PLAYING IT SMART by ALAN KRIGMAN

Why do blackjack players fret over 12 versus two-up but not 10-up

Blackjack buffs rarely balk at the Basic Strategy rule to hit 12 against a dealer's seven or higher. But, facing a two or three, many players pause and more than a few stand, wondering if "the book" is really right about hitting in these cases. Upcard aside, of course, a 10 could pop and bust the hand at once.

Standing on 12 won't lose immediately. But it can't push and only wins on a dealer's bust. Using the "infinite shoe" approximation, namely that each rank has a fixed one-out-of 13 probability, here are players' chances of various final totals when hitting 12:
• Four out of 13 (31 percent) to reach 13 through 16 by pulling ace through four, neither improving nor worsening and winning only when the dealer busts.
• One out of 13 (7.7 percent) each to draw five through nine and end with 17 through 21, respectively; that's five out of 13 (38 percent) of improving to a hope of a push or win when the dealer doesn't bust.
• Four out of 13 (31 percent) to lose immediately with a 10.

The outlook for a dealer "making a hand" with seven- through ace-up ranges from roughly 74 through 88 percent respectively. Given such poor player prospects, almost everybody takes the shot.

Solid citizens tend to err in underestimating the likelihood that dealers will make hands with nominally weak upcards, however. The chances, surprisingly, all exceed 50-50: two-up: 65 percent, three-up: 63 percent, four-up: 60 percent, and five- and six-up: 58 percent. Standing on 12 is therefore also tenuous under these conditions. Were dealer busts the only criterion, players would hit 12, and 13 through 16 as well, regardless of the upcard.

Other elements enter the picture, though. With hands from 12 to 16, the lower the total, the less apt a player is to go kablooie with a single hit. A 12 only busts with a 10, the chance being four out of 13 – 31 percent. A 13 is vulnerable to a nine or a 10, five out of 13 – 38 percent. A 14 bites the dust with eight, nine, or 10, lifting the probability to six out of 13 – 46 percent. A 15 will exceed 21 on seven, eight, nine, or 10, seven out of 13 – 54 percent. And a 16 will break on six, seven, eight, nine, or 10, eight out of 13 – 62 percent.

Between the extremes of either the dealer or the player landing in the soup, are the questions of where the respective hands are likely to finish if they don't bust. Differences here are small.

For dealers, chances fall as the ending total rises. For any upcard, probabilities are greatest to get to 17, and least to 21. The decline through 18, 19, and 20 is gradual except with six-up where an ace in the hole gives extra oomph to the chance of a 17.

Distinctions for players starting at 12 to 16 and finishing at 17 to 21 are even finer. With an infinite shoe, chances would be uniform. For example, pulling a five or nine to a 12, or a two or a six to a 15 all involve one card out of 13 – 7.7 percent.

With a real shoe, small deviations arise. Pretend the 12 is two-10. Two cards you don't want are gone from the reserve, lowering the chance you'll fail to improve (with two) or bust (with 10). And the density of fives through nines, cards you'd like, increases in what's left to be drawn. Conversely, if you have five-seven, two good cards are missing while the density of those that can hurt or won't yield improvements goes up.

Similarly with dealer upcards, a 12 is weaker if hit against five or six than two through four. The former would help if you still could draw them; the latter wouldn't hurt or help. All these factors go into forming Basic Strategy, which is to always hit 12 versus seven through ace, two, or three, and to hit two-10 against four-up in shoes smaller than eight decks if the dealer must stand on soft 17. How bad is flouting the book? Say you bet $10 in an eight-deck game and have two-10 versus two. It's an underdog either way. Standing loses an average of $2.95 and hitting $2.55. Is $0.40 theoretical savings worth the anxiety? Here's how the scribbler, Sumner A Ingmark, saw such situations.

While taking action's oft extolled,
And heroes, far from meek, are bold,
One's fate, though shaped, can't be controlled.

(c) 2008, ICON/Information Concepts Inc

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