Ace-King Part 1: The Best Drawing Hand

John Racener
A-K looks nice, but it can get you in trouble if you don't understand its true equity.

Ask anyone: they'll tell you ace-king, both suited and unsuited, is a premium Hold'em starting hand. So how come it's such a trouble hand for beginners?

As with all the premium hands, the pots you play with A-K are typically going to be larger than average, forcing you to make more frequent and more difficult decisions.

Before you can attempt to formulate strategy for the hand, you're going to need a firm grasp on the real strength of A-K. The best way to do that is by looking at the true equity of the hand in various scenarios.

A-K vs. the World

A-K is a tricky hand, in that the range playing back at it is very wide in its statistical strength. It's much more difficult to know where you stand with A-K than with many other hands. There is no worse spot to be in than not knowing whether hitting the flop will be a good or bad thing.

Because A-K is a drawing hand (meaning it needs to hit the board in some way to be more than just ace-high), many players believe it's best played in pots with multiple players. Since it has to hit to be good anyway, they feel it's desirable to get as much money in the pot as they can.

The second school of thought is to play A-K like a premium hand, raising heavily to isolate A-K against a single opponent.

Before you go any further with one school or the other, let's take a look at the statistics of A-K against both of these options.

A-K vs. a Single Opponent

The following hands are included in this comparison: AA, KK, QQ, 66, A-Q offsuit, A-Q suited and 7-8 suited.

It makes no sense to run the numbers against every possible hand, so I've chosen the majority of possible situations: overpair, pair under one of your cards, underpair (dead-end), underpair (unhindered), dominated ace and low suited connector.

(All equity calculations courtesy of PokerStove)

Hand Hand % A K %
A A 87.9 12.1
K K 65.9 34.1
Q Q 53.8 46.2
6 6 52.1 47.9
A Q 28.7 71.3
A Q 24.4 75.6
7 8 39.3 60.7

The first thing to note is this list only gives you a brief glimpse into A-K's equity in this context. The idea wasn't to make a comprehensive list, but to get an idea of where A-K stands pre-flop against one opponent.

Also note that the numbers change by a few percentage points when you change suits around, as shown with the two A-Q examples.

The average equity of A K for all of these examples is 49%. This might be surprising, considering that it's a top 5 starting hand. Although this number is accurate, it's a good example of how statistics - even accurate statistics - rarely tell the full truth.

For example, for every time your A-K runs into AA, you're going to have multiple run-ins with hands such as A-Q, A-J, and K-Q. Statistically, you're more likely to run into QQ than KK, and there are more nondominated suited-connector hands than the contents of this list combined.

If you factored in all of the possible hands, and the frequency of playing A-K against them, you would see the A-K average win percentage climb to a very profitable level.

A-K vs. Multiple Opponents

Now to run some equity numbers on how A-K holds up against multiple hands in a single pot. I'm using the same range as I used for the single-opponent calculations, but I will set up a few scenarios.

First, let's start with a direct comparison. We're going to assume that your A K got all-in against seven opponents pre-flop, allowing all hands to see a river (unlikely, I know, but this is exclusively for statistical evaluation):

Hand Hand %
A K 10.6
A A 30.8
K K 8.7
Q Q 8.1
6 6 15.5
A Q 11
7 8 15.2

(You might have noticed that I changed the suits of some cards, and left out the second A-Q example. I had to do this to remove all instances of two players holding the same card at once.)

In this unlikely scenario, A-K is going to win the hand 10% of the time (or 1 in 10). Considering you're only getting 7-1 on your money, this is a -EV scenario. In fact, any scenario that has AA in the mix is going to lose you significant money.

(On a separate note, take a look at AA: a 30% win rate while getting 7-1. It's for this reason players such as Mike Caro believe AA is best played multiway to optimize long-term results.)

If we take a more likely scenario, the numbers will change dramatically. In this scenario we're going to put A-K into a limped pot against the type of hands you'll commonly see all at once. If no one raises, chances are no one is holding AA or KK.

Hand Hand %
A K 19.5
A Q 18.6
A 9 2.7
6 5 12.5
10 10 24.1
3 3 15.2
7 9 7.4

In this more likely scenario, our suited A-K is 20% to win the pot. We're going to win 1 in 5, while getting 7-1 on our money. Now we're back in the black.

Rock-Bottom Equity

As I mentioned earlier, this first article is exclusively aimed at helping you understand your equity with A-K. The numbers in this article are the control to start from - ground zero.

These numbers are true equity, which is not to be confused with other forms of odds. These numbers only give you an idea of where to start with a hand like A-K. Your goal is to manipulate the numbers and your opponents into giving you better odds on the hand than the base equity offers.

In short: Hand equity is not always the same as the odds. The odds in play are false, due to lack of knowledge. You don't know 100% what your opponent has, and the same goes for them against you.

This means the odds change based on fold equity (your bluffing latitude) and on the choices you make with the knowledge you have.

You have the ability to choose to play or fold the hand. If you fold every time the A-Q hits the queen, and make the call every time your ace hits against KK, you're going to make far more money than the equity predicts.

Another way to think about it: if every time you play your A-K vs. A-Q, you get it all-in for 1,000BBs, and every time you run your A-K into AA, you lose 10BBs, you've just upset the equity predictions.

Even though the equity prediction is accurate in terms of how often you'll win the hand, if you manipulate the amounts of the wins and losses, you make far more money than the equity would appear to allow. (I know this example is clearly not possible; it's just meant to make the concept easy to understand.)

Knowledge and action change odds. If the best and worst basketball teams in the world face off against each other, with the former knowing that they're ridiculous favorites to win, it may well affect their respective play - to the extent even of the lesser team getting the upper hand.

We've all witnessed surprise upsets and underdog victories as a result of this exact scenario. If both teams had gone into the game knowing nothing of their own skill in relation to their opponents' - if both teams believed they were the best - the better team's odds of victory would be almost dead-on accurate.

If you want to blow your noodle with this propensity of odds to defy logic, check out the Monty Hall problem, which in short goes like this: (wording from Wikipedia)

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?"

Statistically, what should you do?

Unless you're a very sharp logistician or mathematician (or have heard this problem before), you will assume that it doesn't matter. Two doors, one prize = 50% chance either way.

This is, in fact, incorrect. You should always request he open the "other" door. By doing so, you actually have a 66% chance at winning the car.

The best way to see this is through a chart with all the possible options outlined, as you can see here.

In the next article in this ace-king series, I'll reveal some tactics for actually playing the hand - ways to help shift the odds in your favor.

Until then, swallow these odds and wrap your mind around the concept of odds and equity being somewhat negotiable.

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