Blackjack Odds and Probability

A Guide to the Most Important Numbers in Blackjack

Of all casino varieties, Blackjack is the one that has been studied the most, with many numbers experts spending long hours studying the games. In many scenarios, these experts have come up with the perfect decision, meaning that in a given situation, this decision will be the most profitable in the long run. This has meant that you’ll be able to find a number of charts which will tell you exactly what to do based upon your two cards and the one card that you can see from the dealer. Although these charts are very useful, it can also pay to have an understanding of exactly how these charts come into being, and here I look at various aspects that will aid your understanding of the game of blackjack. I’ll finish with a guide to the blackjack charts itself.

Dealer Bust Out Rate

This is one of the most important considerations in the game. The dealer bust out rate is how often the dealer will bust knowing their up card. The bust out rate is as follows for each up card:

• 2 – 35.30%
• 3 – 37.56%
• 4 – 40.28%
• 5 – 42.89%
• 6 – 42.08%
• 7 – 25.99%
• 8 – 23.86%
• 9 – 23.34%
• 10 – 21.43%
• Ace – 11.65%

As you can see from the chart, the dealer will bust most often when the up card is a 4, 5 or 6. These bust so often, that when you look at a strategy chart, it is advisable to stand on any number from 12 to 21 (you’ll obviously hit on any number below 12). Conversely, if the dealer has an Ace, it is very unusual for them to bust, meaning a chart will suggest you hit on every number up to 16.

Busting when Hitting

You can use the chart above in conjunction with the following one, which shows you how often you’ll bust when hitting on a certain number. Obviously, you would have to be mad (or extremely lucky) to hit on 20, but I’ve included all numbers from 12 to 20 here.

• 20 – 92% chance of busting
• 19 – 85%
• 18 – 77%
• 17 – 69%
• 16 – 62%
• 15 – 58%
• 14 – 56%
• 13 – 39%
• 12 – 31%

Using both charts, you’ll not want to hit if you have a higher bust out chance than the banker.

Number of Decks in Play

When playing online blackjack, you’ll find that you’ll be able to play with differing numbers of decks at some sites. The following chart shows you the house edge depending on the number of decks.

• 1 – 0.17%
• 2 – 0.46%
• 4 – 0.60%
• 6 – 0.64%
• 8 – 0.66%

Clearly, the less number of decks in play, the lower the house edge there is, so you should always aim for the games with the least number of decks. However you should ensure that if playing with just one deck that the rules are standard and not some variation of the game.

Blackjack Strategy Charts

On a blackjack chart you will find all of your hands listed on the vertical axis and the dealers up card on the horizontal axis. Having read across and down, you will come upon one of the decisions that will be the best mathematical move for you. Here is an example chart:

Chart Key

• H – Hit
• S – Stand
• P – Split
• D – Double

	2	3	4	5	6	7	8	9	10	A
5	H	H	H	H	H	H	H	H	H	H
6	H	H	H	H	H	H	H	H	H	H
7	H	H	H	H	H	H	H	H	H	H
8	H	H	H	H	H	H	H	H	H	H
9	H	D	D	D	D	H	H	H	H	H
10	D	D	D	D	D	D	D	D	H	H
11	D	D	D	D	D	D	D	D	D	H
12	H	H	S	S	S	H	H	H	H	H
13	S	S	S	S	S	H	H	H	H	H
14	S	S	S	S	S	H	H	H	H	H
15	S	S	S	S	S	H	H	H	H	H
16	S	S	S	S	S	H	H	H	H	H
17+	S	S	S	S	S	S	S	S	S	S
A,2	H	H	H	D	D	H	H	H	H	H
A,3	H	H	H	D	D	H	H	H	H	H
A,4	H	H	D	D	D	H	H	H	H	H
A,5	H	H	D	D	D	H	H	H	H	H
A,6	H	D	D	D	D	H	H	H	H	H
A,7	S	D	D	D	D	S	S	H	H	H
A,8	S	S	S	S	S	S	S	S	S	S
A,9	S	S	S	S	S	S	S	S	S	S
2,2	P	P	P	P	P	P	H	H	H	H
3,3	P	P	P	P	P	P	H	H	H	H
4,4	H	H	H	P	P	H	H	H	H	H
5,5	D	D	D	D	D	D	D	D	H	H
6,6	P	P	P	P	P	H	H	H	H	H
7,7	P	P	P	P	P	P	H	H	H	H
8,8	P	P	P	P	P	P	P	P	P	P
9,9	P	P	P	P	P	S	P	P	S	S
T,T	S	S	S	S	S	S	S	S	S	S
A,A	P	P	P	P	P	P	P	P	P	P
Dlr	2	3	4	5	6	7	8	9	10	A