The Mathematics of Blackjack: When to Hit, Stand, Split or Double Down

A lot of players gravitate towards blackjack in casinos because of its low house edge. Unlike various other casino games, in blackjack you have an element of control, in that you decide whether to stand, hit, double down or even split. At a surface level, it gives you the added confidence that you can somewhat influence the outcome, albeit with a lot of luck. But underneath the illusion of control, there are all sorts of rules and calculations that can be made to really improve your chances of winning.

Before diving into these precise calculations and the blueprints for decreasing the house edge, we have to confess that they do not guarantee wins. They are guidelines that would improve the mathematical odds of you making a profit in the long run. They won’t save you from difficult hands or from the odd chance that the dealer makes a blackjack. With that in mind, let’s see at what you can do – and how it helps your chances.

What Action to Take and When in Blackjack

All blackjack tables and online games provide you with two actions: Hit or Stand. Most games also provide options to double down or stand, but there are some variants or special derivations that may not include these actions. Assuming you are playing at a table with all four actions, they all have their uses, but for the maximum money making potential, you will need to recognize when to use each action.

Your course of action will depend on the value of your hand and the dealer’s upcard. The dealer will always have the edge, because they follow strict rules that maximize their winning potential, but you can decrease that edge through calculated decisions.

Mathematics in Hitting in Blackjack

We want to beat the dealer and get a higher value, but without going bust. Falling in between those two is the sweet zone, where you have the best opportunity to beat the dealer.

Most basic blackjack strategies will tell you to hit when the following criteria are true:

• Your hand has a value of 8 or less
• If the dealer has a value of 7+ and yours is up to 16

But let’s look at the probability here. We have to assess the dangers, namely, your chances of getting a higher value than the dealer and then the odds of going bust.

Odds of Going Bust:

• 12 Value Hand: 30.18%
• 13 Value Hand: 37.75%
• 14 Value Hand: 45.28%
• 15 Value Hand: 52.83%
• 16 Value Hand: 60.37%
• 17 Value Hand: 67.92%

This applies to both you and the dealer. These are just close approximations as it depends on the number of decks and the cards already drawn. Yet still, most blackjack strategies will tell you to hit on 16 if the dealer has a value over 7 or higher, because they have an approximately 30% chance of beating you otherwise with a 10.

When Hitting is Needed

Virtually all strategies agree on one basic principle. If you have a double digit value but are less than 10 ahead of the dealer, then in most cases you should hit. Unless, that is, the dealer has a value of 6 or your value is 17 or higher. If the dealer draws a 7 and you have 12, then you should hit. The chances of going bust at 12 are around 30%, but your biggest worry is that the dealer will draw a card with a value of 6 or better.

If you draw a 3 and improve that 12 to 15, you are still advised to hit, until your value is 17, when you have the best chance of either pushing or winning.

When to Stand in Blackjack

Most blackjack strategies will tell you to stand on 17, and for good reason. The chances of going bust are nearly 2/3. Even when the dealer hits on a soft 17, your chances of going bust are too high. But on the good side, this will force the dealer to compete with you, and the odds of going bust will be transferred to their hand.

Some blackjack strategies tell you to stand when you have double digit numbers from 12 up to 16, and the dealer has a value of 6 or lower. Remember the numbers 5 and 6 as they are a pretty tough hand for the dealer. The dealer will be prompted to draw a card, and usually, a second one to beat you. Their chances of going bust on a 5 or a 6 are extremely high, so a lot of strategies tell you to stand if you have a value of 12-16 to their 5 or 6. And the value of the dealer going bust there is around 42%, so mathematically you are in pretty safe hands.

Taking Advantage of Doubling Down

Now we have to think bigger picture on this one, because that is where doubling down really makes the difference. The basic strategy charts almost universally tell you to double down if you have a value of 10 or 11. This is because you have a great chance of getting a 8+, which would put you beyond the dealer’s capacity to hit. Of course, it does not mean you will win every time, but doubling down is useful in another area.

The idea is that you will make double the money when you win these hands, so that in the long run you can take advantage of any wins. The odds on hitting a 10 are again 30%, but the odds on getting 8+ are around 45%. But you can forget all of that if the dealer has a value of 10 or an Ace upcard. This is because they have an equal chance of catching you and then your doubling down will be in vain. You can also double down on 9s, but only when the dealer has a value of 3-6. So while doubling down could bring down the house edge, it also comes with the risk of losing double your money in a single hand.

Which Hands are Best for Splitting

Pairs of 8s or Aces are your best bet for splitting, but for different reasons. The Aces can be split and then if your game allows you, are perfect for doubling down. You may just win 2 blackjacks from the round, making a good lump sum. 8s must be split because they can be used to build two strong hands, but also because it avoids leaving you with a weak hand of 16. A hand of 16 is always risky. You should hit on 16 if the dealer has anything bigger than a 6, but your chances of going bust are very high.

Standing on a 16 gives you an approximately 25% chance of winning, an outlook that is much better if you split two 8s. If the dealer has low cards (2-6) then your chances of winning jump up to 55-60%. Should the dealer have stronger hands, your chances of winning are narrower, but not as low as standing on the pair of 8s.

Other Tips for Reducing House Edge in Blackjack

The house edge in blackjack is low as it is, but a basic strategy can reduce it from 4% down to around 0.5%. One popular way is to use a blackjack counting system and combine it with your blackjack basic strategy. In the early rounds, apply the basic strategy to gain an edge. Then, when the remaining cards are higher or lower in value, adjust your strategy.

Surrender is also highly useful, as you can cut your losses in the right circumstances. For example, when the dealer draws a 10 or Ace, and you have 16 that cannot be split. It is best to avoid the high risk of going bust (or losing to their hand).

Side bets have the promise of bringing mega payouts, such as betting on Perfect Pairs, 21+3 or Super Sevens. But in general, these side bets have a higher house edge. They are calculated to bring the house a profit in the long run. So if you want to keep the house edge low, you should avoid them.