What If You Hit Rather than Doubled on Your 11s in Blackjack?

23 March 2005

By Alan Krigman

Everyone more than casually familiar with casino blackjack knows "the book" says to double down on two-card totals of 11 versus anything but a dealer's ace. It's the strongest Basic Strategy double measured in terms of "expectation," the statistically projected profit, especially compared with simply hitting.

Few solid citizens realize, though, that despite expected profits being higher by doubling than hitting, the opposite move may actually offer greater chance of winning, lesser likelihood of losing, or both. This, because doubling prevents taking additional cards when it might be advantageous to do so. Think of how often you've doubled on an 11 looking at a scary upcard such as a nine, and drew something like a four. You're sweating out a miracle, wishing you could take another hit.

Under certain circumstances, an individual may be more sensible than the know-it-alls insist by hitting as opposed to doubling on their 11s. For instance, even ignoring the implications for chances of winning and losing, a person who's made an exceptionally large bet for whatever reason could justify hitting on the basis of utility. That is, winning twice as much might be nice, but losing twice as much might spell curtains.

Can the changes in likelihood of winning and/or losing a hand justify violating Basic Strategy in more ordinary situations? This is ultimately a subjective decision which you have to make yourself. But you can do so rationally by weighing how much the probabilities change and the sacrifice made in expectation.

When the dealer's upcard is four, five, or six, chances of winning, pushing, and losing by doubling or hitting an 11 are identical. This, because you'd only hit once anyway. Add a four to the 11 when the dealer had six-up and drawing another card would be foolhardy were it allowed. Declining to double in such a case is strictly a matter of halving your theoretical profit on the round to avoid putting extra money at risk.

Versus two or three, pulling an ace yields a 12, on which hitting again would be marginally preferable to standing. More notably, facing seven through 10, players starting with 11 and being under 17 after hitting would improve their prospects with another draw.

The accompanying table shows approximate probabilities of winning, pushing, and losing as well as the profit expectations per dollar of initial bet when players hit or double on 11 versus a dealer's two, three, and seven through 10. Results will vary slightly depending on the number of decks in the shoe.

Effects of hitting as opposed to doubling on totals of 11
	win		push		lose		expectation
	hit	dbl	hit	dbl	hit	dbl	hit	dbl
2	57.8%	57.9%	8.1%	7.7%	34.1%	34.4%	$0.24	$0.47
3	59.1%	59.2%	7.8%	7.5%	33.1%	33.3%	$0.26	$0.52
7	59.6%	57.9%	9.9%	7.4%	30.4%	34.7%	$0.29	$0.46
8	56.5%	55.0%	10.0%	7.4%	33.5%	37.6%	$0.23	$0.35
9	52.9%	52.0%	10.0%	7.3%	37.1%	40.6%	$0.16	$0.23
10	51.3%	51.1%	9.4%	6.8%	39.3%	42.1%	$0.12	$0.18

In general, the data suggest that the ancillary benefits of hitting rather than doubling are small compared to the penalties in expectation. Against twos and threes, the probability of a win actually falls by hitting but is offset by the chance of a loss being a bit less; here, expectation drops nearly in half. Against seven through 10, hitting raises the likelihood of winning and lowers that of losing. The latter has a greater impact than the former, with magnitudes being low but not trivial. The concession in expectation in these cases is large, but far less than half.

Here's an example of interpreting the table. Hitting rather than doubling on 11 against nine-up raises the chance of winning from 52.0 to 52.9 percent, increases that of pushing from 7.3 to 10.0 percent, and lowers that of losing from 40.6 to 37.1 percent; the expectation goes from $0.23 to $0.15 per dollar of initial bet.

What should you do? Think about why you're in the casino putting your hard-earned dough on the line. Then recite to yourself this rhyme from the remarkable writer, Sumner A Ingmark:

In for a penny, in for a pound,
Go-for-broke gamblers think this profound,
Folks less aggressive doubt it's so sound.