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# Why You Should Do What with 11 against 10 or Ace in Blackjack

22 March 2004

A two-card 11 is a strong blackjack hand. A dealer's 10 or ace is a formidable upcard. What happens when both occur concurrently?

Against 10, the definitive version of "The Book" says to double. With ace, most \$0.25 Basic Strategy charts simply say hit. The \$100 rule is: hit in the preponderance of cases when dealers must stand on soft 17 and shoes a) include three or more decks, or b) have two decks and the 11 is a 9-2 or 8-3; otherwise, double.

Some solid citizens hesitate to risk the extra dough doubling against 10, however. And others go for broke by doubling into ace. Why the rule and what are the effects of flouting it?

Basic Strategy gives the decision in each situation that yields the greatest "expectation." You can picture expectation as the average gain or loss per dollar bet after huge numbers of hands. It's found from the laws of probability, computer simulations, or "combinatorial analyses." For the multi-deck games now prevalent, doubling on 11 against 10 has an expectation of about \$0.18 profit based on what's wagered at the beginning of the round, while hitting is projected to earn \$0.12. For ace-up, doubling is worth approximately \$0.14 per dollar and hitting \$0.11.

These values presuppose "playable hands." That is, the dealer does not have a blackjack. This criterion is used because, normally, players lose only one unit if the dealer has a blackjack, whether they originally hit or doubled, so the decision is irrelevant. And, for the same reason, expectations and therefore Basic Strategy are insensitive to when the dealer checks for a blackjack -- at the outset or the end or the round.

Going strictly by expectation, which minimizes the impact of house advantage, conclusions to be drawn from these figures are clear. Doubling is better against a 10 (by \$0.06 on the dollar); hitting is superior versus an ace (by \$0.03 on the dollar).

There's more. Expectation is important to gambling, but it's not the sole factor. Circumstances of the moment may present other immediate performance criteria that lead to alternate decisions.

Pretend you're feeling your oats and bet way above your usual amount. You get an 11 and the dealer shows that 10 or ace. Now, you might be more apt to want to make a decision based on your chances of actually winning or losing than on a theoretical expected profit. And this could work in various ways. For instance you might choose to hit when Basic Strategy is to double if it'll improve your shot at winning at least something. Or, perhaps, you'd opt to double although the smug know-it-all at first base says "you're supposed to hit," if the additional payoff will get you out of the hole while not reducing your prospects of success inordinately.

The accompanying table gives the probabilities of the various resolutions under each of the conditions. The data show that against a 10, chances of winning are about the same hitting or doubling, but doubles will push less and lose more; hitting accordingly doesn't help win more often but does decrease losses. When the dealer is sporting an ace, doubling simultaneously lowers the possibility of winning and raises the likelihood of losing; shooting for the moon in this situation accordingly heightens risk coming and going.

Chances of alternate resolutions of bets
with 11 versus a 10 or an ace, hitting or doubling
(playable hands -- dealer does not have blackjack)

 dealer has 10-up win push lose hit 51% 10% 39% double 51% 7% 42%

 dealer has ace-up win push lose hit 52% 11% 37% double 49% 8% 43%

What you do with your 11 against that 10 or ace is between you and the butterflies in your stomach. Knowing the probabilities should help. Not that the butterflies will listen. For, as the poet of percentages, Sumner A Ingmark, presciently penned: