Blackjack probabilities for the dealers final score

Card distribution in the shoe
Card 2 3 4 5 6 7 8 9 X A Sum
Count:{$ sgtb.cards_total $}
Distribution:{$ sgtb.cards_dist.card_2 $}%{$ sgtb.cards_dist.card_3 $}%{$ sgtb.cards_dist.card_4 $}%{$ sgtb.cards_dist.card_5 $}%{$ sgtb.cards_dist.card_6 $}%{$ sgtb.cards_dist.card_7 $}%{$ sgtb.cards_dist.card_8 $}%{$ sgtb.cards_dist.card_9 $}%{$ sgtb.cards_dist.card_10 $}%{$ sgtb.cards_dist.card_1 $}%

 

 

Probabilities of the dealers last hand under the condition of his first hand
DFH 2 3 4 5 6 7 8 9 X A
p(DFH) {$ sgtb.dlh.prob_DFH.dfh_2 $} {$ sgtb.dlh.prob_DFH.dfh_3 $} {$ sgtb.dlh.prob_DFH.dfh_4 $} {$ sgtb.dlh.prob_DFH.dfh_5 $} {$ sgtb.dlh.prob_DFH.dfh_6 $} {$ sgtb.dlh.prob_DFH.dfh_7 $} {$ sgtb.dlh.prob_DFH.dfh_8 $} {$ sgtb.dlh.prob_DFH.dfh_9 $} {$ sgtb.dlh.prob_DFH.dfh_10 $} {$ sgtb.dlh.prob_DFH.dfh_1 $} {$ sgtb.dlh.prob_DFH.dfh_0 $}
p(bust) {$ sgtb.dlh.prob_bust.dfh_2 $} {$ sgtb.dlh.prob_bust.dfh_3 $} {$ sgtb.dlh.prob_bust.dfh_4 $} {$ sgtb.dlh.prob_bust.dfh_5 $} {$ sgtb.dlh.prob_bust.dfh_6 $} {$ sgtb.dlh.prob_bust.dfh_7 $} {$ sgtb.dlh.prob_bust.dfh_8 $} {$ sgtb.dlh.prob_bust.dfh_9 $} {$ sgtb.dlh.prob_bust.dfh_10 $} {$ sgtb.dlh.prob_bust.dfh_1 $} {$ sgtb.dlh.prob_bust.dfh_0 $}
p(BJ) {$ sgtb.dlh.prob_BJ.dfh_2 $} {$ sgtb.dlh.prob_BJ.dfh_3 $} {$ sgtb.dlh.prob_BJ.dfh_4 $} {$ sgtb.dlh.prob_BJ.dfh_5 $} {$ sgtb.dlh.prob_BJ.dfh_6 $} {$ sgtb.dlh.prob_BJ.dfh_7 $} {$ sgtb.dlh.prob_BJ.dfh_8 $} {$ sgtb.dlh.prob_BJ.dfh_9 $} {$ sgtb.dlh.prob_BJ.dfh_10 $} {$ sgtb.dlh.prob_BJ.dfh_1 $} {$ sgtb.dlh.prob_BJ.dfh_0 $}
p(21) {$ sgtb.dlh.prob_21.dfh_2 $} {$ sgtb.dlh.prob_21.dfh_3 $} {$ sgtb.dlh.prob_21.dfh_4 $} {$ sgtb.dlh.prob_21.dfh_5 $} {$ sgtb.dlh.prob_21.dfh_6 $} {$ sgtb.dlh.prob_21.dfh_7 $} {$ sgtb.dlh.prob_21.dfh_8 $} {$ sgtb.dlh.prob_21.dfh_9 $} {$ sgtb.dlh.prob_21.dfh_10 $} {$ sgtb.dlh.prob_21.dfh_1 $} {$ sgtb.dlh.prob_21.dfh_0 $}
p(20) {$ sgtb.dlh.prob_20.dfh_2 $} {$ sgtb.dlh.prob_20.dfh_3 $} {$ sgtb.dlh.prob_20.dfh_4 $} {$ sgtb.dlh.prob_20.dfh_5 $} {$ sgtb.dlh.prob_20.dfh_6 $} {$ sgtb.dlh.prob_20.dfh_7 $} {$ sgtb.dlh.prob_20.dfh_8 $} {$ sgtb.dlh.prob_20.dfh_9 $} {$ sgtb.dlh.prob_20.dfh_10 $} {$ sgtb.dlh.prob_20.dfh_1 $} {$ sgtb.dlh.prob_20.dfh_0 $}
p(19) {$ sgtb.dlh.prob_19.dfh_2 $} {$ sgtb.dlh.prob_19.dfh_3 $} {$ sgtb.dlh.prob_19.dfh_4 $} {$ sgtb.dlh.prob_19.dfh_5 $} {$ sgtb.dlh.prob_19.dfh_6 $} {$ sgtb.dlh.prob_19.dfh_7 $} {$ sgtb.dlh.prob_19.dfh_8 $} {$ sgtb.dlh.prob_19.dfh_9 $} {$ sgtb.dlh.prob_19.dfh_10 $} {$ sgtb.dlh.prob_19.dfh_1 $} {$ sgtb.dlh.prob_19.dfh_0 $}
p(18) {$ sgtb.dlh.prob_18.dfh_2 $} {$ sgtb.dlh.prob_18.dfh_3 $} {$ sgtb.dlh.prob_18.dfh_4 $} {$ sgtb.dlh.prob_18.dfh_5 $} {$ sgtb.dlh.prob_18.dfh_6 $} {$ sgtb.dlh.prob_18.dfh_7 $} {$ sgtb.dlh.prob_18.dfh_8 $} {$ sgtb.dlh.prob_18.dfh_9 $} {$ sgtb.dlh.prob_18.dfh_10 $} {$ sgtb.dlh.prob_18.dfh_1 $} {$ sgtb.dlh.prob_18.dfh_0 $}
p(17) {$ sgtb.dlh.prob_17.dfh_2 $} {$ sgtb.dlh.prob_17.dfh_3 $} {$ sgtb.dlh.prob_17.dfh_4 $} {$ sgtb.dlh.prob_17.dfh_5 $} {$ sgtb.dlh.prob_17.dfh_6 $} {$ sgtb.dlh.prob_17.dfh_7 $} {$ sgtb.dlh.prob_17.dfh_8 $} {$ sgtb.dlh.prob_17.dfh_9 $} {$ sgtb.dlh.prob_17.dfh_10 $} {$ sgtb.dlh.prob_17.dfh_1 $} {$ sgtb.dlh.prob_17.dfh_0 $}

This chart shows the probabilities of the dealers last hand under the condition of his first hand. While playing Blackjack, the player sees the dealers first hand. Using this information is fundamentally important! If the Blackjack dealers first card is low, say 2 through 6, his probability for busting is high. In these situations the player shall buy carfully and count on the dealers final score to bust.

On the other side, when the Blackjack dealers first hand is 7 throught Ace, his probability of achieving a good score is high. In these situations the player shall buy more courageous, even though his probability to bust is higher.

A chart about the probabilities for the dealers final score does not directly give the player any hint about the correct strategy. But by looking at this chart, the player can much better understand the expectation values as shown on the other charts.

Compare this table with the probabilities for the players final score.

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