equity against opponents range

There is a huge difference between all in equity and equity against someone's range All-in

Sometimes when we are on a downswing we take a look at the large pots that we recently lost. It is easy for us to identify the spots where we got it in good and failed to win. These “bad beat” hands increase our variance and can definitely decrease our win rate but they are not the most telling sign of whether or not you are playing well. What we should actually be more interested in is trying to figure out our equity versus our opponents’ range in all in pots. This can be a difficult thing to evaluate in a live setting where you can't go back and look at hand histories.

There was a hand a few weeks ago from the Commerce Casino $5-10 no limit game that demonstrated this concept. I started the hand was $1600 and the villain who was in the small blind had me covered. One player open limped from the cutoff and I raised to $45 with A♠ Q♠ in position. The small blind, a mid 50s Korean aggressive pro, three bet me to $245. Even though this was a large three bet I decided to call because I knew that the villain was capable of re raising light and I felt like my hand did well against his range of re stealing.

The flop came out 8♠ 7♥ 6♠ giving me the nut flush draw with two overs. The small blind fired a huge continuation bet out of $500 and even though this bet size left little chance of him folding my draw was so large that shoving, even with just a hint of fold equity, had to be the right play. So I took about 15 seconds and moved all-in. When the small blind did not snap call me I knew I had made the right play. He ended up tanking for about five minutes asking me if I had a set of eights and finally called. The turn fell the 2♣ and the river brought the A♥. I tabled my hand and said, “Ace”. He then proudly tabled A♦ K♦ and said, “Bigger Ace”.

Now if we calculate the all in equity between A♦ K♦ of diamonds and A♠ Q♠ on this flop we see that A♦ K♦ is 48%. With the pot odds that he was given this is clearly the right call, right? Well, let's take a look at his equity versus my range.

Let’s say I sometimes call preflop with a range of some 66-88, one 9Ts one 56s and pocket 9s. Let’s also include AK♠, AQ♠, AJ♠, KQ♠ and JT♠. If we run Poker Stove on that range vs his A♦ K♦ we find that is equity is only 18%. The fact that I ended up with the bottom of my range does not mean that his call was correct. In fact given the pot odds it was clearly wrong.

The people that will make a call in this spot and lose will curse their fortune claiming that they run bad and got it in good. But, here as you can see, it doesn't necessarily matter what their opponent’s’ holding actually was it matters if your play was correct against their range.