August 25, 2020

Basic (but badass!) understanding of blockers

In the previous article, we implicitly touched the topic of blockers. Since we were holding QQ, there was only one combo of QQ out there. This is an obvious example of blockers, i.e. effects of your cards on your opponent's possible holdings. Let's look at a few more, including a few more subtle ones - including using blockers for deciding to bluff or not, which is what I am thinking might approach the badass part of the title.

Let's look at two samples:

Blockers can increase the value of a call

Hero: TT
Board: 78

Let's say we face a 2X pot overbet on this river. For some players that can literally mean that they either have T9 or that they are bluffing (maybe not a fair assumption, but even if T9 is only part of the value range, the point we are about to make will hold), for instance with the missed diamonds or spades. 

Even if your opponent is playing completely unexploitable here (i.e. has exactly as many bluffs in relation to value as he should, which for a 2X pot bet should be 40%[1]), your cards give you extra information that likely makes this a profitable call: Since you hold TT, you automatically cut the number of T9 combos from 16 down to 8. Furthermore, if you think your opponent would only play the suited version of T9 given the action and positions, it is actually just two combos available out there.

Blockers can give profitable bluffs

Hero: A9
Board: 78

Let's say we face a 1/3 pot bet on this river after our open-ended straight draw bricked. This bet is not very polarizing, and could probably be top pair, overpairs, two pairs and the like - depending on the action so far in the hand. Since we hold the ace of diamonds, we can be hundred percent sure our opponent does not have the nut flush. Thus a very large raise should be a more profitable play than if we did not have this card.

Bunching - the least exact blockers that are

In the example of pot odds, we were waiting for an ace. Do you think the likelihood of getting that ace is different from getting a ten - if that was what we were missing? In fact it might be. Using bayesian probabilities, we might estimate that hands with aces are played much more often than hands with tens. So even if we don't know this, the number of players choosing to see the flop might very well give us useful information. This concept is sometimes referred to as bunching. It is not a super important concept, but interesting enough - we can maybe think about them as (very!) fuzzy blockers. I've seen arguments, I think Barry Greenstein made it back in the days, that if 7 people folded in front of you, it can be enough to make AK a favorite (it is normally around 47%) against low pocket pairs all-in.

For more on blockers, I strongly recommend the two Play Optimal Poker books by Andrew Brokos (hey, I am even mentioned in the acknowledgements-section on the second after having found a couple of small "bugs" in an early edition!). Having briefly touched on blockers, we'll jump to a similar light-touch introduction to balance before concluding this mini-series of 7 gems of poker math. 

[1] - This follows from a formula Bet/(2*Bet+Pot) that we have not covered, as I want to keep this very practical and I have found it relatively hard to use in practice - but it has to do with the pot odds you offer your opponent. The effect of the formula is that if you have plenty of bluffs, but also some very strong hands, you can bet very large. And if you are less polarized based on the action so far, you'll "run out of bluffs" and thus could be exploited by overfolding if you bet very large.

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