Soft 18 versus Nine through Ace: Make the Best of a Bad Lot

Basic strategy for blackjack says hit soft 18 - ace-seven - against dealer upcards of nine, 10, and ace. However, the apostate often stand on this hand. And more than a few believers wonder whether the bozos who wrote "the book" made a boo-boo.

Soft 18 versus a high upcard is enigmatic because no possibility is propitious and dangers dog every decision. The optimum option in such cases is the least objectionable. That is, the option which the laws of probability indicate should lose the smallest fraction of the money out on this hand over an extended period.

Expectations for soft 18 versus nine-, 10-, and ace-up are shown below for each player option. Figures assume the dealer does not have a blackjack. Values are expected losses on the hand for every $100 bet at the beginning of a round in a six-deck game.

upcard	hit	stand	double	surrender
9	$ 9.85	$18.26	$28.48	$50.00
10	14.29	17.96	34.27	50.00
ace	9.53	10.03	36.23	50.00

As an example of interpreting the data, hitting soft 18 versus a 10-up yields an expected loss of $14.29 for every $100 bet before the deal; standing raises this to $17.96.

The indicated expectations are all losses, confirming that soft 18 is always an underdog against nine, 10, or ace. They also show that hitting minimizes the projected penalty, with expectation worsening successively for standing, doubling, and surrendering.

Solid citizens occasionally double down on soft 18 against an ace. Their logic is as follows: If the dealer has a blackjack, the second bet will be returned so doubling won't matter. If the dealer doesn't have blackjack, the player has a good chance to win by drawing a single card, since only six of the 13 possible ranks will hurt while three will help and four will leave a reasonably strong 18 versus an impotent ace.

The expectations, which presume the dealer doesn't have blackjack, expose the flaw in this fuzzy-headed figuring. Ignoring dealer blackjacks, hitting soft 17 against ace anticipates a loss of only $9.53 per $100 initial bet. Standing increases the penalty by a modest $0.50, to $10.03. However, doubling more than triples the damages, to $36.23.

The dealer has roughly 31 percent chance of a blackjack with an ace-up, making the double irrelevant. The problem is that with no blackjack, the chance a dealer will bust starting with an ace is low - less than that with any other upcard. And, the chance is higher that a dealer playing the ace will beat rather than push or lose to an 18. The following list shows probabilities of each dealer final result when blackjack is eliminated in a six-deck game, assuming no knowledge of the player's hand.

result	probability
17	18.81%
18	18.92
19	18.89
20	18.94
21	7.74
bust	16.70

These values prove 18 is not "reasonably strong" against an ace. Players only win if the dealer busts or finishes with 17; chances this will happen are (16.70 + 18.81) or 35.51 percent. Players lose if the dealer ends with 19, 20, or 21; chances of this are (18.89 + 18.94 + 7.74) or 45.57 percent. And players push if the dealer pulls 18; chances here are 18.92 percent. Players should therefore lose (45.57 - 35.51) or roughly 10 percent more than they win with 18 versus ace-up. And, by doubling, there's six ways for players to be below 18 for every three to be above it.

Of course, anything can turn out well or badly in a particular instance. And those who want to believe gambling is all luck are tough to sway with anything as droll as facts and figures. Especially facts and figures involving ethereal chances going into a situation rather than hard cash exchanged afterwards. As Sumner A Ingmark, droll drafter of ethereal rhyme, once said:

Some hands you're dealt are weak,
And others start out strong,
The first destroy the meek,
The rest can still go wrong.