One fundamental concept in poker strategy is combos, as well as their corollary, blockers. Remember, the best way to get in edge in this game is by studying and knowing the math better than your opponents. Your hard work will pay off.
Combos are the next step in thinking about ranges. Essentially, it’s how many ways our opponents could make each hand that’s in their range. We may be able to figure out what bluffs and value hands are in their range, but figuring out how many combos of each will let us make more precise equity calculations.
Let’s talk combos.
Figuring out combos involves just a little multiplication. Let’s start with an example. Let’s say that we’re playing against a fairly straightforward opponent and they 3-bet pre-flop. Their range probably includes AA, KK, QQ, and AK. How many combos do they have?
To figure out the paired hands, we use this formula: C= (A(A-1))/2 where C is the number of combos and A is the total number of that card type. So, in this case, C= (4*3)/2 for a total of 6 combos. That means there’s 6 combos of AA, 6 combos of KK, and 6 combos of QQ for a total of 18 pocket pairs.
For AK, we use C= A*B where A is the first card and B is the second card. That means C= 4*4, thus giving us 16 combos of AK. This means that there’s 34 combos in our opponent’s total range, and about half of them are pocket pairs.
Bringing in Blockers
This math changes a bit when we start taking cards out of the deck and putting them into our hand. These are called blockers. Obviously if we’re holding an ace, then our opponent can’t have that combo. So, let’s say that we’re holding AT.
This means that the formula for pocket aces goes down to c= (3*2)/2 for a total of 3 combos. By holding the ace blocker, we’ve cut the total number of pocket aces combos
in half and drastically decreased the likelihood that they’re holding that hand. We call this “blocking aces.”
How about AK? Well, let’s plug it into our formula: C= 3*4 for 12 combos. This means that we’ve cut out 4 combos of AK. Wrapping it all together, we see that our opponent now has 15 combos of pocket pairs and 12 combos of AK for a total number of 27.
Now that our numbers have changed, we can adjust our calculations accordingly. It’s become more likely that our opponent has QQ than AA, for instance, and so we can be happier when the flop brings an ace.