Which Blackjack Hands Are Strong, and Which Weak?

10 April 2002

By Alan Krigman

Blackjack buffs undergo an epiphany when they realize that the goal of the game isn't to get close to - without exceeding - 21, but to beat the dealer. Most come to this revelation understanding that success lies in accounting both for their own total and the dealer's upcard in deciding how to play a hand.

How, indeed? Intuition helps when you have 19 or 20. Stand, regardless of the upcard. Similarly when you have a hard total of five. Hit, irrespective of the dealer's outlook. What about eight-eight versus nine? A weak position. Hitting is risky since eight of 13 ranks put you over 21 and lose instantly. Not all the remaining five ranks are exactly show-stoppers. Standing leaves you vulnerable to any dealer non-bust finish. And a lot of seasoned players hesitate to split the pair, thinking that eight is a poor jump-off against nine, so why willingly do it twice?

Basic Strategy gives the "correct" decisions for all combinations of player totals and dealer upcards. "Correct," meaning the greatest statistically expected profit when solid citizens are favored and least theoretical loss when they're the underdogs. Deducing Basic Strategy from the laws of probability is not an elementary task. Fortunately, the gurus have done the math, and cast the results into a set of rules almost anybody can learn, and which are not exactly a secret the bosses are trying to hide.

Many players know Basic Strategy perfectly, yet miss the idea that some situations are inherently strong and others weak. Most recognize they're solid with something like 20 against four-up, and need two miracles - a gift for themselves and garbage for the dealer - to win with a total such as hard 15 versus nine. But, few bettors could tell you whether they have an edge with much else. This information is given in the accompanying table.

Dealer upcards for which players have the advantage with various starting hands
Hard Totals	Favorable Upcards	Pairs	Favorable Upcards
5	none	A-A	all
6	none	2-2	4 through 7
7	6	3-3	4 through 7
8	3 through 7	4-4	3 through 7
9	2 through 8	6-6	5 and 6
10	all	7-7	4 through 6
11	all	8-8	2 through 7
12	none	9-9	2 through 8
13	none
14	none	Soft Hands	Favorable Upcards
15	none
16	none	A-2	2 through 8
17	6	A-3	2 through 8
18	2 through 8	A-4	3 through 7
19	all	A-5	3 through 6
20	all	A-6	2 through 7
21	all	A-7	2 through 8

 

The list is for multiple decks, dealer stands on soft 17, soft doubles are permitted, doubling is allowed after splits, and players follow strict Basic Strategy. Data for ace- and 10-up are for "playable" hands, in which dealer doesn't have blackjack.

Also of interest are the best and worst upcards for each player hand. In general, sixes are the most desirable initial dealer cards for players, promising the greatest gain in favorable situations and the least pain under adverse conditions. Here are the exceptions: best for players is seven-up with hard 18, hard 19, and soft 18; eight-up with hard 20; and 10?up with hard 21. Conversely, in the majority of cases, 10s are the most dangerous upcards for players to face. Exceptions are: worst for players is ace-up for hard 17, nine-up for hard 18, and two-up for hard 21.

A few properly-played situations are marginal. Hits on ace-six against two and ace?five against three, and splits of twos against seven have positive expectations but amounts are below $0.10 per $10 bet at the start of the round. Hits on ace-four versus two and ace-five versus seven, as well as splits of twos against three and sixes against four have negative expectations, but also with magnitudes under $0.10 per $10 opening bet.

Anyone can win at blackjack with a series of 20s against stiffs like fives and sixes. And, who's to knock making money? But, much of the intrinsic pleasure in the game comes from starting with junk, playing proficiently, and having results mesh like well?oiled gears assembled by skilled machinists. Or, as the poet laureate of the pits, Sumner A Ingmark, optimistically observed:

Watching random elements fall neatly into place,
Makes you think a guiding spirit predisposed the race.