Thanks to everyone.

And especially thanks Arty, I think you seemed to understand exactly what I was asking. And I also think you pointed out just exactly why the group was having such a hard time here.

1) If we are betting a polarized range we should usually exhaust all of our bluffs without SDV before we start bringing hands with SDV into our bluffing range
2) 99 maybe is a better bluff than 76s but it is DEF a better check
3) seems like, if we are in a spot where we have some kind of range advantage and we are betting hands with show down value and checking hands that have no SDV and no equity then we are doing something wrong
4) that makes sense though in two ways; one, we should be checking 99 (which is what I thought) and two; we shouldn't even get here with 76s which is also what I kinda thought accept I didn't think it really mattered much for the sake of argument but I can see from your work with snowie that it actually kind of does.

Thanks


SO, for anyone who didn't get where I was coming from I just want to say that

even though it could be counterintuitive that we would check some hands that have some SDV even though we will check and fold them but bet some hands that are strictly weaker as bluffs.. this def does come up.

It's because some of the hands we want to check and will have to fold to a bet will be a lot more valuable when the street checks back and maybe we don't want to be bluffing too often in a given spot.

EG:

CO opens and we 3 bet, he 4 bets small and we flat with JJ (Feel free to tweak the stack sizes, bet sizes, villain propensities, pay out structure/ICM however you need to get this to be an OK line pre-flop)

Flop: A88r
check
check
Turn: Qr
It prob makes all the sense in the world to bluff hands worse than JJ maybe if we have TT or 99 or some hand we were bluffing with but called getting a huge price with a playable hand (KTs? KJ?)
but with exactly Jacks it can make sense to check even if we will fold to a bet.

It may seem like "why would we induce a bluff that we can't call?" and maybe you'd think "It does not make sense to bet a weaker hand in the same spot where we would check and fold a stronger hand"

But this actually can make sense for a couple reasons.

If we are "turning JJ into a weaker hand" by betting it then we can have about the same EV of bluffing with some weak hand or betting with this JJ hand. But maybe the weaker hand doesn't have enough value or equity to make us any money even when the turn checks thru.

It's not just about the value of betting this hand vs that hand it is also the difference in value of checking vs betting each hand. If one hand is gonna be about break even as a check vs a bet and the other hand is clearly better as a bet than a check and we want to have parts of our range that bet and parts that check then there is no paradox here.

Anyone disagree with that in terms that, preferably without using the idea of "protecting hands"? Not that I am saying that getting your opponent to surrender their equity when you have a hand that is prob best right up until you bet and are called is ALWAYS bad. It isn't. But I don't want to have a long discussion about why I think protecting hands is not a good way to think and that there are better, more efficient ways to think about betting strategy. Basically, (blocker affects aside) your hand only matters if there is a show down and you don't win extra money for having the best hand when your opponent folds and so we ought to at least try to avoid sucking the value out of our hands by using them as bluffs when we have better bluff candidates and would like to have a range of hands that will check and fold.


*btw, what I mean about having too much overlap is that we get better board coverage, all else equal, by having hands in our range that hit different boards.

So, for instance, if we are playing a tight range from UTG at a live low stakes cash game and a good player sits down and starts making things hard on our UTG range by flatting us in position very deep and; Never giving us action when we c-bet AK8r and putting a ton of pressure on us when the flop comes 776/654/889/79T etc..
Maybe we will want to add some hands to our open raising range from UTG to give us better board coverage. That way if we don't get action on AK8r we will have some bluffs to leverage our range advantage with and if the board comes 654 we can have the nuts on occasion.

Maybe hands like QJs and 87s will have about the same EV in a vacuum and maybe break about even over all. But, even though QJs is the objectively stronger hand, we will already have hands in our range that will do some work for us on QQJ, JJQ, QJT, KQJ, and even like AJT. But we won't have hands that can do work for us on 876, 765, 776, 872, 773, 988, etc.

So in a case like that it could be that we should use the hand that has less overlap with other hands in our range so that we have better board presence.


That's what I was getting at.

I'm not so convinced that 76s belonged in our range in my OP but I can buy the idea that we may want to have some stuff like 87s in our UTG range when we play deep enough at full ring cash games and six max online cash games even though maybe we don't want to open some objectively stronger hand even if it has about the same EV as the other in a vacuum because we would want to include the hand that adds the most EV to our strategy at large.

Right?

There is way too much to deconstruct in those posts but basically if a hand is unprofitable in a certain position hiding it in your range is not going to be able to change that. It's only going to lower the EV of your whole range.

For example 32o is not a profitable open from utg in a 6max game. Just because you hide it in a really strong range doesn't change that fact nor does it help your range by "covering more boards".

The only time board coverage situations are really relevant is when stacks are deep enough and ranges are wide enough that having the nuts in your range sometimes is important.

Also again I don't know why you are arbitrarily ignoring things like blocker effects that are quite relevant to the conversation.



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Thanks, but I think that ZKesic kind of nailed the answer to the basic question of "which hand is the better bluff?" when he wrote A more extreme formulation of the question would be something like "The flop is KJ8, which hand should we be more likely to check with out of QQ and 22?"
Clearly QQ makes zero sense as a bluff, because nothing better folds, but 22 can make better hands (and a ton of combos with 2 overcards) fold.

When we're building a polarized betting range, we obviously want to put money in the pot with hands that increase their EV by doing so (often by making villain fold some equity either immediately on the flop, or on "good" turns), but we usually check with hands that have SDV and that do better when villain's range stays wide and the pot stays small.

All that said, sometimes a hand is so weak (no immediate equity, no backdoors, no showdown value) that it's not even a +EV bluffing candidate. A hand like 32o has so little going for it on KJ8 that it should probably be misclick open-folded, and not even considered as a bluffing candidate. 76s (with BDFD) does at least have some turns and rivers it can barrel ftw, and that means bluffing with it is slightly more profitable than just giving up.

that's cool man.
no hard feelings
I think if I was to respond to this it would be repeating the stuff in my long post so I guess just read the rest of that if you wanna know my thoughts.

You could be right.

I think you are either misunderstanding what I'm saying (maybe cause I didn't explain well) or you and I disagree about some axiom of game theory and strategy at large.

no biggie.

Thanks for your two cents.

by the way I know people get sarcastic on here and that trolling and leveling and all come up a lot so please don't read any of that into this I'm being sincere.

yup.
all this

I actually got a kick out of the very two post being "99 is too high in our range to bluff with"
and "76s is too low in our range to bluff"

that's what the group was arguing about. I didn't think both of those answers could make sense. Turns out they actually could make sense. But, I THINK, if we have a range advantage and we are in a spot where we are turning some hands with SDV into bluffs it can only ever be the case that we have first exhausted all of our bluffs that do not have SDV.

What do you'all think? Does that sound right?

No worries. Didn't read anything into it. I may go back and try to address your thoughts but in the moment I certainly didn't fully understand what you were saying.

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I think that makes some sense for sure.

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Start thinking in terms of EV, against most opponents betting 76s or 99 here is going to be -EV for you especially if they start raising you/overdefend (overdefending being if villain raises something like 86s here which should prolly be folded).

I'd expect the EV of checking for 99 to be better then betting as well as 76s, i mean if the risk -> reward is there in that you have an initially profitable bluff OTF then yes it going to be +EV and if you don't have that initial profitable bluff OTF don't even think about bluffing, but what happens if villain calls?

You are going to be drawing dead vs their calling range as opposed to if you bluffed with something like Q9. Also equity wise 99 and 76 is just ****e vs a lot of opponents ****e as well...

Aww you guys are so nice to each other when your talking about GTO. You have a little disagreement and you deal with it all amicably. This relationship you have with each other is honestly really endearing. Did you meet online??

I don't want to ruin the moment, but you missed something out in your summery, so I just thought I'd say... Me n Rob were right again

I wanted to go back and address some of these comments individually because I don't agree with some of the things you are saying. I am not trolling just expressing my ideas on this subject to have them critiqued by others and to help others learn.

Minor quibble but a polarized range is defined as betting strong value hands and air so by definition we would be doing this if we bet polarized.

Also if we arrive in a spot where we exhaust our pure bluffs and have to bet hands that have significant showdown value it's likely we would select a bet size that would not make sense for a polarized range or would want to bet a large amount any way.

The bolded part does not make sense. You certainly want to check hands that have low equity and no showdown value. Just look at 7h6h from Arty's snowie example. It hardly ever gets bet and mostly gets check folded.

I don't think anyone was arguing against this. I wasn't arguing against it. I was arguing that in this contrived example 76s is too weak to use as a bluff but that doesn't mean all hands that aren't pairs or immediately draws are too weak to bluff. Take ATs for example. According to my equity It's only a 70/30 dog vs even a pretty conservative range of only made hands. It only has back doors going for it but it would be a much better betting candidate here because of blocker effects (76s had 24% equity for what it's worth).

Your argument seems to be focused a lot on showdown equity. This is not always an appropriate substitute for EV.

That is probably the perfect example where having a polarized betting range won't be ideal and we will select bet sizes more appropriate for our range vs our opponents range.


So here is where I get lost. I don't know why you are comparing the EV of 2 different hands as if it means something. You should take the most +EV line with any hand and if the EV of 2 options is equal with that hand you can choose either option 100% or choose both options with certain frequencies.

If JJ makes more money checking you should check it. It doesn't matter what the EV of your other hand is. You take the most profitable line with that hand too. Your range is just a consequence of the fact that different hands have the same betting line to maximize their EV. This is how poker solvers work.


I would say we disagree on what protecting your equity means. What you describe above (i.e. making an opponent fold his equity share) is what I would call bluffing though I will agree the term is antiquated and there are plenty of situations where we have the best hand now and would prefer a fold.

What I was describing is betting to prevent villain from correctly bluffing you thereby robbing you of some of your equity. There are even situations where you can bet and not expect to be called by worse and your still better off betting than allowing villain to force you into a 0 EV call.

I think I agree with what you're saying here but I am certainly confused by the way things are worded. Again it's as simple as take the most EV line with your hand and don't worry so much about constructing the perfect range of hands off the table.


You seem to be omitting all those other boards were we already have the best hand. That's where we make our money for the times we whiff. That's also where we lose our money when we start adding random opens to our UTG range that may or may not be profitable.

Board coverage is something to consider but mostly only when stacks get deeper and having the nuts in your range is more important. If you and the new pro sitting to your left have 200+bb stacks then yeah you may want to worry about board coverage but there's so many other factors that influence the EV of a single hand at that depth board coverage is probably only a minor factor. And again tons of other boards that aren't so terrible for our range.

Your EV for your strategy at large is just the summation of the EV of your individual hands. You maximize the EV of your individual hands and you will maximize your overall EV. It doesn't have a whole lot to do with board coverage. There are literally times where you will be caught with a weak range completely due to the chance nature of the game. That doesn't mean you try to throw in hands in your range to eliminate that possibility.

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^ Good stuff, JG.