The Rule of Four and Two

To be a good poker player it is not absolutely necessary to know every single mathematical approach to the game, but there are some very valuable and relatively simple equations that you can do while sitting at the table which could very well give you an edge over your opponents. One example of this is the mathematical principle of the “rule of four and two”. The rule of four and two allows you to estimate the amount of equity you have with a certain hand as long as you can put your opponent on some kind of range. The amount of equity you have is relative to the size of the pot and the two should never deviate too far from one another. Let’s say we have a 48% chance of winning the hand after the flop then we can call most bets that are up to the size of the pot which would give us two-to-one odds which is 50%. Here you can see how the two are related, but how do we find out what our estimated equity in a certain situation is? This is where the rule of four and two comes into play. Let’s look at an example.

Let’s say we’re playing in a six-max $1/$2 cash game and we are on the button with Ac7c. Our opponent raises from early position to $6 and we decide to call. Everyone else folds their hands so it is just us and our single opponent. The flop comes out Kc7h4c. Now here we have made a pair of 7s, but we could be already beat by a K. However, we also have a flush draw to the best hand with two clubs in our hand and two on the board and if we hit an A then our hand may be good as well. There is $15 in the pot (small blind-$1, big blind-$2, opponent’s raise-$6, and our call-$6). Before the fourth card we can multiply our number of outs, which are cards that would more than likely give us the best hand, by four and come up with our estimated equity. There are three 7s left in the deck, 3 As, and nine clubs, which would give us three-of-a-kind, a higher pair, or a flush respectively. If we multiply those outs (3 7s + 9 clubs + 3As = 15 outs) then we come up with an estimated equity of 60% of winning the hand. Now let’s say our opponent bets $10. That brings the pot up to $25. We would need to call $10 to win $25 which gives us pot odds of 2.5:1. Math indicates that we should call and see another card here. Let’s say that the turn card is the 8d. This doesn’t help our hand at all and though we still have the same amount of cards that will help us, our equity has dropped substantially because there is only one card left to come. So we take our 15 outs and multiply them by two now which gives us an estimated equity of 30%. This means that if our opponent were to bet more than 30% of the pot then we should be folding because, in the long run, this is a call that will cost you money.

Now let’s look at another example:

We’re playing in the same game and we’re on the button with the same hand: Ac4c. Our opponent again raises to $6 in early position. We call and every one else folds. This time the flop comes out Qd2h5s. Now our outs are severely diminished as is our equity. The cards that we would need to catch to make the best hand (assuming our opponent is holding one Q in his hand) are the three remaining As and the four 3s to give us the straight. We take those seven cards and multiply them by four to give us an estimated equity of 28%. But what if our opponent is holding exactly AQ? That takes away our A outs and leaves us with only the four 3s, giving us a 12% chance of winning the hand. Now unless our opponent bets roughly 1/10 the size of the pot, which would be incredibly uncommon, we should not be calling here because the math dictates it.

This is just a basic introduction to the idea of estimating equity and while the numbers are not exactly precise, they’ll only be off be a couple percent at most, so you can get a pretty good understanding of where you stand. However, there are other variables to consider such as reverse implied odds and card ratios, but we’ll cover that later. For now I just wanted to give you a general idea of how to calculate equity and how it relates to the size of the pot.

As always, questions and comments are welcome.