Blackjack expectations for splitting a pair of cards

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 $}%

 

 

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 $}

This chart shows the expectations when the player has to decide whether to  split  a pair of cards, or to  continue  with the strategies for buy versus stay or in case of two fives for double versus buy.

Expectations for splitting versus buying or doubling are named E(A-A), E(2-2) through E(X-X).

The benefit for splitting is twofold: First, splitting two cards which give a bad score can be advantageous. Say, the players hand is 8-8, which gives him a bad score of 16. Buying on 16 is risky too, because the probability for busting is high. Therefore splitting a pair of 8-8, can be advantageous to the player. The drawback for splitting is, that the player must bring in another stake of the same amount. If the dealers probability for achieving a high score is big enough, doubling the stake can be more disadvantageous than the advantage gained by the probability of getting a better final score. So there is a trade off for these two factors. In case, players can split cards and have the possibility to split the stake as well, consider the strategy for teammate splitting. If the dealers probability for busting his final score is high, bringing in another stake is definitely advantageous.

Example: If the player were to split a pair of 8-8 against the dealers 6, he would multiply his stake in approximately {$sgtb.split_default.exp_8.dfh_6$} additional bets out of each one hundred games.

After the player splitted two cards, each bet shall be played according to the strategy for buy versus stay. If it is allowed to double after split, the player shall continue with the strategy for double versus buy.