CardSharp

One mistake I see a lot of holdem players making is that they incorrectly estimate the strength of their hand on the flop. This can lead to some ugly mistakes in play. While most players eventually learn by experience what hand/board combinations are strong and which are vulnerable or near-certainly beat, this process can be expensive and is mostly unnecessary. Here’s a quick and dirty method for figuring out where you stand on the flop that you may find helpful.

The basic method is to count up the hands that beat you and compare it to how many hands your opponents would play. This is a basic but meaningful indicator of the strength of your hand on the flop.

Step 1: Estimate how many hands your opponents could be on

There are 1326 (52 choose 2) distinct 2-card poker hands you can hold and 1225 (50 choose 2) your opponents can hold since they can’t possibly have your cards. However, your opponents usually won’t play all those hands. For example, if an opponent plays roughly 1/4 of their hands in a given situation, there’s roughly 300 hands they’d play. You don’t necessarily know exactly how many, but it’s a decent estimate and that’s all we’re after here and your estimate will be more accurate the better you know your opponent’s opening habbits.

Step 2: Figure out which hands beat you and how many of them there are

The next step is to count up the number of two card combinations that beat you. This isn’t that hard once you practice it a bit, but it can be daunting the first couple of times. An example will make it clear:

Suppose you’ve got AdKs on an Ah7h2d board. You’re beat by all three sets, A7, A2, and 72. You’re also a slightly dog to any heart draw containing the 2 of hearts. If coming up with that list is difficult for you, then you need to practice reading the board, which I’ll cover in another article. Once you have the list, you need to figure out how many combinations of each type are possible. There’s only one possible AA set – the hole cards would have to be exactly the two remaining aces. There’s 3 possible sets of 7’s – 3choose2 for the three unseen sevens. Ditto the twos. That makes a total of 8 possible sets. There are 6 A7 combinations – 2 choices of aces, and 3 choices of twos. Ditto A2. There are nine combinations of 72. This makes a total of 29 hands that beat you, plus 10 2hXh combinations where you’re a slight dog.

Step 3: Decide if those hands are plausible

As you can see from the above example, often times you’re beaten by hands you can be pretty sure your opponent didn’t open with. For example, an opponent playing 1/4 of their hands is probably playing any A and any pair, but probably not playing 72. So in the above example, while there are 29 hands that in theory beat you, only 20 of them are really plausible.

Step 4: Compute the odds

Now you’ve got a basic odds problem on your hands. If 20 out of the 300 hands your opponent might be on beat you, it’s 14:1 against you being beat.

Step 5: Adjust for multiple opponents

If you have multiple opponents, you can compute the logical “or” of the chance one beats you to determine the chance one or more beats you. Or, as a rough estimate for a couple of opponents when you’re a likely favorite, just divide the left side of the odds against being beat by the number of opponents. So in our example above, against 2 guys who play 25% of their hands, it’d be roughly 7:1 against you being beat.

Caveats

There’s a big “gotcha” in all this – it makes no attempt to apply any sort of advanced hand reading to your opponents, and as such the whole system becomes invalid once they take additional actions beyond the flop that reveal more about the strength of their hand. So this system really is only useful before any action occurs on the flop and even then is merely a guide. The whole point is simply to figure out, in a general sense, how strong your hand is so you have some idea how to proceed. I don’t really recomend you do this at the table – it’s too time consuming. However, it’s an interesting thing to practice at home because you’ll see there are some obvious patterns to it, and as you notice these you’ll develop intuition. And ultimately that’s the goal.