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Best of Alan Krigman

Gaming Guru

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Should You Just Hit 11 vs Ace, or Go for the Double?

4 September 2001

How do you play a two-card 11 against ace-up in blackjack? Some stalwarts double - particularly at tables with "peek-a-boos" when they know the dealer doesn't have a natural. Others hit.

Basic Strategy dictates doubling in one-deck games and in two?deckers when the 11 comprises 7-4 or 6-5; otherwise hit. With four and usually six or eight decks essentially standard, for all practical purposes this means "the book says hit." Knowing that the dealer has a playable hand, not a blackjack, is irrelevant.

So, why do solid citizens who normally walk the line go astray in this situation? A few use old single-deck Basic Strategy charts. More often, it's because players have an edge either way. Therefore, while expected return is greater by hitting than doubling, the gutsier move is still favored and conquest breeds bravado. Especially since nobody keeps accurate records over thousands of 11-vs-ace hands and folks remember when they knew better than the know-it-alls but repress when they didn't.

Distinctions between the alternatives arise from the chances of various player and dealer final point totals. The following list shows prospects for the two options, assuming extended shoes.

Probabilities of various final
point totals
for player doubling or hitting 11
against a playable dealer ace-up
final hand double hit dealer
12 to 16 38.4% 0.0% 0.0%
17 7.7% 11.1% 18.9%
18 7.7% 11.1% 18.9%
19 7.7% 11.1% 18.9%
20 7.7% 11.1% 18.9%
21 30.8% 34.3% 7.8%
bust 0.0% 21.3% 16.6%

Dealer and player point total probabilities can be combined to find the chances of winning, losing, or pushing with a double or a hit.
These outcomes are shown in the accompanying chart.

Probabilities of various outcomes
for player doubling or hitting 11
against a playable ace
outcome double hit
player win 48.6% 51.6%
player lose 43.2% 37.3%
push 8.2% 11.1%

To find expected profit per dollar bet at the beginning of a round for each option, subtract the chance of a loss from that of a win - and, in the case of doubling, multiply the difference by two. Expectations per dollar turn out to be $0.143 hitting and $0.108 doubling. So, betting $10 per round, after 10 such hands you expect to earn $14.30 hitting and $10.80 doubling. Hitting is worth $3.50 extra. As shoes get smaller, the divergence narrows.

There's more. "Volatility." It has to do with the fact that in 10 hits or doubles starting with $10, you could be up or down by $100 or $200, respectively. These figures make the expected $14.30 and $10.80 seem meager and the $3.50 difference trivial. This isn't just fantasy or greed, it's short-run statistics.

In a statistically small number of rounds, volatility swamps expectation. An important question is then: what are your chances of being some meaningful amount ahead or behind on 11 vs ace one way or the other? Here are figures for a $60 profit or loss after 10 trials at $10. Hitting gives you 6.2 percent chance of being at or above this level and 0.6 percent chance of being at or below it. Doubling gives you 20.9 percent chance of being $60 or more up and 12.1 percent chance of being $60 or more in the hole.

Comparing the two shows the trade-offs. Doubling rather than hitting triples your shot at this representative target profit for the hand, but raises your chances of losing a comparable amount by a factor of 20. From another perspective, you're about twice as apt to be $60 ahead as $60 behind if you double, and 10 times more likely to be $60 ahead as $60 behind if you hit.

What should you do? As always, it's a matter of personal preference. But, the figures afford a rational basis for making up your mind. To avoid inveiglement, invoke the verity voiced by the venerated versifier, Sumner A Ingmark:

The money that you wanna make,
Determines how much risk you take.
Or, worsely, conversely.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.