More than the Blackjack Basic Strategy

The best Blackjack Strategy is based on probability calculations of the game. For each non fundamental decision a player can do, he must evaluate whether to buy or to stay, to double or to buy, or to split. This strategy can be determined analytically for each possible card distribution in the shoe. For a reshuffled shoe we name this the Basic Blackjack Strategy. Depending on the card distribution in the shoe, this strategy however varies. It also does not give the player any hint, when to place a low or a high stake.

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 $}%

Using this calculator, one can adjust the card distribution in the shoe and determine the best strategy according to the resulting expectation values.

Total expectation depending on the current card distribution in the shoe
DFH 2 3 4 5 6 7 8 9 X A Total
E(total) {$ sgtb.total_expectation.dfh_2 $} {$ sgtb.total_expectation.dfh_3 $} {$ sgtb.total_expectation.dfh_4 $} {$ sgtb.total_expectation.dfh_5 $} {$ sgtb.total_expectation.dfh_6 $} {$ sgtb.total_expectation.dfh_7 $} {$ sgtb.total_expectation.dfh_8 $} {$ sgtb.total_expectation.dfh_9 $} {$ sgtb.total_expectation.dfh_10 $} {$ sgtb.total_expectation.dfh_1 $} {$ sgtb.total_expectation.dfh_0 $}

Depending on the Total Expectation, the player shall vary the amount of his stake. If the total expectation is  below zero  he shall place minimum stakes or skip playing. If it is  above zero  he shall place high stakes as the theory says that in these circumstances the player has a moderate advantage over the dealer.

Expectations when the player has to decide whether to buy or to stay
DFH 2 3 4 5 6 7 8 9 X A
E(8/18) {$ sgtb.buy_stay.exp_18.dfh_2 $} {$ sgtb.buy_stay.exp_18.dfh_3 $} {$ sgtb.buy_stay.exp_18.dfh_4 $} {$ sgtb.buy_stay.exp_18.dfh_5 $} {$ sgtb.buy_stay.exp_18.dfh_6 $} {$ sgtb.buy_stay.exp_18.dfh_7 $} {$ sgtb.buy_stay.exp_18.dfh_8 $} {$ sgtb.buy_stay.exp_18.dfh_9 $} {$ sgtb.buy_stay.exp_18.dfh_10 $} {$ sgtb.buy_stay.exp_18.dfh_1 $}
E(7/17) {$ sgtb.buy_stay.exp_17.dfh_2 $} {$ sgtb.buy_stay.exp_17.dfh_3 $} {$ sgtb.buy_stay.exp_17.dfh_4 $} {$ sgtb.buy_stay.exp_17.dfh_5 $} {$ sgtb.buy_stay.exp_17.dfh_6 $} {$ sgtb.buy_stay.exp_17.dfh_7 $} {$ sgtb.buy_stay.exp_17.dfh_8 $} {$ sgtb.buy_stay.exp_17.dfh_9 $} {$ sgtb.buy_stay.exp_17.dfh_10 $} {$ sgtb.buy_stay.exp_17.dfh_1 $}
E(16) {$ sgtb.buy_stay.exp_16.dfh_2 $} {$ sgtb.buy_stay.exp_16.dfh_3 $} {$ sgtb.buy_stay.exp_16.dfh_4 $} {$ sgtb.buy_stay.exp_16.dfh_5 $} {$ sgtb.buy_stay.exp_16.dfh_6 $} {$ sgtb.buy_stay.exp_16.dfh_7 $} {$ sgtb.buy_stay.exp_16.dfh_8 $} {$ sgtb.buy_stay.exp_16.dfh_9 $} {$ sgtb.buy_stay.exp_16.dfh_10 $} {$ sgtb.buy_stay.exp_16.dfh_1 $}
E(15) {$ sgtb.buy_stay.exp_15.dfh_2 $} {$ sgtb.buy_stay.exp_15.dfh_3 $} {$ sgtb.buy_stay.exp_15.dfh_4 $} {$ sgtb.buy_stay.exp_15.dfh_5 $} {$ sgtb.buy_stay.exp_15.dfh_6 $} {$ sgtb.buy_stay.exp_15.dfh_7 $} {$ sgtb.buy_stay.exp_15.dfh_8 $} {$ sgtb.buy_stay.exp_15.dfh_9 $} {$ sgtb.buy_stay.exp_15.dfh_10 $} {$ sgtb.buy_stay.exp_15.dfh_1 $}
E(14) {$ sgtb.buy_stay.exp_14.dfh_2 $} {$ sgtb.buy_stay.exp_14.dfh_3 $} {$ sgtb.buy_stay.exp_14.dfh_4 $} {$ sgtb.buy_stay.exp_14.dfh_5 $} {$ sgtb.buy_stay.exp_14.dfh_6 $} {$ sgtb.buy_stay.exp_14.dfh_7 $} {$ sgtb.buy_stay.exp_14.dfh_8 $} {$ sgtb.buy_stay.exp_14.dfh_9 $} {$ sgtb.buy_stay.exp_14.dfh_10 $} {$ sgtb.buy_stay.exp_14.dfh_1 $}
E(13) {$ sgtb.buy_stay.exp_13.dfh_2 $} {$ sgtb.buy_stay.exp_13.dfh_3 $} {$ sgtb.buy_stay.exp_13.dfh_4 $} {$ sgtb.buy_stay.exp_13.dfh_5 $} {$ sgtb.buy_stay.exp_13.dfh_6 $} {$ sgtb.buy_stay.exp_13.dfh_7 $} {$ sgtb.buy_stay.exp_13.dfh_8 $} {$ sgtb.buy_stay.exp_13.dfh_9 $} {$ sgtb.buy_stay.exp_13.dfh_10 $} {$ sgtb.buy_stay.exp_13.dfh_1 $}
E(12) {$ sgtb.buy_stay.exp_12.dfh_2 $} {$ sgtb.buy_stay.exp_12.dfh_3 $} {$ sgtb.buy_stay.exp_12.dfh_4 $} {$ sgtb.buy_stay.exp_12.dfh_5 $} {$ sgtb.buy_stay.exp_12.dfh_6 $} {$ sgtb.buy_stay.exp_12.dfh_7 $} {$ sgtb.buy_stay.exp_12.dfh_8 $} {$ sgtb.buy_stay.exp_12.dfh_9 $} {$ sgtb.buy_stay.exp_12.dfh_10 $} {$ sgtb.buy_stay.exp_12.dfh_1 $}

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Expectations whether the player shall double or buy the next card
DFH 2 3 4 5 6 7 8 9 X A
E(11) {$ sgtb.double_buy.exp_11.dfh_2 $} {$ sgtb.double_buy.exp_11.dfh_3 $} {$ sgtb.double_buy.exp_11.dfh_4 $} {$ sgtb.double_buy.exp_11.dfh_5 $} {$ sgtb.double_buy.exp_11.dfh_6 $} {$ sgtb.double_buy.exp_11.dfh_7 $} {$ sgtb.double_buy.exp_11.dfh_8 $} {$ sgtb.double_buy.exp_11.dfh_9 $} {$ sgtb.double_buy.exp_11.dfh_10 $} {$ sgtb.double_buy.exp_11.dfh_1 $}
E(10) {$ sgtb.double_buy.exp_10.dfh_2 $} {$ sgtb.double_buy.exp_10.dfh_3 $} {$ sgtb.double_buy.exp_10.dfh_4 $} {$ sgtb.double_buy.exp_10.dfh_5 $} {$ sgtb.double_buy.exp_10.dfh_6 $} {$ sgtb.double_buy.exp_10.dfh_7 $} {$ sgtb.double_buy.exp_10.dfh_8 $} {$ sgtb.double_buy.exp_10.dfh_9 $} {$ sgtb.double_buy.exp_10.dfh_10 $} {$ sgtb.double_buy.exp_10.dfh_1 $}
E(9) {$ sgtb.double_buy.exp_9.dfh_2 $} {$ sgtb.double_buy.exp_9.dfh_3 $} {$ sgtb.double_buy.exp_9.dfh_4 $} {$ sgtb.double_buy.exp_9.dfh_5 $} {$ sgtb.double_buy.exp_9.dfh_6 $} {$ sgtb.double_buy.exp_9.dfh_7 $} {$ sgtb.double_buy.exp_9.dfh_8 $} {$ sgtb.double_buy.exp_9.dfh_9 $} {$ sgtb.double_buy.exp_9.dfh_10 $} {$ sgtb.double_buy.exp_9.dfh_1 $}

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Expectations whether the player shall split a pair of cards or continue as usual
DFH 2 3 4 5 6 7 8 9 X A
E(2-2) {$ sgtb.split_default.exp_2.dfh_2 $} {$ sgtb.split_default.exp_2.dfh_3 $} {$ sgtb.split_default.exp_2.dfh_4 $} {$ sgtb.split_default.exp_2.dfh_5 $} {$ sgtb.split_default.exp_2.dfh_6 $} {$ sgtb.split_default.exp_2.dfh_7 $} {$ sgtb.split_default.exp_2.dfh_8 $} {$ sgtb.split_default.exp_2.dfh_9 $} {$ sgtb.split_default.exp_2.dfh_10 $} {$ sgtb.split_default.exp_2.dfh_1 $}
E(3-3) {$ sgtb.split_default.exp_3.dfh_2 $} {$ sgtb.split_default.exp_3.dfh_3 $} {$ sgtb.split_default.exp_3.dfh_4 $} {$ sgtb.split_default.exp_3.dfh_5 $} {$ sgtb.split_default.exp_3.dfh_6 $} {$ sgtb.split_default.exp_3.dfh_7 $} {$ sgtb.split_default.exp_3.dfh_8 $} {$ sgtb.split_default.exp_3.dfh_9 $} {$ sgtb.split_default.exp_3.dfh_10 $} {$ sgtb.split_default.exp_3.dfh_1 $}
E(4-4) {$ sgtb.split_default.exp_4.dfh_2 $} {$ sgtb.split_default.exp_4.dfh_3 $} {$ sgtb.split_default.exp_4.dfh_4 $} {$ sgtb.split_default.exp_4.dfh_5 $} {$ sgtb.split_default.exp_4.dfh_6 $} {$ sgtb.split_default.exp_4.dfh_7 $} {$ sgtb.split_default.exp_4.dfh_8 $} {$ sgtb.split_default.exp_4.dfh_9 $} {$ sgtb.split_default.exp_4.dfh_10 $} {$ sgtb.split_default.exp_4.dfh_1 $}
E(5-5) {$ sgtb.split_default.exp_5.dfh_2 $} {$ sgtb.split_default.exp_5.dfh_3 $} {$ sgtb.split_default.exp_5.dfh_4 $} {$ sgtb.split_default.exp_5.dfh_5 $} {$ sgtb.split_default.exp_5.dfh_6 $} {$ sgtb.split_default.exp_5.dfh_7 $} {$ sgtb.split_default.exp_5.dfh_8 $} {$ sgtb.split_default.exp_5.dfh_9 $} {$ sgtb.split_default.exp_5.dfh_10 $} {$ sgtb.split_default.exp_5.dfh_1 $}
E(6-6) {$ sgtb.split_default.exp_6.dfh_2 $} {$ sgtb.split_default.exp_6.dfh_3 $} {$ sgtb.split_default.exp_6.dfh_4 $} {$ sgtb.split_default.exp_6.dfh_5 $} {$ sgtb.split_default.exp_6.dfh_6 $} {$ sgtb.split_default.exp_6.dfh_7 $} {$ sgtb.split_default.exp_6.dfh_8 $} {$ sgtb.split_default.exp_6.dfh_9 $} {$ sgtb.split_default.exp_6.dfh_10 $} {$ sgtb.split_default.exp_6.dfh_1 $}
E(7-7) {$ sgtb.split_default.exp_7.dfh_2 $} {$ sgtb.split_default.exp_7.dfh_3 $} {$ sgtb.split_default.exp_7.dfh_4 $} {$ sgtb.split_default.exp_7.dfh_5 $} {$ sgtb.split_default.exp_7.dfh_6 $} {$ sgtb.split_default.exp_7.dfh_7 $} {$ sgtb.split_default.exp_7.dfh_8 $} {$ sgtb.split_default.exp_7.dfh_9 $} {$ sgtb.split_default.exp_7.dfh_10 $} {$ sgtb.split_default.exp_7.dfh_1 $}
E(8-8) {$ sgtb.split_default.exp_8.dfh_2 $} {$ sgtb.split_default.exp_8.dfh_3 $} {$ sgtb.split_default.exp_8.dfh_4 $} {$ sgtb.split_default.exp_8.dfh_5 $} {$ sgtb.split_default.exp_8.dfh_6 $} {$ sgtb.split_default.exp_8.dfh_7 $} {$ sgtb.split_default.exp_8.dfh_8 $} {$ sgtb.split_default.exp_8.dfh_9 $} {$ sgtb.split_default.exp_8.dfh_10 $} {$ sgtb.split_default.exp_8.dfh_1 $}
E(9-9) {$ sgtb.split_default.exp_9.dfh_2 $} {$ sgtb.split_default.exp_9.dfh_3 $} {$ sgtb.split_default.exp_9.dfh_4 $} {$ sgtb.split_default.exp_9.dfh_5 $} {$ sgtb.split_default.exp_9.dfh_6 $} {$ sgtb.split_default.exp_9.dfh_7 $} {$ sgtb.split_default.exp_9.dfh_8 $} {$ sgtb.split_default.exp_9.dfh_9 $} {$ sgtb.split_default.exp_9.dfh_10 $} {$ sgtb.split_default.exp_9.dfh_1 $}
E(X-X) {$ sgtb.split_default.exp_X.dfh_2 $} {$ sgtb.split_default.exp_X.dfh_3 $} {$ sgtb.split_default.exp_X.dfh_4 $} {$ sgtb.split_default.exp_X.dfh_5 $} {$ sgtb.split_default.exp_X.dfh_6 $} {$ sgtb.split_default.exp_X.dfh_7 $} {$ sgtb.split_default.exp_X.dfh_8 $} {$ sgtb.split_default.exp_X.dfh_9 $} {$ sgtb.split_default.exp_X.dfh_10 $} {$ sgtb.split_default.exp_X.dfh_1 $}
E(A-A) {$ sgtb.split_default.exp_A.dfh_2 $} {$ sgtb.split_default.exp_A.dfh_3 $} {$ sgtb.split_default.exp_A.dfh_4 $} {$ sgtb.split_default.exp_A.dfh_5 $} {$ sgtb.split_default.exp_A.dfh_6 $} {$ sgtb.split_default.exp_A.dfh_7 $} {$ sgtb.split_default.exp_A.dfh_8 $} {$ sgtb.split_default.exp_A.dfh_9 $} {$ sgtb.split_default.exp_A.dfh_10 $} {$ sgtb.split_default.exp_A.dfh_1 $}

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Expectation whether the player shall insure against a dealers Blackjack or not
DFH 2 3 4 5 6 7 8 9 X A
E(insurance) {$ sgtb.expect_insure $}

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