What is the correct basic strategy for single deck Blackjack?

The following basic strategy is for single deck games without DAS (double-after-splits).

+– Player’s hand
|
| dealer dealer
| |-might bust-||-might stand-|
V 2 3 4 5 6 7 8 9 X A <——- dealer’s upcard
—+——————————-
XX | S S S S S S S S S S never, ever, ever split
99 | PS PS PS PS PS S PS ps s s split if (d <= 9), except 7
88 | Ps Ps Ps Ps Ps Ph ph ph ph ph always split
77 | ps ps Ps Ps Ps ph h h s h split if (d <= 7), stand against 10
66 | ph ps ps Ps ps h h h h h split if (d <= 6) 55 | DH DH DH DH DH DH DH DH H H never split, treat like hard 10 44 | h H H DH DH H h h h h never split, double against 5, 6 33 | h h Ph PH PH ph h h h h split if (d >= 4) and (d <= 7) 22 | h ph Ph PH PH ph h h h h split if (d >= 3) and (d <= 7) AA | PH PH PH PD PD PH PH Ph Ph Ph always split —+——————————- A9 | S S S S S S S S S S always stand A8 | S S S S *DS S S S S S double against a 6 A7 | S DS DS DS DS S S h h h* double 3-6, hit against 9, 10, A A6 | DH DH DH DH DH H h h h h double low, hit high A5 | h h DH DH DH h h h h h \ A4 | h H DH DH DH H h h h h \ double against 4,5,6 A3 | H H DH DH DH H H h h h / A2 | H H DH DH DH H H h h h / —+——————————- 21 | S S S S S S S S S S always stand 20 | S S S S S S S S S S always stand 19 | S S S S S S S S S S always stand 18 | S S S S S S S s s s always stand 17 | s s s s s s s s s s always stand on HARD 17 or above 16 | s s s s s h h h h h \ 15 | s s s s s h h h h h \ 14 | s s s s s h h h h h > hit if dealer might stand,
13 | s s s s s h h h h h / stand if dealer might bust
12 | h h s s s h h h h h / (special case against 2, 3)

11 | D D D D D D D D D D always double
10 | D D D D D D D D H H double if (d < 10)
9 | DH DH DH DH DH H H h h h double if dealer might bust
8 | h H H DH DH H h h h h double only against 5, 6
7 | h h h H H h h h h h
6 | h h h H H h h h h h (4-2)
5 | h h h H H h h h h h (3-2)
4 | h h h H H h h h h h (2-2 pair if no more splitting allowed)
—+——————————-
S=stand H=hit D=double P=pair(split)
DH= double if allowed, otherwise hit
DS= double if allowed, otherwise stand
[uppercase] = ‘strong’ hand, favorable to player
[lowercase] = ‘weak’ hand, favorable to house

(*) notes:
Playing A7 against dealer’s ace:
hitting gains 4.08% if dealer must hit on soft 17
standing gains 0.74% if dealer must stand on soft 17

Playing A8 against dealer’s 6:
doubling gains 1.96% if dealer must hit on soft 17
doubling gains 0.03% if dealer must stand on soft 17
(this rule may be ignored to simplify the strategy)

Why are single deck games better than multi-deck games?

There are some surface differences, such as single and double deck usually being hand-held, while four or more decks are dealt from a shoe, but there are fundamental mathematical differences too.

Single deck blackjack is usually better than multiple deck blackjack for card counters, basic strategists, and the clueless. Additional decks make busts less likely, since one can draw to hands like 2,2,2,2,2,2,2,2,2 (for 18) which are improbable/impossible in single deck. Busting less often helps the dealer’s hand more than yours, since the dealer is forced by the rigid rules to hit more often than you. Blackjacks are also less frequent, which is bad since you get paid 3 to 2 for those. All in all, multiple decks will cost a basic strategist nearly 0.5% in advantage, which is more than all but the very best package of favorable extra rules will give you. This was an intuitive explanation; a complete mathematically sound (albeit huge) proof can be generated by a combinatorial analysis program.

Card counters face the additional problem that the count is less volatile with multiple decks and hence offers less frequent opportunities for large favorable bets. Consider the difference between an urn with 1 black and 1 white marble versus an urn with 100 black and 100 white marbles. Draw half the marbles: what is the probability that all the remaining marbles are white? In the 1 and 1 case, there is a 1 in 2 chance. In the 100 and 100 case, there is only a 1 in 100,891,344,545,564,193,334,812,497,256 chance!

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