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Best of Alan Krigman

Gaming Guru

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Everything you need to or should know about soft blackjack hands

20 August 2012

Soft hands at blackjack are those which total 13 or above when an ace is present and tabulated as 11. For instance, A-4 is a soft 15, A-2-5 is a soft 18, and A-9 is a soft 20. Technically, A-A could be viewed as a soft 12 but solid citizens normally treat it as a pair to be split; after a split, if one or both separated aces is topped with another ace, the new pair can be resplit on the increasingly rare occasions when it’s allowed, or the two aces add up to 12 with no further action permitted. Similarly, in principle, A-10 could be considered as a soft 21 – for example if a bettor wanted to double down; in practice, however, most casinos prohibit treating it other than as a blackjack.

Players can elect to stand, hit, or double-down on two-card soft hands. On those comprising three or more cards, doubling is banned so the choices are to stand or hit.

Assuming 10, J, Q, and K are considered equivalent, blackjack has 550 combinations of two player cards and one dealer upcard. Excluding players’ A-A and A-10, 80 combinations, with an overall probability of 9.49 percent, involve soft hands.

Basic Strategy is the set of options yielding the highest player “expectation” or, equivalently, the lowest house edge for each player hand and dealer upcard. Expectation is derived using the laws of probability, but can be pictured as the average gain or loss per dollar bet at the start of a round. Table 1 shows whether Basic Strategy is to double (D), hit (H), or stand (S) for soft situations and also whether the expectation when doing so is positive (+) or negative (-). Under Basic Strategy, 17.30 percent of all soft two-card hands call for doubling, 54.83 percent for hitting, and 27.87 percent for standing. Of the soft hands, 59.60 percent have positive expectation and 40.40 percent negative. Soft hands calling for doubling or standing always have positive expectation. Of the hits, 26.32 percent have positive expectation and 73.68 percent negative.

Table 1. Basic strategy for soft hands, and indication of whether expectation is positive (+) or negative (-)

soft
hand    upcard									
        2       3       4       5       6       7       8       9       10      A
A-2     H (+)   H (+)   H (+)   D (+)   D (+)   H (+)   H (+)   H (-)   H (-)   H (-)
A-3     H (+)   H (+)   H (+)   D (+)   D (+)   H (+)   H (+)   H (-)   H (-)   H (-)
A-4     H (-)   H (+)   D (+)   D (+)   D (+)   H (+)   H (-)   H (-)   H (-)   H (-)
A-5     H (-)   H (+)   D (+)   D (+)   D (+)   H (-)   H (-)   H (-)   H (-)   H (-)
A-6     H (+)   D (+)   D (+)   D (+)   D (+)   H (+)   H (-)   H (-)   H (-)   H (-)
A-7     S (+)   D (+)   D (+)   D (+)   D (+)   S (+)   S (+)   H (-)   H (-)   H (-)
A-8     S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)
A-9     S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)   S (+)

Everything else being equal, it’s wiser to follow than flout Basic Strategy. Everything else is not always equal, though. In particular, doubling requires blackjack aficionados to put more money at risk than they bet at the start of the round. Some folks may not have the temperament to do so under whatever circumstances pertain, or may not have sufficient bankroll to justify the consequences of a loss. Another consideration is that, on the average, hitting or standing on all but three of the hands in question will win more often – albeit bringing in less profit – than doubling. The three exceptions are A-6 vs 4, 5, or 6 when the second choice, hitting, is projected to have the same success rate as doubling. When such conditions become important to an individual, it’s helpful to know the next best alternative and how much the expectation decreases when passing on the opportunity to double down. The second best choice, H=hit or S=stand, and the cost in cents per dollar of initial bet are as shown for each of the 18 authorized Basic Strategy soft doubles in Table 2. Soft hands containing three differ from those made up of two cards primarily because doubling isn’t possible; the table provides guidance for what to do in this situation – namely stand on soft 18 versus 3, 4, 5, and 6 and hit on all the other totals calling for doubles in the two-card versions.

Table 2: Next best alternative to doubling and sacrifice in expectation per dollar bet

hand          H/S     ¢ per $     hand          H/S     ¢ per $     hand          H/S     ¢ per $
A,2 vs 5      H	      0.0029	  A,7 vs 3      S       2.8496	    A,7 vs 4      S	  6.6688
A,4 vs 4      H	      0.2025      A,4 vs 5      H       3.801       A,5 vs 6      H	  8.3256
A,5 vs 4      H	      1.9054      A,3 vs 6      H       4.4753      A,6 vs 5      H	  9.6952
A,3 vs 5      H	      2.0534      A,5 vs 5      H       5.3941      A,7 vs 5      S	  9.9637
A,2 vs 6      H	      2.3451      A,6 vs 4      H       6.1357      A,7 vs 6      S	  10.1259
A,6 vs 3      H	      2.7475      A,4 vs 6      H       6.3757      A,6 vs 6      H	  12.8964

Enquiring minds may want to know why it’s preferable to split A-A rather than treat the pair as a soft 12. The answer is in the substantially higher expectations for splitting than any of the other possibilities. The greatest difference is 49¢ on the dollar relative to either hitting or doubling against six-up. The least difference is 14¢ on the dollar relative to hitting against an ace. Having this information, if you still have to think about the options for A-A, maybe you should really think about whether to play blackjack. Or, as that poetic pundit, Sumner A Ingmark, proclaimed:

If what you can lose has you sweating it,
You probably shouldn’t be betting it.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.