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You've gone through the basics of blackjack from our Blackjack 101: The Basics and understood the strategies from our Making the Right Plays in Blackjack: When to Hit, Double or Split article, let's focus on the math behind the strategies so you can understand how to tweak the basic strategy of blackjack to your advantage and reduce that edge! Be aware that this is an advanced guide, but will give you a better understanding of the workings of Blackjack strategy.
✋Math to The Danger Zone
Last lesson we talked about when to hit or stand, and in general you should stand at 17 or above, and hit or double down at 11 or lower. Hand values in the middle we referred to as the "danger zone" because you could be at risk if you take a card, and at risk if you stand and let the dealer play out their hand.
Unfortunately, the advanced strategy of Blackjack is not that straightforward, and math now comes into play to making correct decisions. For the purposes of this post, we are going to make a few assumptions:
If you are showing 20, the only card you can hit to be safe is an ace. Let's assume you have two face cards, but the dealer is also showing a face card and you want to win this hand (Caution - we do NOT recommend ever hitting on 20.) You can only take an ace, and your odds of getting one are:
If we were at 19, and the dealer showed 20, and we wanted to hit, we could take EITHER an ace or two to be safe, and those odds are:
The Danger Zone
The danger zone is when we show between 12 and 16 and the up card of the dealer is a Seven or greater, giving the dealer a good chance of having a hand they can stay on immediately. This is a danger for the player because:
In order to take basic strategy to the next level, we need to evaluate the dealer's up card versus the likelihood that they will be safe, or not. The below chart looks at the probability that the dealer will be safe (11 or less;, in the danger zone (12 to 16), or be forced to stand (hard 17 or greater). We're also assuming that aces are counted as 11.
What does this mean?
Conventional wisdom says that you should stand if you have 12 and the dealer shows a 6, but to take the simple blackjack strategy to the next level and do it in a manner that won't get you kicked out of casinos for card counting, you need to look at the percentages and treat blackjack like a poker hand.
What are the odds that you'll hit and be safe compared to the odds that the dealer will be in the danger zone?
✅Trust the Math!
Think of it this way - if the dealer is likely to be safe - showing a 2 for example - it's not necessarily smart to assume that your 14 will be good and you shouldn't risk hitting. 69% of the time the dealer will NOT draw a ten, allowing them to hit freely and possibly get in the range where they stand and beat you. With 7 safe values at 14, half the time you will hit safely and improve your hand, and 31% of the time you'll actually get a card that is able to beat the dealer (2, 3, 4 and 5).
Now we know if the dealer is showing a two, there's no way they will stand on two cards, but knowing that they will be able to take three cards safely more often than not, the risk of you busting on three cards now needs to be weighed against the likelihood that the dealer will get a hand to stand with and defeat you.
We'll dive into more of the math when it comes to splitting, doubling down and insurance in the next lesson.
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
✋Math to The Danger Zone
Last lesson we talked about when to hit or stand, and in general you should stand at 17 or above, and hit or double down at 11 or lower. Hand values in the middle we referred to as the "danger zone" because you could be at risk if you take a card, and at risk if you stand and let the dealer play out their hand.
Unfortunately, the advanced strategy of Blackjack is not that straightforward, and math now comes into play to making correct decisions. For the purposes of this post, we are going to make a few assumptions:
- The dealer is playing with an 8 deck shoe
- This is the first hand played
If you are showing 20, the only card you can hit to be safe is an ace. Let's assume you have two face cards, but the dealer is also showing a face card and you want to win this hand (Caution - we do NOT recommend ever hitting on 20.) You can only take an ace, and your odds of getting one are:
- 32 aces in the shoe
- 413 cards left (2 in your hand, one up in the dealer's)
- Odds of getting an ace --> 32/413 = 7.75% <-- This is slightly better than trying to hit a three-outer on the river in poker
If we were at 19, and the dealer showed 20, and we wanted to hit, we could take EITHER an ace or two to be safe, and those odds are:
- 32 aces and 32 two's in the shoe - 64 cards in total
- 413 cards left
- Odds of getting either an ace or two --> 64 / 413 = 15.5%
- One Value (Ace) --> 7.75% Chance of hitting
- Two Values (A, 2) --> 15.5% Chance of hitting
- Three Values (A, 2, 3) --> 23..25% Chance of hitting
- Four Values (A to 4) --> 31% Chance of hitting
- Five Values (A to 5) --> 38.75% Chance of hitting
- Six Values (A to 6) --> 46.5% Chance of hitting
- Seven Values (A to 7) --> 54.25% Chance of hitting
The Danger Zone
The danger zone is when we show between 12 and 16 and the up card of the dealer is a Seven or greater, giving the dealer a good chance of having a hand they can stay on immediately. This is a danger for the player because:
- We NEED to hit in order to give ourselves a chance against the dealer's assumed hand.
- We MAY bust depending on what card we're dealt.
- The dealer may not need to hit if their hand can get to 17 or greater.
In order to take basic strategy to the next level, we need to evaluate the dealer's up card versus the likelihood that they will be safe, or not. The below chart looks at the probability that the dealer will be safe (11 or less;, in the danger zone (12 to 16), or be forced to stand (hard 17 or greater). We're also assuming that aces are counted as 11.
| Dealer's Up Card | Safe Zone | Safe Zone % | Danger Zone | Danger Zone % | Stand | Stand % | |
| 2 | Ace to Nine | 69.0% | Ten | 31.0% | N/A | 0% | |
| 3 | Ace to Eight | 61.3% | Nine to Ten | 38.7% | N/A | 0% | |
| 4 | Ace to Seven | 53.6% | Eight to Ten | 46.4% | N/A | 0% | |
| 5 | Ace to Six | 45.9% | Seven to Ten | 54.1% | N/A | 0% | |
| 6 | Ace to Five | 38.5% | Six to Ten | 61.5% | N/A | 0% | |
| 7 | Two to Four | 23.1% | Five to Nine | 38.2% | Ace or Ten | 38.7% | |
| 8 | Two to Three | 15.4% | Four to Eight | 38.2% | Ace, Nine, Ten | 46.4% | |
| 9 | Two | 7.7% | Three to Seven | 38.5% | Ace, Two, Eight to Ten | 53.8% | |
| 10 | N/A | 0% | Two to Six | 38.5% | Ace, Seven to Ten | 61.5% | |
| Ace | Ace to Six | 45.9% | N/A | 0% | Seven to Ten | 54.1% |
What does this mean?
Conventional wisdom says that you should stand if you have 12 and the dealer shows a 6, but to take the simple blackjack strategy to the next level and do it in a manner that won't get you kicked out of casinos for card counting, you need to look at the percentages and treat blackjack like a poker hand.
What are the odds that you'll hit and be safe compared to the odds that the dealer will be in the danger zone?
✅Trust the Math!
Think of it this way - if the dealer is likely to be safe - showing a 2 for example - it's not necessarily smart to assume that your 14 will be good and you shouldn't risk hitting. 69% of the time the dealer will NOT draw a ten, allowing them to hit freely and possibly get in the range where they stand and beat you. With 7 safe values at 14, half the time you will hit safely and improve your hand, and 31% of the time you'll actually get a card that is able to beat the dealer (2, 3, 4 and 5).
Now we know if the dealer is showing a two, there's no way they will stand on two cards, but knowing that they will be able to take three cards safely more often than not, the risk of you busting on three cards now needs to be weighed against the likelihood that the dealer will get a hand to stand with and defeat you.
We'll dive into more of the math when it comes to splitting, doubling down and insurance in the next lesson.
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.
