The Almighty Ace

Isn’t it strange that those making the rules of poker vested one card with so much power? They weren’t satisfied with simply making the ace the highest card in the deck; they also made it the only card that can take on two different ranks for the purposes of making a straight. Then, they went even further and also made the ace the lowest card in the deck — giving it such an absurd level of importance in high-low split games that it’s almost a requirement to have an ace in your starting hand. There’s an inordinate number of benefits to holding an ace in any form of poker, and in this column, I’d like to focus on one of the less obvious ones: When you’re holding an ace, there’s a good chance that your opponent is not.

The value of holding an ace that blocks your opponent from having the nuts is well-known to pot-limit Omaha (PLO) players. The so-called dry-ace bluff — making a large bet on an unpaired three-flush board when holding just the ace of that suit — is practically a PLO cliché. It’s a very hard bluff for your opponent to call, precisely because your opponent can’t ever have the nuts (it can be very hard to call without the nuts in PLO, and it’s especially hard to call big bets over multiple streets with a hand that can’t improve, like the second-nut flush).

There are similar benefits to removing an ace as a possibility in your opponent’s hand in no-limit hold’em, but to a lesser degree. The dry-ace bluff isn’t generally a big deal in no-limit hold’em, because most players treat king-high or queen-high flushes as if they are the nuts. And there’s no real equivalent situation before the flop, because your having an ace doesn’t stop your opponent from having one or two himself. But we don’t need a certainty, like the dry-ace bluff in PLO. There is a lot of money to be made in no-limit hold’em by just knowing that it’s less likely your opponent has two aces, or even one ace, before the flop.

There are four aces in the deck, so, obviously, when you have one of them in your hand, that leaves only three for your opponents. There are six combinations of aces available in the deck (A♣ A♦, A♥ A♠, A♦ A♥, A♠ A♣, A♣ A♥, A♦ A♠), but once you see the A♣ in your hand, there are only three combinations (A♦ A♥, A♥ A♠, A♦ A♠) remaining for the field. It is suddenly only half as likely as it was before you looked at your cards that your opponent has two aces. Other strong hands like A-K and A-Q go from 16 combinations to 12, making it 25 percent less likely that your opponent has those holdings.

What does this mean in practice? Let’s say an opponent has raised; you know his game very well and know that he’ll call a reraise only with a pair of fours or better, A-8 or better, or K-Q. If you reraise him with, say, 10-3 offsuit, he has 171 combinations in his range that he can call with. If, instead, you have A-3 offsuit and choose to reraise, he has only 151 combinations to call you with. So, there is less chance that he’ll call you, and you have a stronger hand when he does. This is why reraising all in is far better with ace-small than with two random cards.
But the effect is present even when comparing ace-small to other possible stealing hands. For example, 8-7 offsuit has 32.7 percent equity against the calling range described above, making it a “better” hand than A-3 offsuit, which has 31.9 percent equity against the same range. Having the ace in your hand, however, makes it less likely that your opponent will call. Let’s say that we’re going against a player on the button who opens with any pair, any ace, K-8 or better, Q-10 or better, connectors down to 9-8 offsuit, and suited connectors down to 6-5 suited, and he calls with the range described above (4-4 to A-A, A-8+, K-Q). If you move in on him with 8-7 offsuit, there is a 57.9 percent chance that he’ll fold. If you move in with A-3 offsuit, there is a 60.5 percent chance that he’ll fold. Despite the lower showdown value, the overall expected value (EV) of the resteal play is higher with A-3 offsuit than it is with 8-7 offsuit, although both are +EV plays with a reasonable resteal all-in stack size against the opponent described above. (I’m omitting the mathematical details here for lack of space, but I think the reader who works them out on his own will greatly benefit from it.)

Of course, neither A-3 offsuit nor 8-7 offsuit is a good hand in no-limit hold’em. That’s not the point. The point is that if you’re considering making a play against an opening raiser who you suspect has quite a few weak hands in his range, it’s slightly better to have an ace — any ace — than medium connecting cards.
I recently put this logic to the test in a $1,500 no-limit hold’em event at Foxwoods. With blinds of 500-1,000 and a 100 ante, the player on the button open-raised to 2,500. I happily moved in on him for 17,000 with A-4 offsuit, knowing it was less likely that my opponent would have a hand. It didn’t exactly work. After the big blind folded, the button called immediately. I shook my head and wondered whether I needed to hit the 4 or the ace. It turned out, neither. The button had two of the three remaining aces, and I busted out.

I’ve run into aces many times before, and sadly, I’m sure that I will run into them again many times in the future. All of the preparation in the world won’t change the spots on the cards for you. But knowing as much as you can about what adds to and detracts from the profitability of a play will help you win a lot more money in the long run. ♠

Matt Matros is the author of The Making of a Poker Player. He is also a featured coach for cardrunners.com.