An Exception to the 16 vs 10 Rule in Blackjack

The worst starting hand in blackjack is hard 16 versus dealer 10. If the 16 is a pair of eights and you split them, expected loss per dollar of your original bet is roughly $0.48. But, say the 16 isn't a pair, or - if it is - you won't split because you'd rather believe the blather about assuming covert cards to be 10s than trust the laws of probability governing the entire known universe. Then, hitting leads to a statistical loss around $0.53 per dollar bet while standing raises the rout to $0.54. These values ignore dealer blackjacks, where decisions are irrelevant.

Expected loss figures underlie basic strategy for the hand. In decreasing order of preference, the following tactics soften the blow in this adverse situation. None is especially good, but each is marginally less onerous than the next.
1) Split the 16 if it's a pair of eights
2) Surrender if the option is available
3) Hit
4) Stand

Life would be easier but less fun if rules never had exceptions. For one thing, gambling gurus would rapidly run out of new notions with which to edify eager solid citizens. For another, know-it-alls who really do wouldn't have smug rejoinders to hurl at know-it-alls who really don't.

There happens to be a 16 versus 10 exception in blackjack. If you've drawn at least once, so your 16 comprises three or more cards, stand rather than hit. I won't mire you with the math since we're already mincing meat worth under a statistical cent on a real dollar. But here's an intuitive explanation.

Imagine a two-card non-pair hard 16. Your hand must be nine-seven or 10-six. Either way, three cards are no longer available to be drawn - your hand and the 10-up - all of which would have busted you. This biases what's left slightly toward hitting.

Imagine a three-card hard 16. It must be in one of two classes:
o Two cards which would have caused you to bust and one which would improve your chances. Illustrations include nine-six-ace, eight-seven-ace, eight-six-two, and seven-six-three.
o One card which would have caused you to bust and two which would improve your chances. Examples are 10-five-ace, nine-four-three, eight-four-four, and seven-five-four.

Hands of over three cards may also total 16. These may have as many as two cards which would cause you to bust and two or more which would improve your chances - such as seven-six-two-ace. They may also have only a single instant loser, or none; examples are nine-four-two-ace and five-four-four-three, respectively. Eliminating at least one card which would improve the hand, and no more than three that would bust it, raises the proportion and corresponding probability of breakers to desirable cards still to be drawn. This biases the shoe slightly toward standing.

The effect is weak, especially for three-card hands with only one in the range from ace to five. Also, a proper analysis would account for differences in withdrawing fives and fours rather than aces and deuces as well as implications of unavailable cards on the dealer's final result. But the expectation gap between hitting and standing on two-card 16 versus 10 starts small, so a minor probability shift reverses the optimum decision. Even taking away one coveted card along with three breakers suffices to make standing statistically better than hitting. And the influence of removal becomes stronger the greater the proportion of helpful to harmful cards absent from the remaining shoe.

So, what of bettors who hit 16 against 10 with two-card hands but stand otherwise? Maybe they just have cold feet. Or a hunch that a biggie is due. A few may even know what they're doing. As the poet, Sumner A Ingmark, a counselor of caution who normally knows what he's eschewing, quaintly quipped:

Sometimes contrarians,
Aren't just barbarians.