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 | 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 $}% |
Using this calculator, one can adjust the card distribution in the shoe and determine the best strategy according to the resulting expectation values.
| DFH | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A | Total |
|---|---|---|---|---|---|---|---|---|---|---|---|
| E(total) | {$ 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 $} |
Depending on the Total Expectation, the player shall vary the amount of his stake. If the total expectation is below zero he shall place minimum stakes or skip playing. If it is above zero he shall place high stakes as the theory says that in these circumstances the player has a moderate advantage over the dealer.
| DFH | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
|---|---|---|---|---|---|---|---|---|---|---|
| E(8/18) | {$ 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 $} |
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| DFH | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
|---|---|---|---|---|---|---|---|---|---|---|
| E(11) | {$ 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 $} |
More on this chart...
| DFH | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
|---|---|---|---|---|---|---|---|---|---|---|
| E(2-2) | {$ 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 $} |
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| DFH | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
|---|---|---|---|---|---|---|---|---|---|---|
| E(insurance) | – | – | – | – | – | – | – | – | – | {$ sgtb.expect_insure $} |
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