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The Math to Blackjack - Splitting, Doubling Down and Insurance
If you caught our previous guide briefly going over the basics of splitting in blackjack, you already know the golden rules: always split Aces and 8s, never split 5s or 10s, and sometimes split small pairs when the dealer’s showing weakness. But those rules only scratch the surface.
In this post, we’re going beyond the basics — diving into the why behind each play, the math that drives your odds, and the subtle situations where splitting (or not) can completely change the outcome of a hand. Whether you’re trying to refine your blackjack strategy or just understand the logic behind the charts, this breakdown will help you make sharper, more informed decisions at the table.
So, let’s dig in: When should you really split — and when is it smarter to double down or stand your ground?
✋Splitting - When To Split, When Not To Split
For this lesson we are going to maintain the assumptions we made at the start of the last lesson to try and keep the odds simple and straight forward:
To start, basic blackjack strategy suggest always splitting Aces and 8s, never splitting 5s or 10s, and only splitting 2s, 3s, 6s and 7s when the dealer shows a card between 2 and 6.
Why Split Eights?
This is pretty easy to explain: with two 8s, you have 16; arguably the worst spot to be in against any dealer's cards. You can't improve easily - your chance of hitting and being safe is 38.5%, meaning you're likely to bust 2 out of 3 hands regardless of what the dealer does, but any hand the dealer stays on beats you. By splitting 8s you're giving yourself a 31% chance of hitting 18 - a decent score; and the possibility of getting an ace, 2 or 3 - roughly a 23% chance - of a card that will allow you the chance to hit to a really high score, or an Ace to get you to 19.
Even if only one hits, the likelihood of you chopping - winning one hand but losing the other - is far greater than one hand that is a high risk to lose.
Why Split Aces?
This one is not as cut and dry. Most casinos - but not all - will force you to ONLY take one card splitting aces, treating it like a double down bet. While you will get two chances to hit a blackjack, again, most casinos do NOT pay 3 to 2 on this as it's not considered natural. You need to check and verify this with the casino you play at to confirm though. So all things considered, look at the math:
The likelihood of getting a card that would equal or beat a dealer's safe hand (17 or greater) is 61.5% - 6 to 10 gets us there. That means 38.5% of the time you are getting a card that puts you at 16 or less. Splitting two aces means one of these hands is likely to need an additional card - a card you can't hit for. The reason for splitting aces is to get two blackjacks. But at 31%, the chance that you'll get two blackjacks is actually quite low: you can expect this to happen just 10% of the time.
You will find a lot of the time that the only way you'll win both hands is if the dealer busts or gets seventeen - assuming you were lucky to hit a 10 and a 7 for example. But depending on what the dealer shows, a better approach might be to actually double down, which we'll go through in the next section.
Why 5s and 10s Shouldn't Be Split?
Not splitting 5s should be obvious: you have 10, and splitting fives leaves you open to having two hands between 12 and 15. Doubling down instead of splitting gives you a no-risk card to get to 20 or even 21 for the same bet. You should only ever consider doubling down on 5s, never splitting.
Tens can be tricky but it will come down to what the dealer is showing. Dealers showing 7 or greater: meaning cards that the dealer might not need to hit again with, opens the door for you missing and needing to hit in the danger zone. Remember: if 10s, the likelihood of getting a card between 2 and 6 is around 38 to 39%, meaning you will have gone from a safe hand to a hand in danger against a dealer's 7.
Where this could be advantageous is if the dealer has a very risky card: 5 or 6 for example. You know the dealer will have to hit, and if they have a 9 or 10 down, the chances of them busting is quite high. This means you could split tens, and stay on whatever you get, allowing the dealer a chance to bust. You need to balance your risk tolerance with this, as this can and often does backfire, but going from a strong 20 to weaker counts but standing and allowing the dealer to draw and miss can be beneficial.
Why Everything Else Depends On The Dealer
All other pairs will need a risky card for the dealer's up-card to make splitting make sense.
Twos - You are going to be in the danger zone 31% of the time with a 10 hitting.
Threes - You are going to be in the danger zone 38-39% of the time with a 9 or 10 hitting.
Fours - You are in the danger zone 46.5% of the time with an 8, 9 or 10 hitting
Sixes - You're in the danger zone 62% of the time with a 6 to 10 hitting
Sevens - You're in the danger zone almost 70% of the time with a 5 to 10 hitting
Splitting might seem like the play at times, but depemding on what your dealer has up, you may want to consider doubling down as opposed to splitting.
✅ Doubling Down - The Better Way?
Doubling down achieves the similar goal of getting a second bet per hand on the blackjack table but only allowing the player to hit one more card, making this a better bet in certain situations. This depends heavily on the rules of your casino though - some will only allow you to do this when you sit with Nine, Ten or Eleven; others will allow you to double down on ANY hand. For the purposes of this article, we'll assume you can double down on ANY hand, and if your casino doesn't allow it below Nine, then you'll have to be satisfied to simply hit.
Nine, Ten & Eleven
Our chart below shows whether you should double down or not based on the hand you hold ("Our Hand") vs. what the dealer shows with their up-card.
* - These spots basic strategy says to hit, not double down, howevver if you see a lot of small cards out and few face cards, it can be advantageous to double down here, taking one card as a ten or eleven greatly increase your chances of winning two bets.
Essentially we want to double down when we have 11 every time except when we are against a dealer's ace. With 10, we want to double down when the dealer shows any card 2-9, but with 9 we only want to double when the dealer will have to hit.
31% of the time with 11 we're going to get 21, and 61% of the time we'll get to 17, making this an advantageous position to be in. Especially considering the dealer is going to need to hit 38.5% of the time when showing a 10, and more often when they have lower cards. With 10, we'll be safe almost the same amount of time, but basic strategy suggests to hit with a 9 hand against a dealer's 9.
Consider this: To be "safe" with nine, we need to hit at least an eight - giving us 7 values (8 to Ace) compared to 6 that won't (2-7). This means that ONLY 54% of the time we'll get to 17, and if the dealer is showing a 7, they have three cards (2, 3, 4) to hit again and be safe PLUS five cards (10, Jack, Queen, King, Ace) to beat our 17. This means it is more likely (61.5% to our 54%) that they will have a hand that either beats us, or will be safe to hit again, putting us at risk.
All Other Hands vs Dealer Less Than Seven
If your casino allows you to double down any time, then the first rule is you don't want to double down when the dealer shows a 7or higher.
When the dealer shows a 5 or 6 though, and your hand is less than 9, this now could be an option to increase your win potential as the dealer's window to be safe is as small as possible. Basic strategy suggests not to, but let's break this down:
Let's say you have 7 and the dealer is showing a 6. You know the dealer has to hit again because they can't stay on soft 17. Knowing they have to take two cards changes the odds for you. Holding a 7, you know that you have 38.5% chance of getting to 17 or 18, and the dealer has a 61.5% chance of hitting a card that puts them in the Danger Zone - putting them at risk for hitting and busting.
The lower the dealer's up card is though, the less likely that they will be in the Danger Zone so one must tread lightly when it comes to doubling down against the dealer.
✋Insurance - The Worst Side Bet
Finally we'll review why the insurance bet is not a side bet you ever want to take. For starters, casinos generally offer 2 to 1 to place an insurance bet - which is half of your original bet - when the dealer's up card is an ace to protect against them having blackjack. If they do, the insurance bet is paid out but you lose the original bet. If they do not have blackjack, the player loses the insurance bet and the hand continues as normal.
So why is this a bad bet? Let's run the math: when the dealer shows an ace, their odds to hit blackjack is 31% - a ten down
Playing the Insurance Bet
Overtime, the player should expect to lose $2.60 every 100 hands that you played the insurance bet
NOT Playing the Insurance Bet
Overtime, the player should expect to lose $1.15 every 100 hands that you played the insurance bet
Let's talk about it!
I hope you've enjoyed my Blackjack series so far! Let me know in the comments what you think of these casino learning series, and what you'd like for us to tackle next! Ask questions on any Blackjack related strategy not already discussed too!
Resources
If you caught our previous guide briefly going over the basics of splitting in blackjack, you already know the golden rules: always split Aces and 8s, never split 5s or 10s, and sometimes split small pairs when the dealer’s showing weakness. But those rules only scratch the surface.
In this post, we’re going beyond the basics — diving into the why behind each play, the math that drives your odds, and the subtle situations where splitting (or not) can completely change the outcome of a hand. Whether you’re trying to refine your blackjack strategy or just understand the logic behind the charts, this breakdown will help you make sharper, more informed decisions at the table.
So, let’s dig in: When should you really split — and when is it smarter to double down or stand your ground?
✋Splitting - When To Split, When Not To Split
For this lesson we are going to maintain the assumptions we made at the start of the last lesson to try and keep the odds simple and straight forward:
- The dealer is playing with an 8 deck shoe
- This is the first hand played
To start, basic blackjack strategy suggest always splitting Aces and 8s, never splitting 5s or 10s, and only splitting 2s, 3s, 6s and 7s when the dealer shows a card between 2 and 6.
Why Split Eights?
This is pretty easy to explain: with two 8s, you have 16; arguably the worst spot to be in against any dealer's cards. You can't improve easily - your chance of hitting and being safe is 38.5%, meaning you're likely to bust 2 out of 3 hands regardless of what the dealer does, but any hand the dealer stays on beats you. By splitting 8s you're giving yourself a 31% chance of hitting 18 - a decent score; and the possibility of getting an ace, 2 or 3 - roughly a 23% chance - of a card that will allow you the chance to hit to a really high score, or an Ace to get you to 19.
Even if only one hits, the likelihood of you chopping - winning one hand but losing the other - is far greater than one hand that is a high risk to lose.
Why Split Aces?
This one is not as cut and dry. Most casinos - but not all - will force you to ONLY take one card splitting aces, treating it like a double down bet. While you will get two chances to hit a blackjack, again, most casinos do NOT pay 3 to 2 on this as it's not considered natural. You need to check and verify this with the casino you play at to confirm though. So all things considered, look at the math:
The likelihood of getting a card that would equal or beat a dealer's safe hand (17 or greater) is 61.5% - 6 to 10 gets us there. That means 38.5% of the time you are getting a card that puts you at 16 or less. Splitting two aces means one of these hands is likely to need an additional card - a card you can't hit for. The reason for splitting aces is to get two blackjacks. But at 31%, the chance that you'll get two blackjacks is actually quite low: you can expect this to happen just 10% of the time.
You will find a lot of the time that the only way you'll win both hands is if the dealer busts or gets seventeen - assuming you were lucky to hit a 10 and a 7 for example. But depending on what the dealer shows, a better approach might be to actually double down, which we'll go through in the next section.
Why 5s and 10s Shouldn't Be Split?
Not splitting 5s should be obvious: you have 10, and splitting fives leaves you open to having two hands between 12 and 15. Doubling down instead of splitting gives you a no-risk card to get to 20 or even 21 for the same bet. You should only ever consider doubling down on 5s, never splitting.
Tens can be tricky but it will come down to what the dealer is showing. Dealers showing 7 or greater: meaning cards that the dealer might not need to hit again with, opens the door for you missing and needing to hit in the danger zone. Remember: if 10s, the likelihood of getting a card between 2 and 6 is around 38 to 39%, meaning you will have gone from a safe hand to a hand in danger against a dealer's 7.
Where this could be advantageous is if the dealer has a very risky card: 5 or 6 for example. You know the dealer will have to hit, and if they have a 9 or 10 down, the chances of them busting is quite high. This means you could split tens, and stay on whatever you get, allowing the dealer a chance to bust. You need to balance your risk tolerance with this, as this can and often does backfire, but going from a strong 20 to weaker counts but standing and allowing the dealer to draw and miss can be beneficial.
Why Everything Else Depends On The Dealer
All other pairs will need a risky card for the dealer's up-card to make splitting make sense.
Twos - You are going to be in the danger zone 31% of the time with a 10 hitting.
Threes - You are going to be in the danger zone 38-39% of the time with a 9 or 10 hitting.
Fours - You are in the danger zone 46.5% of the time with an 8, 9 or 10 hitting
Sixes - You're in the danger zone 62% of the time with a 6 to 10 hitting
Sevens - You're in the danger zone almost 70% of the time with a 5 to 10 hitting
Splitting might seem like the play at times, but depemding on what your dealer has up, you may want to consider doubling down as opposed to splitting.
✅ Doubling Down - The Better Way?
Doubling down achieves the similar goal of getting a second bet per hand on the blackjack table but only allowing the player to hit one more card, making this a better bet in certain situations. This depends heavily on the rules of your casino though - some will only allow you to do this when you sit with Nine, Ten or Eleven; others will allow you to double down on ANY hand. For the purposes of this article, we'll assume you can double down on ANY hand, and if your casino doesn't allow it below Nine, then you'll have to be satisfied to simply hit.
Nine, Ten & Eleven
Our chart below shows whether you should double down or not based on the hand you hold ("Our Hand") vs. what the dealer shows with their up-card.
| Our Hand | Dealer Show Ace | Dealer Shows 10 | Dealer Shows 9 | Dealer Shows 8 | Dealer Shows 7 | Dealer Show 6 & ⬇️ |
|---|---|---|---|---|---|---|
| Nine | NO | NO | NO | NO* | NO* | YES |
| Ten | NO | NO | YES | YES | YES | YES |
| Eleven | NO | YES | YES | YES | YES | YES |
Essentially we want to double down when we have 11 every time except when we are against a dealer's ace. With 10, we want to double down when the dealer shows any card 2-9, but with 9 we only want to double when the dealer will have to hit.
31% of the time with 11 we're going to get 21, and 61% of the time we'll get to 17, making this an advantageous position to be in. Especially considering the dealer is going to need to hit 38.5% of the time when showing a 10, and more often when they have lower cards. With 10, we'll be safe almost the same amount of time, but basic strategy suggests to hit with a 9 hand against a dealer's 9.
Consider this: To be "safe" with nine, we need to hit at least an eight - giving us 7 values (8 to Ace) compared to 6 that won't (2-7). This means that ONLY 54% of the time we'll get to 17, and if the dealer is showing a 7, they have three cards (2, 3, 4) to hit again and be safe PLUS five cards (10, Jack, Queen, King, Ace) to beat our 17. This means it is more likely (61.5% to our 54%) that they will have a hand that either beats us, or will be safe to hit again, putting us at risk.
All Other Hands vs Dealer Less Than Seven
If your casino allows you to double down any time, then the first rule is you don't want to double down when the dealer shows a 7or higher.
When the dealer shows a 5 or 6 though, and your hand is less than 9, this now could be an option to increase your win potential as the dealer's window to be safe is as small as possible. Basic strategy suggests not to, but let's break this down:
Let's say you have 7 and the dealer is showing a 6. You know the dealer has to hit again because they can't stay on soft 17. Knowing they have to take two cards changes the odds for you. Holding a 7, you know that you have 38.5% chance of getting to 17 or 18, and the dealer has a 61.5% chance of hitting a card that puts them in the Danger Zone - putting them at risk for hitting and busting.
The lower the dealer's up card is though, the less likely that they will be in the Danger Zone so one must tread lightly when it comes to doubling down against the dealer.
✋Insurance - The Worst Side Bet
Finally we'll review why the insurance bet is not a side bet you ever want to take. For starters, casinos generally offer 2 to 1 to place an insurance bet - which is half of your original bet - when the dealer's up card is an ace to protect against them having blackjack. If they do, the insurance bet is paid out but you lose the original bet. If they do not have blackjack, the player loses the insurance bet and the hand continues as normal.
So why is this a bad bet? Let's run the math: when the dealer shows an ace, their odds to hit blackjack is 31% - a ten down
Playing the Insurance Bet
- 31% of the time you'll lose your original bet, but win the insurance at 2 to 1. Since this was half the original bet, you win back your bet. If you had bet $10, with a $5 insurance bet, your $15 total bet won $10, losing $5.
- 69% of the time you'll lose the insurance bet, but then allow the hand to play out. The odds state that the player will win 42% of the time and 9% of the time the hand ends in a push. So this 69% could break down more:
- 42% the player wins, turning that $15 into $20 for a $5 profit
- 9% the player pushes, turning that $15 into $10 for a $5 loss
- 18% the dealer wins, turning that $15 into nothing for the player
| Percentage | Hand Result for Player | Over Time - % times Hand Result |
|---|---|---|
| 31% - Dealer Has Blackjack | $5.00 Loss | -$1.55 |
| 42% - Player Wins | $5.00 Profit | $2.10 |
| 9% - Hand Pushes | $5.00 Loss | -$0.45 |
| 18% - Dealer Wins but Not by Blackjack | $15.00 Loss | -$2.70 |
Overtime, the player should expect to lose $2.60 every 100 hands that you played the insurance bet
NOT Playing the Insurance Bet
- 31% of the time you'll lose your original bet because the dealer has blackjack. The $10 bet is lost.
- 69% of the time you'll lose the insurance bet, but then allow the hand to play out. The odds state that the player will win 42% of the time and 9% of the time the hand ends in a push. So this 69% could break down more:
- 42% the player wins, turning that $10 into $20 for a $0 profit
- 9% the player pushes, turning that $10 into $10 for no gain
- 18% the dealer wins, turning that $10 into nothing for the player
| Percentage | Hand Result for Player | Over Time - % times Hand Result |
|---|---|---|
| 31% - Dealer Has Blackjack | $10.00 Loss | -$3.10 |
| 42% - Player Wins | $10.00 Profit | $4.20 |
| 9% - Hand Pushes | $0.00 | $0.00 |
| 18% - Dealer Wins but Not by Blackjack | $10.00 Loss | -$1.80 |
Overtime, the player should expect to lose $1.15 every 100 hands that you played the insurance bet
Let's talk about it!
I hope you've enjoyed my Blackjack series so far! Let me know in the comments what you think of these casino learning series, and what you'd like for us to tackle next! Ask questions on any Blackjack related strategy not already discussed too!
Resources
- Remember you can practice your blackjack game for FREE right here: >>> Play Blackjack <<<
- There are amazing strategy guides on Casino.us. Dive into all things Blackjack Strategy right here: How to Win at Blackjack
- Prefer to learn with videos? Then the Blackjack Academy is for you! Totally free, with 69 lessons ranging from Beginner to Advanced levels.
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