Originally Posted by spoonitnow

5. Effect of Blockers on a Villain's Range with Example Calculations

Suppose that in some preflop scenario, we hold A3s and Villain's range is {QQ+, AK}. That gives him 12 possible combinations of AK, 6 of QQ, 6 of KK and 3 of AA, for a total of 27, and 33.33% of that range is KK+. If instead, we held JJ, then Villain would have 16 possible combinations of AK, 6 of QQ, 6 of KK and 6 of AA, for a total of 34, and 35.3% of that range would be KK+. The point is that blockers have the potential to weaken our opponents' ranges significantly.

For the fun part (an example calculation for understanding blockers) I'm going to look at a fun 3-bet bluffing scenario:

Suppose with 100bb stacks, Villain 4x opens a range of {22+, AQ+} from early position. If we assume that Villain only continues against a 3-bet with {JJ+, AK}, then how often does Villain fold if we hold 87s? A4s?

If we hold 87s, then there are 104 hands combinations that make up {22+, AQ+}. Villain continues with {JJ+, AK}, which is 40 combinations. This means that Villain continues 38.5% of the time, and that Villain folds 61.5% of the time.

If we hold A4s, then there are now only 96 hand combinations that make up {22+, AQ+} since we're taking away 3 possibilities each for AA and 44, and 4 possibilities each for AQ and AK. Villain continues with {QQ+, AK}, which is now only 27 combinations. This means that when we hold A5s, Villain continues just 28.1% of the time, and folds 71.9% of the time.

If we assume Villain opened for 4x in EP and we 3-bet to 12x in LP, we need Villain to fold 68.6% of the time to break even just from our fold equity. Against the exact same ranges from our Villain, A4s was a guaranteed +EV bluff while 87s was not because of the blocker.