22 can flop sets and stack off the wide range just like the tight one, plus it can be the best hand at SD.

Your implication that a tight range won't be able to get away from anything if you spike a set is not how it works. It's all relative to what your range is and how you play your hands. Say he only has QQ+ in his range. If he knows you know that, and you're only giving him action when you spike huge, then it could be an easier fold then 2nd pair in a blind vs blind senerio, where ranges are wide.

The wide range won't stack off nearly as much as the tight range. It also doesn't have good showdown value. It barely has 50% equity even against really bad hands by the river.

No. But we need to come up with some sort of strategy for the Villain, so we can compare EV. So I think it's fair enough to say that the Villain will stack off with over pairs.

Not sure what you mean by this.

pg_780 do you play limit hold 'em?

yes

exclusively?

This is not what I'm saying. We'll obviously balance our raises with bluffs, so he's indifferent to calling or folding with his over pairs. We'll do the same when we're up against his wide range.

The conclusion is the same. 22 does better against the tight range.

The chances of someone stacking off to your set are much higher when he has a wide range, because you should be bluffing more and value betting more. If villain has any poker deduction skills at all, his overpair could be a very easy fold, given the board. This is what I mean by relativity.

Any hand which is +EV to play vs a tight range will also be +EV to a wide one. (assuming villain playing skill is equal)

You're making leveling assumptions between villains. I think as a generalization any poker theorist would agree that 22 will do much better against a tight raiser who's more likely to have an overpair or TPTK then a loose opener's range. A loose opener's range is only going to stack off when he has like 2 pair, and sometimes not even then, a loose opener's range will have a lot of semibluffs involved with it as well and is knowingly only going to bet huge on the river when it has a flush or straight anyway. If it's playing 86s and you spike a set against him, even if he has top pair and you raise him on the turn it's much easier to fold plus you're going to have reverse implied odds with the set because you'll be facing draws against 86s hen if you have AA or AK on K52r facing a dry board in any poker situation.

It's common sense really.

You're speaking of strictly pre-flop equity, which you're correct, but we're talking about big pot equity.

I've played a decent amount of NL, but FL on-line is where I do all my grinding.

that's probably where you're misconception is. i'm not saying you don't know NL but limit is a different game and I can understand why you'd think this way from your limit experience.

Nope, you're not getting it.

The assumptions I'm making are pretty fair. (That villain knows we know something about his range) This is a game theory perspective, but we're talking TAGs or LAGs, so they are at least someone capable of thinking.

Still, there isn't a single hand where you'd call a UTG raise but fold to a BTN raise.

I understood your point after your ninja edit and responded to it in a different post.

But as a quick repost. We can simply balance our nuts with bluffs, so the Villain is indifferent to calling or folding.

Let's assume that against a tight range that you're post flop EV for 22 is 4 bb.
Let's assume that against a wide range that you're post flop EV for 22 is 2 bb.

Now let's say that you need to call a 3bb raise pre flop.

TOTAL EV for 22 against tight range = +1 bb
TOTAL EV for 22 against a wide range = -1 bb

Preflop: you should call against the tight range and you should fold against a wide range.

If my range is wider, he should need less of a hand to stack off. You're saying the opposite

(waking up)

I've heard of balance before...

I have no frame of reference for these numbers, but I don't buy that 22 is a call vs 8% range, but a fold vs a 25% range.

Well than you'll understand that the Villain is INDIFFERENT to calling or folding his over-pairs against our strategy. So, your argument that he can simply get away from his big hands is invalid.

Well do agree that 22 will do better against a tighter range post flop.

And if so, then you must agree that if the pre flop raise amount is in-between those two EVs, then it will be correct to call against the wider range and fold against the tighter one.

I'll word it better:

If the villain is the same, it can't be +EV to call with 22 vs his UTG range, but -EV to call 22 vs his BTN range. (If we're in the BB, say)

Okay, we're playing GTO now. (That's always kind of my approach)

In order to keep our balance, we should widen our range along with his and he should still be indifferent to calling or folding on the flop given our entire value raising range--which will be wider now, in proportion to his widened range.

So he shouldn't be more likely to stack off with his tight range or his wide range, because we are supposed to have an adjusted value raising range which he, in turn, should have adjusted to.

But we could also have a vbet/bluff balance against a wider range. Just because villain will pay us off more when he has a tighter range doesnt give the hand more value. If he is not paying off enough then we gain value on our bluffs.

It doesn't make any sense to want to tighten your calling range as your opponent widens his raising range. You would just be exploiting yourself.

This

It doesn't change if it's the same Villain. Against the very same Villain, it is higher EV to play 22 against a tight range, than it is vs a wide range (this is even more true when you're out of position).

And if this is true. Than it can absolutely be true that you could be getting the correct price to call with it pre flop against a tight range but not the right price against a wide range.

Below is the math for the SAME VILLAIN:
POST-FLOP EV of 22 (so the EV once you're on the flop)
Against a tight range = +4 bb.
Against a wide range = +2 bb.

So even though it's +EV once you're on the flop to play 22 against either range, you can see that it's higher EV against a tighter range.

Assume you had to call a 3bb raise pre flop.

It's -EV to call against the wide range, but it's +EV to call against the tight range.

----------------------

Now as long as you assume that it's higher EV to play with 22 against a tight range, than we could absolutely find a pre flop raise number in which it would be correct than to fold against a wide range.

You can just tell me what the EV is against the tight vs wide range (post flop), and I can obviously give you an easy pre flop raise amount.

But you are just pulling numbers out of your ass saying "assume EV with 22 is higher vs a tight range, then do all this math and look we prove that 22 is higher EV vs a tight range than a wide one." That doesnt mean anything, you are only proving your own assumption.

The higher EV of 22 vs the tight range (if that's indeed true) is because players stack off with overpairs way too much, which means you've exploited him, whether you've intended to or not. If everyone you played against played perfectly GTO, and so did you, the 22 would do better against the wider range.

Rainbow Bright, there are a few points you've made since my last post that I do agree with, but I'm going to bed soon and may not address them until some later date.

This point here is still a real sticking point for me as I feel you have still not addressed it sufficiently imho:


"Someone who is a LAG will neither have a strong enough range which will pay you off nor will he fold enough to post flop that you can bluff him and make a profit."

If this statement were to be true, this LAG needs to be virtually unexploitable. He has to be a really good hand reader, and have a decent skill edge over the Hero cold calling with T9s.

Let's look at it from the LAG's(villain) perspective and assume the following:

1) He is going to raise his 50% laggy opening range from the CO
2) The TAG(Hero) player is going to call with a wide range on the button that includes hands like T9s

If your statement is true for the LAG player never paying off, but never efficiently being bluffed off the best hand frequently enough for villain to be able to profitably call preflop with x range (unexploitable player). Then we should be able to apply it the other way around and say:

Once Hero calls preflop with x range, Villain is unable to get enough folds, but will also not get paid off when he hits.

Forgive me if I'm misinterpreting something here but this is the message your logic is sending when you say:

"Someone who is a LAG will neither have a strong enough range which will pay you off nor will he fold enough to post flop that you can bluff him and make a profit."

So now both players in the hand are unexploitable? While it is theoretically possible 2 players could play perfectly balanced and that is what one must do post flop in order for that statement to be true, the chances of it ever happening are as close to zero as it gets.

The HERO player in this example has one advantage by default: Position.

Card strength/playability(yes I agree with you that a more playable hand can be better than a hand with higher equity, and never disputed that, pretty sure I posted an example displaying my thoughts itt) there should be emphasized as an advantage as well, but becomes less and less important in the presence of a:

Skill Advantage.

Basically if Hero is a bad TAG on the button and a good LAG opens up in the CO, hero should play really tight and avoid this guy until he learns how to hand read and exploit villains better. This can even mean folding small pp's *gasp* because they are too fit-or-fold but will make costly mistakes in more marginal spots.

If Hero is an OK TAG on the button and a GOOD LAG opens up in the CO, he should still play fairly tight but can definitely add in a few more hands to his calling range.

If Hero is a GOOD TAG on the button and a GOOD LAG opens up in the CO, hero call significantly wider. The playing field is now level in terms of skill, Hero has a positional advantage. The LAG is opening up enough trash here that calling with good hands (hint 9TS * gasp * ) becomes a no-brainer.

The whole "well the lag can balance by check folding the right amount etc" argument is meaningless because Hero has just as much ability to balance his range + he has position.

And I'd just like to add, that the balancing act is much easier in position that it is out because it is less complicated. Oop, we have more possible lines that can be taken by having to act first. For example: we have c/f, c/c, c/r. In position, if we are checked to, we only have one decision to make on the flop if we also decide to check. So our checking range is its own category, but oop our checking range is divided into 3 sub categories. Balancing here is difficult, which is just more incentive to play more hands in position.

And when our opponents are really loose, we can widen up those ranges even more to put them into more spots where they have to play this difficult balance game at a disadvantage.

This is generally pretty clear to me at the tables when I see how ridiculously almost every villain is when they raise preflop and check the flop.

They either a) c/f the majority, b) c/c the majority, or c) c/r the majority(this one is usually the lowest but on certain flop textures it is occasionally obvious that a c/r is inevitable when they decline cbetting the flop).

Basically, it is much easier to accurately guess what somebody is going to do after they check a flop, than after they bet a flop.

So in a nutshell, I'm still overall certain, that against wider opening ranges, we can widen our calling ranges.

That does not mean we always should, especially if Phil Ivey is in the CO. There are of course other things like skill and hand playability to factor in. I was never advocating that we just open up poker stove, slide the bar over to x% and paste that into our calling range based on y% opening range.

I am only saying that as a general rule the wider the raiser, the wider my calls. If Player A is top a notch LAG I will definitely play tighter vs him than I would Player B who is just a 53/40 drooler. But I will call with a wider range on the button vs Player A's CO range than I would his MP range.

Sorry tldr, I hope that makes sense to you because it well, makes sense.

As far as the whole 22 vs T7o thing you posted goes. I do agree, and I don't think PG meant to disagree on that point either.

The thing that makes 22 a vastly more playable hand its ability to more frequently realize massive equity on the flop. Its certainly an easier hand to play, and overall should be a profitable hand to play whereas I would imagine that most full ring or 6max players are losing with T7o just from it being folded close to 100% in the blinds.

This is a pretty extreme example however, and goes without saying.

"So having more equity pre flop does not guarantee that you'll be able to realize that equity more."

This statement is true in the context of the above example.

However, if we apply it in terms of range vs range, then it doesn't apply. If we have a stronger range, then we do get to realize our equity more.

If you open 50% of all hands, you pick your top 50%, and your perfect clone has position on you and calls you with his top 40%, he gets to pick his range, he is going to realize his equity more often than you are.

If you open 60%, and he calls 50%, he once again realizes his equity more often.

All things being equal, but you being out of position you cannot overcome this disadvantage. So the more you open your raising range, the more he can open his calling range HAS TO BE TRUE!

Great. Mine as well.

Yeah, but we're not talking about the EV of our entire value range. We're just talking about the EV of 22. For example, no matter what a pair of 22 is NEVER going to be in our value raising range regardless of how wide the Villain opens. So on the flop, our value raising range will always be the same with 22, it will be the times when we flop a set. Right?

I don't think this is correct or I'm not understanding you correctly. In my opinion. from a GTO standpoint, the Villain should devise a flop betting range which he can bet for value (on the river), and he should in turn balance it with bluffs. You agree with this right?

Now let's assume that we have a static calling range regardless of his opening range (it doesn't matter because we're just arguing the EV of a single hand vs his two ranges). Let's say our static calling range is 15%.

So high tight range of QQ+ will be able to bet for value against our static calling range of 15% at a high frequency on most flops. The reason this is the case is that we need to defend enough to be able to keep him from bluffing with any two cards (obviously this might be difficult -- but we should defend as much as possible that is still +EV). If we defend against his flop bets by raising with our sets, we should balance it with bluffs to make the Villain in different to calling or folding. If I remember correctly, assuming normal raise amounts and 2 players to a normal flop and 100bb effective stacks, this will usually come out to something like 20% of his flop betting range.

So let's say that he can value bet 100% of flops with his range, but he will need to defend 20% against our raises. He will be stacking off with 20% of his pre flop range. Right?

Now let's look at this with his wide range. His wide range won't hit the flop nearly as often. So he won't be able to bet 100% of his range on the flop. Let's assume that he will be able to only bet 50% of his entire pre flop range on the flop. The other 50% he needs to check-fold / check-call some %.

So he needs to stack off with 10% of his entire pre flop range. Let's assume that he will check-fold the other 50%.

Let's do some crude EV calculations.

TIGHT RANGE: 20% stack off. Our post flop EV -- assuming we're never behind:
Postflop EV for 22= (.2 * 104.5) = 20.9

WIDE RANGE: 10% stack off. 50% check-fold:
Postflop EV for 22:
Villain bets and stacks off = (.1 * 104.5) = 10.45
Villain check-folds = (.5 * 7.5) = 3.75
TOTAL EV AGAINST WIDE RANGE = 10.45 + 3.75 = 14.2

CRUDE POSTFLOP EV for 22
Tight Range = 20.9
Wide Range = 14.2

But this was assuming the hand started on the flop. But we know it didn't. In my example I made the pre flop raise size 3x, but if for some reason the pre flop raise size was 17bb, then the following would be true.

TOTAL EV of 22
vs Tight Range = 20.9 - 17 = 3.9 bb
vs Wide Range = 14.2 - 17 = -2.8 bb

CONCLUSION: The correct play would be to call 22 against the tight opening range, but to fold it vs a wide opening range.