Posted by Junelli 3:12 PM
Fold Equity - Why Aggressiveness Makes Mathematical Sense - A mathematical look at playing A-K in no-limit hold’em
by Matt Matros

People misuse aggressiveness. They hear the advice, "Play aggressive poker," and translate it to, "Bluff a lot." Aggressiveness is a lot more than bluffing. Too many players are aggressive by putting in a lot of money with their weak or mediocre hands, but slow-playing their other hands. They even get passive with big hands like A-K, wanting to "look at a flop." This approach is often a recipe for disaster. In this column, I’m going to explain why I think A-K is usually a reraising hand in no-limit hold’em.

Let’s say the under-the-gun (UTG) player has raised to three times the big blind at a ninehanded no-limit hold’em table. Three players fold and you look down at A-K offsuit. You have 15 big blinds in front of you. What’s your play? Lots of players tell me it’s their "style" to just call there and take a peek at the flop. "And if I hit my hand," they say, "I’m going with it."

Here is some quick mathematics to show why I think this is bad strategy. First, note that A-K offsuit will miss the flop about two-thirds of the time. So, presumably, we’re mucking to a bet on the flop almost two-thirds of the time. I’ll allow for some bluff-raises with gutshot draws from us or for the occasional check-fold from the UTG player, and say that we will have to muck on the flop about 60 percent of the time. Next, let’s assign the UTG player a typical UTG range of hands — pocket pairs of sevens or higher, A-Q, A-K, A-J suited.
If we hit the flop with our A-K, pocket pairs of 7-7 through Q-Q hate the flop (unless they flopped a set). They’ll bet out a lot of the time — say, 75 percent of the time, anyway — trying to represent top pair, but they’ll almost always stop putting money in the pot after we give them action.

So, let’s do the math. When we cold-call with our A-K preflop, 60 percent of the time we lose just the three big blinds it cost us to call; 10 percent of the time or so, we hit the flop and our opponent check-folds. We win four and a half big blinds (our opponent’s raise, plus the blinds who folded before the flop). The other 30 percent of the time is when our opponent bets and we’ve hit the flop.
If we look at the range of hands we’ve given him, and assume that he calls our raise only with a set, an overpair, or top pair, we’ll see that on about 8 percent of flops, both of us end up all in. On those flops, we have 40 percent equity ("equity" is a term I covered in my last column). That’s right — if our opponent actually wants to get all in with us, we’re an underdog to win the pot. On 22 percent of flops, he bets out and folds to our raise. Let’s say he chooses to bet out four and a half big blinds. In that case, we win nine big blinds on the hand (the four and a half from his bet, the three from his preflop raise, and the one and a half from the blinds that folded preflop).

Add up all of the big blinds we win or lose in every possible scenario, and you’ll find out that cold-calling with A-K against that UTG player’s raise wins about 0.4 big blinds per hand in the long run, which is not bad. But A-K is supposed to be a big hand. We’re not supposed to be satisfied with winning less than a small blind with it.

Now let’s compare flat-calling to the play I recommend — moving all in preflop. If we move in (jam), I’m going to assume that the UTG player mucks his sevens, eights, nines, A-J suited, and A-Q offsuit, but calls us with A-Q suited, A-K, and pairs of tens or higher. If we look at the money we win when he folds, compared to the money we lose when he calls, it turns out that in the long run, we earn 1.2 big blinds per hand by jamming with A-K — triple what we earned by calling.

The biggest reason it works out this way is that we got the UTG player to fold a whopping 45 percent of the time preflop when we moved in. If you don’t believe that, what hands do you think he calls with that I have him folding? A-Q, nines, and eights? If he calls with all of those hands, jamming is still almost twice as good as calling. By moving all in, we give ourselves something called fold equity. We have two kinds of equity: our equity in the pot against our opponent’s range of hands in a showdown, and our equity in picking up money for free by getting our opponent to fold before the showdown.

Let’s go inside the numbers from the above calculations a bit. When we moved in preflop, the UTG player folded 45 percent of the time, and we won four and a half big blinds. The other 55 percent of the time, we lost a little — about one and a half big blinds. As you can see, this was easily offset by the times we picked up the four and a half big blinds without a fight. Also notice that when our opponent had tens, jacks, or queens, we won the hand about 43 percent of the time. If we had just called, we would’ve won the hand less than 30 percent of the time. This is because A-K wants to see all five cards. A-K offsuit has a 43 percent shot to beat two queens by the river, but only a 31 percent chance to be beating two queens after the flop. We need to give ourselves a chance to spike an ace on the turn or the river — and if we hit an ace at any point, we want to get paid. We won’t get paid if our opponent has an underpair on an ace-high flop and we still have money in front of us. That’s why it’s important to get the money in before the flop.

You could nitpick the argument I just made. You might say, for example, that I ignored the rest of the players in the hand. But I would say that we want all of those players to fold, and the best way to get them out is to move all in. You also might say that some players will open from UTG with A-5 offsuit and play badly enough to lose all of their chips on an ace-high flop, or even a king-high flop. I would say that if the player is that bad, you’re probably way ahead of him preflop and want to isolate right then and there.

Here is the central point: With hands that want to reach a showdown, like A-K preflop, or a straight-flush draw with two cards to come, it’s important to get money into the pot as soon as possible. The more money there is in the pot, the harder it is to fold, and the more likely you are to get your showdown. So, don’t be one of those passive A-K players. Learn to love the words, "I’m all in."

Matt Matros finished third in the 2004 World Poker Tour Championship, and cashed four other times in major tournaments last year. His book, The Making of a Poker Player.

4 Comment(s):

Posted by  Junelli, at 4:05 PM, June 16, 2005  

I posted this article because I found the numbers to be very interesting. Over the past year or so, I've played AK much more passively, often limping in from early position. I'll usually muck if I don't hit, and checkraise the flop if I do. I've even laid down AK preflop to a $250 all-in bet.

However, after reading this I'm going to try to be more aggressive and gain some fold equity.

Side note, in the No-Limit games I've played, I've never seen anyone move all-in preflop (for a huge amount) with a hand as good as AK. I've seen AQ, AJ, T2, 99, etc.

__________________________________________________

Posted by  Anonymous, at 4:11 PM, June 16, 2005  

(the question is, what are they calling with Mark?)

Once again, a great article from a pro that doesn't consider his audience.

If you're a pro and reading this article I suspect you'd read it and file it away as just another point of view to think about.
If you're a hack, like me, you'll push with AK every time you get it now. The problem lies in the quality of your opponents.

Since he's a math guy, would anyone like to venture a guess on the percentage of opponents that will fold their high pairs, or worse, to our all-in play? My guess is in the neighborhood of 10%.

Our "fold equity" is drastically lower online, or at most B&M casinos I know. This clearly explains why...in our circles...AK is the most overplayed hand in NL.

(I don't mean to imply that anyone reading this is a hack, in case you're sitting there thinking "speak for yourself")

(but face it, you are)

__________________________________________________

Posted by  Junelli, at 4:50 PM, June 16, 2005  

In my opinion, most of the players I play against will fold hands like 66, 77, 88, 99, AT, AJ, etc.

Unless you play very low limits, players will fold to an all-in reraise (especially if it's substantial). Obviously in the lower limits, nobody will fold those hands. But my experience in the bigger cash games, is that you do actually gain some fold equity.

Of course, you need to observe who are the solid players who will fold in that situation, and who will call with anything.

I'm definitely a hack, but there's not a chance in hell I call a huge all-in bet preflop (from a solid player) with 77.

Also, you don't just gain fold equity. If you're playing against a loose player who won't fold to your raise, you actually benefit when he calls you with his marginal hands (AJ, AQ, AT, KQ, QJ, etc.).

Online is a different beast. I don't think this article is applicable for online play.

__________________________________________________

Posted by  Anonymous, at 10:12 PM, June 20, 2005  

It's a better tournament play than cash game play, because human nature says you call big bets less with your tournament life on the line than you do for mere $$$ when you can reach in your pocket for more.

__________________________________________________

Post a Comment