Laying Down Pocket Kings Pre-Flop to a Single Opponent

It’s a familiar story to anyone who has played a fair amount of no limit texas holdem. You’re in the middle stages of a tournament. You find yourself in early position with pocket kings. You make your standard raise to 3-4 times the blinds. A player in late position goes back over top of you for all of your chips. You call and he turns over the dreaded hand … pocket aces (gasp!).

Many experienced players will simply shrug their shoulders, utter the phrase “that’s poker”, and move on. However, I constantly run into players who continue to analyze this situation long after it’s over. Since it cost them their tournament life, they beat themselves up, somehow feeling like they should have possessed the clairvoyance to read their opponent for aces and lay down their kings accordingly.

However, their constant rehashing and rethinking of the situation is likely in vein. Mathematically speaking, kings should always be played just like aces against a single opponent pre-flop. Let’s examine why.

Consider the Probability

Getting dealt pocket kings is pretty uncommon. After all, during a stretch of 220 hands, you’re only supposed to get them once on average. In addition, having an opponent get dealt pocket aces at the same time is even more uncommon. Let’s take a look at the math:

• Odds of a single player being dealt pocket aces: 1 in 220 (.45%)
• Odds of someone at your table (other than you) being dealt pocket aces (.45% * 9 players) = 4%
• Odds of cracking pocket aces with pocket kings: 1 in 5 (ish)

This means that roughly 1 in 24 times when you have kings, you will run into aces. The other 23 times, you will have the best starting hand at the table. Even when you find yourself behind to the aces, you will still win about 1 time in 5.

What’s your good folding judgment *really* worth?

“But I had to lay it down; I just knew he had aces!”

Ok, let’s pretend that you decide that it’s OK to lay down your kings based on a solid read of your opponent. Just how much is that good judgment worth? In other words, how often do you have to be right to make it worth your while? Let’s take a look:

Say that you’re up against a single “typical” opponent pre-flop. By typical, I mean not too aggressive, and not too conservative. Sometimes you’ll be up against one extreme or the other, but on the whole, the extremes will likely cancel one another out. The blinds are 50/100. You raise to 400 under the gun, and your opponent re-raises you all in 1500 from late position. (Whether or not it’s a smart move on his part is another discussion).

What types of hands might a typical opponent with an average chip stack make this move with? I would venture to say that AK, AA, KK, QQ, and sometimes even JJ all fit the profile. Against a much looser opponent who is just trying to take it away from you, you could sometimes be facing other hands, AQ, TT, 99, Ax, etc. With a tighter opponent, it will almost always be AA-QQ, or AK.

Let’s say for the sake of argument, that each logical hand we might be up against represents a single unit of possibility. For this example, we’ll use 6 total possibilities (AA, KK, QQ, JJ, Ax, and "other").

Assuming you took each of those hands to a showdown, here’s what each showdown is worth, statistically speaking (Note, the win percentages are merely rough estimates):

Let’s see what happens when we fold to what we “perceive” as someone else’s pocket aces. The chart below shows the expected value of our folds over a series of 10 hands.

Conclusion

As the numbers above show, in the absence of telepathic talent, kings should be played identically to aces against a single opponent pre-flop. Trying to make that "perfect read" on your opponent gives you a very small margin of error, and may have you setting yourself up for a negative expected value.

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