Is The Blackjack 'Book' Right about Soft 17?

Most blackjack buffs know "the book" says always stand on a "hard" total of 17 -- such as 10-7 or 4-5-8, but never on "soft" 17 -- for instance A-6 or A-2-4. The rule for soft 17 is: a) double down when allowed on A-6 against a dealer's three through six; b) hit under all other conditions. Like every Basic Strategy decision, the soft 17 rule maximizes expected profit when bettors are favored, and minimizes expected loss when they're underdogs.

But soft 17 is one of those enigmas that leads skeptics to wonder "who wrote 'the book,' anyway." Particularly when the dealer shows a six or seven, and standing intuitively suggests a win or push, respectively. These very dilemmas arose on tables at which I played this past weekend, and the ensuing dialogs demonstrated the flaw of relying on instinct in a rigorous realm.

In the first case, a player signaled "stand" on A-6 against a six. The usual know-it-all (not me) asserted "you're supposed to double." The guy on the hot seat replied "if I stick and the dealer has an ace, I'll push. If I hit or double, I may not get better and might get worse." Peer pressure induced the fellow to recant and double. He drew an eight, fulfilling his prophesy of doom. But he won when the dealer broke, quod erat demonstrandum.

In the second example, a player asked to stand on A-3-3 against seven-up. This rankled several solid citizens at the table who grumbled it would change the flow of the cards and ruin the game for everyone else. The player in question, not to be browbeaten, stood at 17 "looking for a push." The dealer indeed flipped a 10. The player would have busted by following Basic Strategy -- the next cards in the shoe being an eight and a nine.

Notwithstanding specific outcomes, standing on soft 17 is poor blackjack. The underlying error is believing that 17 is a strong total. It isn't. A 17 wins more often than it loses only against six-up. Standing on hard 17 against anything else isn't good, but simply the best of a bad lot. This, since nine out of 13 possible draws bust, losing immediately, and only four enhance the total.

With soft 17, four draws out of 13 leave the total intact, four improve it, five reduce its value, and none cause it to break. Further, when soft 17 is hit rather than doubled, a draw that lowers the total leaves opportunity to go again when appropriate.

The weakness of standing on soft 17 against six or seven can be seen in light of the probabilities of various dealer finishes with these upcards. Chances are given in the accompanying chart.
Chance of various final dealer results (%)

	17	18	19	20	21	bust
six-up	16.6	10.6	10.6	10.2	9.7	42.3
seven-up	36.9	13.8	7.8	7.9	7.4	26.2

Against six-up, a total of 17 will win if the dealer busts (42.3 percent probability), push if the dealer finishes with 17 (16.6 percent), and lose when the dealer makes 18 through 21 (41.1 percent). Therefore, expectation is a gain of 42.3 - 41.1 = 1.2 percent -- 1.2 cents per dollar bet. Against seven-up, a total of 17 will win if the dealer busts (26.2 percent), push if the dealer finishes with 17 (36.9 percent), and lose when the dealer makes 18 through 21 (36.9 percent). Accordingly, expectation is a loss of 36.9 - 26.2 = 10.7 percent -- 10.7 cents per dollar bet.

Statistics for hitting and doubling soft 17 are trickier because probabilities of various player totals must also be considered. Overall, against six-up, expectation is to earn 13 cents per dollar of initial bet by hitting and 26 cents by doubling -- both beating the 1.2 cents by standing. Against seven-up, doubling projects a loss under a cent per dollar initial bet but hitting makes soft 17 a favorite, expecting to net over 5 cents on the dollar -- compared to losing 10.7 cents per dollar by standing.

So, who did write 'the book'? Not casino bosses, who'd earn more if nobody knew Basic Strategy. Not gamblers, who remember hunches that worked and forget those that failed. It was math mavens, who calculated precise probabilities for all the options.

The poet, Sumner A Ingmark, extolled such exactitude when he explained:

Having set the games in motion, the gambling master slumbers,
Knowing that casino outcomes will follow from the numbers.