Doubling 11 against an ace

I got an interesting question from a blackjack player on the merits of doubling down on 11 against a dealer's ace. It read:

"If I'm holding an 11 and the dealer shows an Ace and she peeks and doesn't have a blackjack, then isn't doubling down the better play since you've eliminated the possibility that she has a blackjack and my 11 has to be stronger than her Ace."

The answer to his question is: It depends on the number of decks of cards and the rules. Let me explain.

Let's assume you are playing a typical six-deck game where the dealer must stand on soft 17 (s17). In this game, your 11 is not stronger than her ace. Sure, her ace counts as 11, which equals your hand total of 11, but there's one big difference. If the dealer goes over 21 while drawing cards to her hand, she can count the ace as a 1. Because of this, her chance of busting with an ace upcard, assuming she has checked her hole card and doesn't have blackjack, is relatively low (in fact, she'll bust only 17 percent of the time). Here are the exact dealer probabilities for the final hands that she will wind up with when she has an ace upcard (and doesn't have a blackjack):

The above probabilities clearly show that the dealer is not very vulnerable when she shows an ace upcard.

Now let's look at what happens when you double down on your 11. The fact that you are doubling means you get only one draw card. Of course, you are hoping for a 10-value card, which will give you 21. But suppose instead you get dealt a small card, like a 3, for a 14. Unfortunately, you are stuck with a 14 because you can't draw again. And that's the big advantage that the dealer has: If she has an Ace-3 for 14, she can draw again. And if during the process of drawing more cards to her hand she goes over 21, she has another chance to make good because she can count her Ace as 1 and continue to draw. You, on the other hand, have no options if you doubled down and have a 7-4-3. By the rules of the game, you must stand with your 14.  And that's why your 11 is not nearly as strong as her Ace in this game.

So here's the best strategy for playing an 11 against a dealer's Ace in a six-deck game with s17: You should hit 11 against a dealer's Ace upcard until you get to a count of at least 17. This means if you hit and draw a 3 for 14, hit again. If your next draw card is a 2, giving you 16, hit again. Just remember to keep drawing cards until the total of your hand is 17 or more.

Now what happens if you find yourself in a six-deck game where the rules specify that the dealer must hit soft 17 (h17), or you are playing a double-deck game. It turns out the probabilities change just enough to make doubling 11 the better play than standing in some situations. I don't have the space to go into the math, so I'll just summarize what the best strategy is.

If you are playing in a six-deck game and the dealer must hit soft 17, then you should double down 11 against the ace (not hit).

If you are playing a double-deck game -- hold onto to your hats for this one -- the right way to play it depends on whether the game is s17 or h17 and sometimes the makeup of the cards in your hand. For example, in a double-deck game with s17 or h17, always double down with this exception: if you hold a 9-2 or 8-3 in an s-17 game, you should hit (with 7-4 or 6-5, you should double down.).

If you find remembering this strategy change based on the rules and number of decks of cards a little daunting, I'd suggest you bring a set of strategy cards with you when you play blackjack. The ones I recommend are the Ultimate Blackjack Strategy Cards by Don Schlesinger, and the Basic Strategy Cards by Ken Smith (they are both in my gambling catalog at smartgaming.com). Schlesinger's strategy cards consist of a set of three covering single-, double-, and multiple-deck games with s17 and h17 (they also contain the strategy that depends upon the composition of your hand). Smith's strategy cards consists of a set of six cards that also cover the h17 and s17 games for single-double- and multiple-deck games (they are a smaller size card that easily fit in a shirt pocket or wallet).

If you are planning a trip to a casino and you know, for example, that they offer double-deck and six-deck blackjack games, but you are not sure of the rules, just bring along the appropriate strategy cards with you. No matter what the rules are when you sit down and play, you'll have the right strategy card handy to make all the right plays.