Interpret the strategy tables

For each non-fundamental decision a player can do an interactive strategy table is computed on this site. By default a shoe with 6 decks is assumed. This is also known as the "Basic Blackjack strategy". With changing distribution of cards in the shoe, the best strategy varies a little. The distribution in the shoe may be changed interactively by entering the remaining number of cards of each value or by decreasing them clicking onto the card button (A, 2, ..., 9 or X).
The percentual distribution is computed automatically and can't be set. You may also specify the number of decks (1..9) used to compute the following tables.
A total of eight tables is computed, some show probabilities and some show expectations. If an expectation is below zero it means Don't do it! and the table background is red. The lower this value is, the more you are encouraged not to do this action.
If an expectation is above zero it means Do it! and the table background is green. The higher this value is, the more you are encouraged to do this action. Probabilities are always between 0% and 100% and not colored. Probabilities are more of theoretical interest but will help understanding the best strategy.

Change the numbers in this table, simulating the distribution of cards in the shoe and watch for modification of expectations and probabilities:

Card distribution in the shoe

Number of decks: 123 456 789

Card:	2	3	4	5	6	7	8	9	X	A	Total
Number:
Distribution:

Total expectations

The total expectation is the magic number in beating the dealer. Depending on this value the player must bet high or low. If the total expectation is below zero he must place minimum stakes or skip playing. If it is above zero he should place high stakes as the theory says that in these few situations the player has a moderate advantage over the dealer.
This table shows the expectations for each Dealers First Hand and the Total Expectation. The last expectation is the number which determines the height of the stake.

DFH	2	3	4	5	6	7	8	9	X	A
E(total)	8.9	12.0	15.5	19.2	22.3	14.2	5.7	-4.1	-17.7	-34.0	-0.85

Probabilities of Dealers Last Hand

This table shows the probabilities of the dealers last hand under the condition of his first hand. Note the high probability that the dealer will bust, if his first hand is low. During the game we can see the dealers first hand before we have to do our decisions. So we buy carefully when the dealers first hand is 2-6, and buy more courageous when the dealers first hand is 7-ACE.
This table is only of theoretical interest and does not influence the players strategy directly.
The probability for the dealers first hand is named p(DFH). The probabilities for the dealers last hand are named p(bust) [= the probability the dealers will bust], p(BJ) [= the probability the dealer will achieve a Blackjack] and p(17) through p(21) [= the probability for the dealers final sum].

DFH	2	3	4	5	6	7	8	9	X	A
p(DFH)	7.7	7.7	7.7	7.7	7.7	7.7	7.7	7.7	30.8	7.7	100.0
p(bust)	35.4	37.4	39.6	41.8	42.3	26.2	24.4	22.9	21.2	11.5	28.2
p(BJ)	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	7.7	30.9	4.7
p(21)	11.8	11.5	11.2	10.8	9.7	7.4	6.9	6.1	3.5	5.4	7.3
p(20)	12.4	12.1	11.6	11.2	10.2	7.9	6.9	12.0	34.0	13.1	18.0
p(19)	13.0	12.5	12.1	11.8	10.6	7.8	12.9	35.2	11.2	13.1	13.4
p(18)	13.4	13.1	12.4	12.2	10.6	13.8	36.0	11.7	11.2	13.1	13.9
p(17)	14.0	13.4	13.1	12.2	16.6	36.9	12.9	12.0	11.2	13.0	14.5

Probabilities of Players Last Hand

This table shows the probabilities of the player last hand under the condition of the dealers first hand and under the condition that the player plays according to the strategy as described with the following six tables. If you are wondering, why the probability for a final score of 11 is slightly above zero, consider the situation where a player might double a score of 9 and then he receives a 2. This table is only of theoretical interest.

DFH	2	3	4	5	6	7	8	9	X	A
p(bust)	3.3	3.1	0.0	0.0	0.0	26.1	26.5	26.9	28.8	29.0	17.7
p(BJ)	4.7	4.7	4.7	4.7	4.7	4.7	4.7	4.7	4.7	4.7	4.7
p(21)	3.8	3.7	2.9	2.9	2.9	7.3	7.3	7.5	7.8	7.7	5.9
p(20)	14.4	14.3	13.5	13.5	13.5	17.8	17.9	18.1	18.3	18.4	16.5
p(19)	9.9	9.9	9.1	9.1	9.1	13.3	13.4	13.6	13.7	13.8	12.0
p(18)	9.9	9.9	9.1	9.1	9.1	14.0	13.4	12.2	12.9	12.9	11.6
p(17)	9.8	9.7	9.0	9.0	9.0	13.2	13.1	13.3	13.5	13.6	11.8
p(16)	9.7	9.8	8.9	8.9	8.9	0.7	0.7	0.7	0.0	0.0	3.7
p(15)	10.9	10.9	10.1	10.1	10.1	0.7	0.7	0.7	0.0	0.0	4.2
p(14)	10.9	10.8	9.9	9.9	9.9	0.7	0.7	0.7	0.0	0.0	4.1
p(13)	12.0	12.0	11.3	11.3	11.3	0.7	0.7	0.7	0.0	0.0	4.6
p(12)	0.7	1.0	11.1	11.1	11.1	0.7	0.7	0.7	0.0	0.0	2.9
p(11)	0.0	0.3	0.3	0.3	0.3	0.0	0.0	0.0	0.0	0.0	0.1

Expectations for buy

This table shows the expectations when the player has to decide whether to buy or to stay. Note that the player should always buy (or double - see below) with a hard-hand of 11 and lower (since he can't bust) or a soft-hand of 7/17 and lower. He should never buy with a hard-hand of 17 and higher or a soft-hand of 9/19 and higher.
Expectations for buy are named E(7/17) and E(8/18) for softhands, and E(12) through E(16) for hardhands.
Example: If you were to buy on 16 against the dealers 7, you would lose approximately 6.1 additional bets in each one hundred games for a fresh shuffled shoe.

DFH	2	3	4	5	6	7	8	9	X	A
E(8/18)	-5.9	-5.8	-5.8	-5.3	-9.4	-23.0	-6.8	8.1	3.0	0.4
E(7/17)	15.2	14.5	13.8	13.5	11.5	15.9	30.8	26.4	20.2	20.5
E(16)	-17.9	-21.3	-24.8	-28.6	-27.7	6.1	5.4	3.2	0.0	10.3
E(15)	-12.6	-15.7	-18.9	-22.3	-21.3	10.5	9.4	6.8	3.2	12.7
E(14)	-7.1	-9.8	-12.7	-15.8	-14.8	15.3	13.9	11.0	6.7	15.5
E(13)	-1.6	-4.0	-6.6	-9.3	-8.2	20.7	18.8	15.4	10.6	18.6
E(12)	3.9	1.8	-0.5	-2.8	-1.7	26.3	24.0	20.1	14.7	21.8

Expectations for doubling

This table shows the expectations when the player has to decide whether to double the stake or to continue as usual. If he doubles he will be dealt only one more card. If he continues as usual he should play according to the strategy described in the table Expectations for buy.
Expectations for double are named E(9), E(10) and E(11).
Example: If you were to double down on 11 against the dealers 6, you would approximately gain 33 additional bets in each one hundred games for a fresh shuffled shoe.

DFH	2	3	4	5	6	7	8	9	X	A
E(11)	23.3	25.9	28.6	31.1	33.5	17.2	12.1	7.3	-1.8	-33.0
E(10)	17.8	20.6	23.4	26.1	29.0	13.9	9.1	3.3	-10.4	-37.1
E(9)	-1.2	2.2	5.6	9.1	12.3	-6.4	-12.3	-24.4	-36.2	-55.9

Expectations for default splitting

This table shows the expectations when the player has to decide whether to split or to continue as usual. If he splits he must place another stake for the second bet. After splitting each bet should be played according to the strategy described in the tables Expectations for buy and Expectations for double. Please note that some casinos do not allow to double after splitting.
If you were to split 9-9 against the dealers Ace, you would lose 33 additional bets in each one hundred games for a fresh shuffled shoe.
Expectations for splitting are named E(A-A), E(2-2) through E(X-X).

DFH	2	3	4	5	6	7	8	9	X	A
E(A-A)	39.5	42.0	44.7	46.6	48.8	30.6	26.2	23.8	16.1	-21.2
E(2-2)	-3.5	-1.5	0.8	4.4	6.7	3.4	-4.7	-13.9	-25.5	-41.4
E(3-3)	-5.9	-2.9	0.5	4.1	6.4	4.2	-4.0	-13.4	-25.1	-41.1
E(4-4)	-21.1	-17.5	-13.7	-9.4	-9.6	-26.6	-26.4	-27.4	-38.3	-52.5
E(5-5)	-44.5	-40.2	-35.5	-30.5	-29.6	-51.0	-58.9	-66.5	-69.1	-76.0
E(6-6)	-2.3	2.6	7.1	10.5	13.1	-8.4	-15.8	-24.3	-34.5	-48.4
E(7-7)	7.7	10.1	13.0	15.9	21.5	19.3	-4.2	-13.0	-22.6	-42.7
E(8-8)	25.1	27.0	29.3	31.5	38.7	58.2	33.9	8.9	-3.7	-22.4
E(9-9)	2.5	5.3	8.2	11.9	10.7	-5.8	9.1	8.0	-19.4	-33.0
E(X-X)	-28.0	-24.3	-20.3	-15.9	-13.4	-26.3	-40.1	-53.1	-54.5	-65.3

Expectations for splitting with a partner player

This table shows the expectations when two players play together. One of the disadvantages when you split is that you have to do another bet of the same amount. Sometimes splitting certain combinations would increase the probability of achieving a higher final score. However as the stake must be doubled, often is not worthwhile to split, specially if the dealer has a good first hand (7-A).
But other players placing bets on your box can but must not double their bets after the placeholder splits. A partner player could therefore place high stakes whereas the placeholder would place low ones on his box. In some situations where it is advantageous to split, but disadvantageous to double the stake, the partner can divide his bet. Only the placeholder must bring in another stake according to the rules.
In these situation the expectations for splitting cards looks quite different because only the smaller bet of the player must be doubled, but not the high one of the partner.
This table is of rare interest as it can only be applied if two or more players attempt to beat the dealer as a team.
Expectations for splitting are named E(A-A), E(2-2) through E(X-X).

DFH	2	3	4	5	6	7	8	9	X	A
E(A-A)	15.6	15.8	15.9	15.3	15.1	7.0	8.3	11.9	15.1	5.5
E(2-2)	4.0	3.4	2.7	2.6	2.8	6.1	5.6	5.1	4.4	3.4
E(3-3)	4.2	4.0	3.8	3.6	3.9	9.9	9.1	8.1	7.0	5.5
E(4-4)	-9.5	-9.3	-9.0	-8.5	-10.6	-17.5	-10.2	-3.2	-3.9	-4.0
E(5-5)	-31.5	-30.5	-29.5	-28.3	-29.3	-38.4	-39.4	-39.1	-31.9	-25.4
E(6-6)	11.7	13.1	14.0	13.4	14.3	6.7	5.9	5.0	4.3	3.5
E(7-7)	18.5	17.6	16.9	16.1	18.5	26.1	16.9	15.5	14.5	9.6
E(8-8)	27.2	26.1	25.1	23.9	27.1	49.6	39.7	29.7	26.8	22.0
E(9-9)	-4.8	-4.8	-4.7	-4.2	-8.8	-22.9	-0.7	13.2	2.3	2.4
E(X-X)	-46.0	-44.6	-43.1	-41.6	-41.9	-51.8	-59.7	-64.4	-49.1	-39.9

Expectation for insurance

Another decision the player can do is to take out insurance against a Blackjack in case the dealers first hand is an Ace. Expectation for insurance is named E(insurance).

DFH	2	3	4	5	6	7	8	9	X	A
E(insurance)										-7.4