Blackjack Probability

The exploits of famous big-money blackjack players such as Ken Uston and the MIT Team can lead beginning blackjack enthusiasts to think that it’s necessary to have a complex strategy to win at the tables. In truth, blackjack is one of the few card games in which the strategy truly rests on a skill: the ability to perform some simple math.

Being able to calculate the odds of losing (and gambling is always based on the odds of losing, not winning) won’t assure a win every time. There are simply too many variables in play. That’s why even the best blackjack strategies are based on the science of probabilities, or the statistically likelihood of a certain outcome given some common conditions.

However, using probability math effectively can certainly improve a blackjack player’s chance of winning a blackjack hand. For example, whatever else is involved in strategy, the one thing that is sure in blackjack is that if you bust, you lose. The following table gives the probability of busting if you take a hit when your cards total certain numbers. 

Hand Value % of Busting   Dealer's Up % of Dealer
21 100%   Card Busting
20 92%   2 35%
19 85%   3 37%
18 77%   4 40%
17 69%   5 42%
16 62%   6 42%
15 58%   7 26%
14 56%   8 24%
13 39%   9 23%
12 31%   10 23%
11 or less 0%   Ace 17%


Here’s the probability of receiving the following two card point total:

1) Blackjack – 4.8% (winning hand)
2) 17 – 20 – 30.0% (automatic stand)
3) 12 – 16 – 38.7% (decision hands)
4) 4 – 11 – 26.5% (must hit)

Here’s the probability that the dealer will receive the following point total:

1) Blackjack or 21 – 12.2% chance
2) 20 points – 17.6% chance
3) 19 points – 13.5% chance
4) 18 points – 13.8% chance
5) 17 points – 14.6% chance
6) Dealer Busts – 28.3% chance

The odds that a dealer will not bust is 71.7% chance (before any cards are flipped)

Knowing these odds makes it possible to understand why a blackjack strategy card tells you to hit or stand in certain situations. There are a lot of combinations and you have to use your best judgement when there isn’t a clear-cut decision. That is part of what gambling is all about.

Here are some situations that you shouldn’t have to make a decision:

Don’t ever split 10′s or 5′s
Don’t hit 15 or 16 unless the dealer has a 7 or higher
Don’t split 2′s through 7′s if the dealer has an 8 or higher
Don’t split 9′s when the dealer is showing a 7, 10 or Ace

Do split or double down every good chance when the dealer is showing a 5 or 6
Do split 8′s every time with the possible exception when the dealer is showing an Ace and you want to surrender
Do double down on 10 except when the dealer is showing a 10 or Ace

Always split Aces
Always double down on 11
Always hit 12 if the dealer is showing a 2 or 3

These situations will pay out in the long run if you make the same decision each time. Will you always win? Absolutely not. Are the percentages in favor of listening to the advice above, Yes!

House Advantage

Now remember that the casino always makes sure it has an edge in the game. This edge is about 2% on average. Casinos get this edge because the dealer always acts last after all other players have bet and made their decisions on whether to hit or stand. This means that more players are likely to bust before the dealer must decide how to play his or her hand.

Furthermore, the house sets the rules, which means that certain options may not be available to players in certain conditions. For instance, a common table rule is that the dealer must hit until 17, or must stand on a soft 17 (a hand that includes an ace that can be counted as either 1 or 11). It’s essential to determine what the house rules are before sitting down to a blackjack table.

Here is the House Advantage statistics for the different variations that you will see:

Single Deck Blackjack: 0.17%
Two Deck Blackjack: 0.46%
Four Deck Blackjack: 0.60%
Six Deck Blackjack: 0.64%
Eight Deck Blackjack: 0.66%

Dealer Hits on soft 17: 0.21%
Player can only double down on 9, 10, 11: 0.09%
Blackjack pays 6 to 5: 1.36% (only usually found in charitable blackjack games)

In order to decrease the house percentage, a player should learn basic blackjack strategy as well as memorize the probability table listed above and use a good blackjack strategy card to follow along with. Looking at this table, it’s obvious that more than half the time, you’re going to get a hit that will bust your hand. The reason for this is simple: There are more cards valued at 10 than any other value in the deck. These cards are 10-Jack-Queen-King. That’s what makes the probability of busting so much higher once your hand begins to run into the teens as a total.

One quick way to calculate the probabilities of busting is this simple rule: If you always assume that the dealer’s down card is a 10, you’ll hardly ever go wrong. So if the dealer shows an 8 up, and you have 16, there’s a high probability that you’ll bust if you take a hit.

That’s the thing with blackjack. To get really good at it, you simply must learn to do the math.

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