Blackjack expectations for buy versus stay

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 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 $}

This chart shows the expectations when the player has to decide whether to  buy  or to  stay . A positive expectation tells the player, how many more times in one hundered games he will multiply his stake, rather than losing it, when he buys instead of staying.

Expectations are named E(8/18) and E(7/17) for soft-hands. For instance, a 6 plus an Ace is named soft-hand. On soft-hands 9/19 and above, the player shall always stay. On soft-hands 6/16 and below, the player shall always buy, since he can't bust anyway.

Expectations for hard-hands are named E(16) through E(12). With a hard-hand of 11 and below the player shall always buy or, if the strategy qualifies for it, double. With a hard-hand of 17 and above, the player shall always stay, as the risk for busting is too high.

Example: If the player were to buy on 16 against the dealers 7, he would multiply his stake in approximately {$sgtb.buy_stay.exp_16.dfh_7$} additional bets out of each one hundred games.

Decide whether to double or to buy.