives you a hard 10.

**8 3** – Gives you a hard 11.

**8 4** – Gives you a hard 12.

**8 5** – Gives you a hard 13.

**8 6 **– Gives you a hard 14.

**8 7 **– Gives you a hard 15.

**8 8 **– Gives you a hard 16, but in some games you can split again.

**8 9 **– Gives you a hard 17.

**8 10** – Gives you a hard 18.

**8 J** – Gives you a hard 18.

**8 Q** – Gives you a hard 18.

**8 K **– Gives you a hard 18.

Of the 13 possible hands, 8 of them are profitable. The hard 10, hard 11, hard 17, all of the hard 18’s, and the soft 19 are all profitable.

In addition, if you can split the 8’s again when you get another one, it also is profitable in the long run.

Because over half the possible outcomes are profitable, you always split 8’s.

## 3 – Why You Don’t Split 4’s

Now let’s look at a situation where you should never split. When you have a pair of 4’s, you have the choice to start with a hard 8, or two hands with a hard 4. In addition, to start with two hands with a hard 4, you have to make an additional wager.

In the last section I listed the possible outcomes of the 13 cards with a hard 8. As you saw, over half of the possible outcomes were profitable, so starting with a hard 8 is good. The only way you should split 4’s is if it was more profitable than starting with a hard 8.

Here’s a list of what can happen starting with a hard 4:

**4 A** – Soft 15.

**4 2** – Hard 6.

**4 3** – Hard 7.

**4 4 **– Hard 8.

**4 5** – Hard 9.

**4 6** – Hard 10.

**4 7** – Hard 11.

**4 8** – Hard 12.

**4 9** – Hard 13.

**4 10** – Hard 14.

**4 J** – Hard 14.

**4 Q** – Hard 14.

**4 K** – Hard 14.

The only possible hands here that you’re somewhat happy with are the hard 7, 8, 9, 10, and 11.

And the problem with them, especially the hard 7, 8, and 9, is you still have to hit and hope for a 10 value card or an ace.

On the other hand, the hard 14’s, hard 13, hard 12, and hard 6 are all unprofitable.

This means that at least 7 out of the 13 possibilities are bad. Compare this to starting with a hard 8, and you can see why you should never split 4’s.

## 4 – Why You Stand on Hard 17 and Hit Soft 17

Determining why you should stand on a hard 17 is fairly easy, but when you try to figure out why hitting a soft 17 is profitable, it takes a little more work.

Standing on a hard 17 is the best play because if you hit, the only cards that can help without making you bust are an ace, 2, 3, and 4. This means only 4 cards help you and 9 make you bust.

This clearly shows why you don’t hit a hard 17.

In addition, on one of the hands the dealer stands on, a 17, you push instead of lose, and when the dealer busts, you win. If you bust and then the dealer busts, you still lose.

The reason why you hit on a soft 17 instead of standing can be shown the same way we looked at the previous sections.

Let’s see what happens with each possible card:

**A** – Another ace gives you two aces and a 6. This is a hard 8 or a soft 18. You already saw above why a hard 8 is a good hand, and a soft 18 is also a profitable hand.

**2** – A soft 19 is a profitable hand.

**3** – A soft 20 is also profitable.

**4** – A soft 21 is a profitable hand.

**5** – Hard 12.

**6** – Hard 13.

**7** – Hard 14.

**8** – Hard 15.

**9** – Hard 16.

**10** – Any of the 10 value cards makes a hard 17.

**J** – Hard 17.

**Q** – Hard 17.

**K **– Hard 17.

4 of the possible cards, an ace, 2, 3, and 4, improve your hand. 4 other cards, the 10 value cards, change the soft 17 to a hard 17. Only 5 cards, a 5 thru 9, make your hand worse.

While the argument can be made that only 4 cards help and 5 hurt–with 4 cards being roughly even–what you have to remember is even on the 4 cards that hurt your hand, you can still win.

This isn’t as clear cut as the previous sections, but the right play is to hit a soft 17.

I’ve shown in each section the reasons why the strategy is correct without diving into the deep end of the mathematical pool.

But in this instance, the decision is so close that it doesn’t show a clear reason for the correct decision. And the truth is, if you stay on a soft 17 instead of hitting, you aren’t going to cost yourself too much in expected value.

But I do want to share with you what the computer simulations show.

When the house rules are that the dealer hits on a soft 17 it moves the house edge 0.22% against you. In other words, it increases the house edge by 0.22%. This isn’t exactly the same as your gain by hitting a soft 17, but it’s close, and it gives you an idea why you should.

I’m not going to try to explain how this number was created, because it’s too complicated for this discussion.

But I have 100% faith in the computer simulations; blackjack is a 100% mathematical game that has been solved by computers.

This is why I always hit on a soft 17.

And you should too.

## 5 – Why Insurance Is a Bad Bet

When the dealer has an ace as his or her up card they offer insurance to the players. The insurance bet is half the size of your original wager, and it pays 2 to 1 when the dealer has a blackjack.

Here’s an example:

If you bet $20 and the dealer shows an ace, insurance costs $10. When the dealer has a blackjack you lose your original $20 bet, but you win $20 on the insurance.

This is why insurance is often called even money, because it makes it look like you break even.

The problem is that insurance doesn’t help you break even. Insurance is actually a separate wager that the casino makes look like a good bet.

To understand why you should never take insurance, think of the insurance wager as a standalone bet.

Your original bet is going to resolve as normal whether you take insurance or not. While you aren’t a favorite to win against any hand the dealer starts with an ace for the reasons discussed in the first section, whether you win or lose the original bet has nothing to do with insurance.

When you look at the insurance wager by itself, you need to consider how many cards win the bet for you and compare the ratio of good and bad cards to the ratio of the pay out when you win.

Of the 13 possible cards the dealer can have with his or her ace, only 4 of them win your insurance bet. The 4 are the 10, jack, queen, and king. This leaves 9 cards that make you lose the bet. This creates a ratio of 9 to 4.

But the bet only pays 2 to 1.

Here’s what the ratios mean:

If the bet paid even odds, or at a break even ratio, it would pay 2.25 to 1 instead of 2 to 1. You determine the fair odds or break even odds by dividing 9 by 4, from the 9 to 4 ratio. Because the ratio the bet pays is less than the ratio of bad to good cards, the bet is unprofitable.

## Conclusion

The easiest thing to do about blackjack strategy is to use a basic strategy card or chart while you play. Keep using one until you have all of the plays memorized, and then never make a play that goes against the strategy.

But now you have simple mathematical evidence of why some of the main strategy plays work.

You don’t have to be a mathematical genius to benefit from the math behind the game. Blackjack uses a standard 52 card deck, or multiple standard decks, so it’s an easy game for a computer program to solve. You don’t have to do all of the hard work, because it’s already been done.

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