[Theory] Hand strength vs. blockers when defending versus bets in different types of spots

Posted by whiteshark

Posted by whiteshark posted in Low Stakes

Posted 3 years, 9 months ago

[Theory] Hand strength vs. blockers when defending versus bets in different types of spots

Background:
I started working through MMAsherdog's "ultimate course" that is offered by BTS. When discussing BB play on the river as the defender, he outlines that the two factors based on which we are calling are always (i) hand strength and (ii) blockers. Against small sizes (and a wide, merged range), hand strength is more important. Against large sizes (and a narrow, polarized range), card removal is more important and specifically we want to block the value part.

He outlined that we always need to be aware of
1. what is the top of our range in terms of hand strength
2. what is the top of our range in terms of blockers

Questions:
I know that in theory, we can never fold our top range. Not all spots will lead us to defend based on MDF=1-a, but we will always need to defend some portion of our range. I always thought about the "top of my range" as a unidimensional concept but his video made wonder whether there are actually two types of "top ranges". The top of our range in terms of hand strength and the top our our range in terms of blocking potential.

So do we always have to call our best hand in terms of raw hand strength and our best blocking hand?

Attempt of an answer:
My current understanding would be that the answer to this question would need to be "No, not always". I would say that sticking to this two-dimensional definition of "top of range" is very helpful, and that there are spots where we call entirely (!) based on one of the two dimensions.

SPOT 1: Nuts/air vs. bluffcatcher, we face an overbet on the river as the defender. Here, all of our hands lose to any of the bettor's value hands. So needing to defend the top of our range in terms of hand strength makes no sense at all. The top of our range is exclusively defined through card removal and we call those hands that block the value range (priority 1) and unblock the bluffs (priority 2). Is this true?

SPOT 2: Flop goes c-bet/call. Turn goes check/check. On the river, two condensed ranges full of medium strength SDV hands and air play against each other. We check, IP bettor bets 1/3 potsize. Here, the bettor's range is so wide that the effect of card removal is marginal. The top of our range is now exclusively defined through raw hand strength. Is this true?

SPOT 3: But what about this one? We land on the river with no heavy range asymmetry, no player has a heavy nut advantage, the river is a neutral card. We face a 2/3 potsize bet. Do we need to call our best hand in terms of hand strength and our best blocking hand here?

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Shaun Pauwels 3 years, 9 months ago

We call with absolute hand strength (and ignore blockers) up until the point that that hand strength doesn't beat value from opponents range. From that point onward we don't care about hand strength and it's all about blockers.

If your opponent is balanced he has value and bluffs at a ratio that would make our bluffcatchers indifferent then the EV of bluffcatchers is 0. If your hand strength beats value combinations then your EV is higher than 0 and you should always call. This is the statement "Always call top of range".

All other hand strengths good enough to bluffcatch, disregarding blockers for the moment, have an EV of 0. They lose against value, they win against bluffs. In those cases it's blockers that change the EV. If you block value combo's then the EV increases, if you block bluffs the EV decreases.

Call all hands that beat a part of villains value range. All of them, blockers don't matter. If you do not reach the desired defense frequency with these hands then you look at other hands and purely based on blockers. Hand strength at that point becomes irrelevant as they are all equal, bluffcatchers.

The bigger someone bets the more polarized they are. Their value range are very strong hands. So that point where you disregard hand strength as they are pure bluffcatchers comes earlier. Which is why MMAsherdog mentions that bluffcatchers are more important when facing a bigger size.

This hand from Ivey is a good example. Iver jams river 2x pot. He is saying he has a very good flush or better. Sammartino's straight is the same value as AA (no heart) would be, a pure bluffcatcher. In those cases you look at blockers. Ah8d would be better than Js9s for example as it blocks flushes and full houses. Anything (that beats all bluffs) that isn't a flush or better for Sammartino has the same value.

Recap: Call all hands that beat opponents value range. If needed to call more, call other hands (that beat all bluffs) based purely on better blockers.

DNegs98 3 years, 9 months ago

I don't know if anyone will find this particularly useful on a practical level but I find it interesting so thought I'd share; there's an exception to the rule of bluff catchers below the value threshold being indistinguishable so you just call blockers. Sometimes what happens is that certain hands have exceptionally high blocker value but very low showdown value so what will happen is that in order to make these hands 0ev instead of printing calls we will actually "bluff" some hands that are ahead of these hands but behind the rest of the calling range.

An example of where I've seen this is when someone is repping a lot of pocket pair boats, say on 889JK where they have a massive overbet jamming range consisting of 99-KK and so the other player actually doesn't particularly value having trips because it doesn't block any of the value region so they start folding hands like A8 in favour of calling KJ but then the other player starts to (very occasionally) jam some weak trips hands which sort of function as a value bluff of sorts where you, in theory at least, get some worse hands to call and better to fold. These hands tend to finish up on the river after a call with something like 10-20% equity which is just a really strange number to see a hand at when you bet and get called, usually you have 0% or some number >50 (can get lower, especially when OOP at low sprs but just in general). It's particularly entertaining to me as there's a line in the actual DNegs masterclass advert where he says something like "if you get to the river and you're not sure if you have a value bet or a bluff you just don't know what you're doing". Obviously this kind of thing is super delicate, do this with too many combos and suddenly you just create a situation where your opponents can comfortably call linearly but I think it's just interesting to appreciate just how deep solvers will actually go in their efforts to maximise EV and having an appreciation for the possibility of this sort of thing can open your eyes to other options to squeeze EV out of hands.