KK facing a 4-bet

I'm sorry to say the second and third sentence show you fundamentally misunderstand what the Minimum Defense Frequency is (see point 1 below) and what its application is in no limit hold 'em (see point 2 below), much less how to calculate it given any deviations from the typical toy scenario used in books and blog posts to give a simple introduction to the concept.

The Minimum Defense Frequency calculates how frequently we need to continue to prevent villain from making a +EV bet with any two cards. Two extremely important points:

1) Such a threshold does not exist here. Indeed, this is the very definition of a "protected pot" - a pot where bluffing is not profitable regardless of how an individual player plays.

2) Even if such a threshold did exist, I'm not shooting for it. That's why I said folding is an EXPLOITATIVE play.

I'm sorry, my language wasn't forceful enough. I do not disagree with it. It is the incorrect number to use. The number represents how much villain RISKS in the event that they lose. When someone puts $140 on top with a pair of napkins with the intention of folding to a shove, then they are only risking $140. This is not the scenario here.

You can argue that it is something less than $390*, but $140 is definitively the wrong number.

*It actually is equal to exactly $390 when viewing it from a theoretical perspective, which you seem to want to do. This is because at equilibrium OOP will either only ever continue with a shove or will only call when it improves OOP's EV**, and so there is no scenario where raising $140 more improves their risk:reward ratio. This is why raising to a committed amount does not exist as a strategy at equilibrium.

I agree with your first clause, and I've said as much. The fact that you think the second clause follows from the first clause, though, is a major red flag.

**If you wanted to be so annoyingly pedantic that I woulda actually gain respect for you in a "I'm not even mad, I'm just impressed" sort of way, you COULD point out that this hand is not an ENTIRELY closed system between the OOP and IP player to where any EV gain for OOP is at the direct expense of IP because of the $75 side pot. But scenarios where an OOP flat improves OOP's EV in greater proportion than any EV loss to IP...well frankly, I'm confident they don't even exist in this particular scenario, but even if they did, the effect would be a rounding error from the $390 number. Like literally a lesser factor than rake, or the margin of error on a sim calculated to 0.5% of the pot, etc.

TL;DR: TFW you're calculating the MDF in a protected pot

Oh okay, this is much closer to the correct calculation and would've earned a less snarky response if I'd seen it before posting.

You are still making a very fundamental error: You are assuming one of the factors you should be solving for, namely UTG's equity in an AIPF scenario.

For UTG's equity to be 70% against UTG+1, you are suggesting that UTG is NOT shoving ATC to exploit guaranteed positive expectation based on our strategy of folding too much. Even JJ and AKs do not have 70% equity against 20% of ATC (which is like 4xs wider than UTG+1 should be in theory). The bottom of UTG's opening range is a slight dog to that range.

So you're implying that UTG is only 5b'ing the top 14% of their initial raising range, which is NOT exploiting us.

And again, so long as we always shove with our continuing range and villain never folds to that shove, the denominator should include $390.

But you're going in the right direction at least.

Minimum defense frequency (MDF) describes the portion of your range that you must continue with when facing a bet in order to remain unexploitable by bluffs. Believe it or not, villain can and should have some bluffs here to attack the $25 side pot, because those bluffing combos have enough equity to play against UTG+1's 8bb all in range. The $25 side pot is about 29% of the total pot. This situation is not the same as a classic "protected pot" in which one player is all in and there is no side pot.

What figures would you use for this calculation?

I think you're overlooking the fact that hero is going to fold some percentage of the time (apparently a very large percentage of the time in the case of the OP), which is an excellent outcome for villain and certainly improves the risk:reward ratio as it knocks a player out of the pot. Interesting point about "raising to a committed amount (not existing) as a strategy at equilibrium" - would your view of this hand change if villain had raised to $130 instead of $140 (i.e. to less than a third of his stack)?

Well, the calc's just sort of way off for a number of reasons because once you account for equity you need to use the full semi-bluff EV equation.

All things told, when UTG shoves the bottom of their range, they win about $45 when we fold and lose about $236 on average when we shove and they call, so if we fold any more than ~81% of our range, then villain can print by just raising range. (Technically, these hands have such poor equity against a shove that they aren't even pot committed when they put 40% of their stack in, so if anyone ever starts adjusting by raise/folding $150, you will have to be aware of that!)

Using your 4.9% 4b strat, you would "have to" shove at least 0.9%, which is AA + another 6 combos (again, this is one rare instance where KK goes ahead of AKs as a preferred shoving hand). Using my 4b strat, you would "have to" shove 2 combos of non-AA hands.

Again, all moot because I'm suggesting an exploitative line.

Sure, maybe 70% is a little high - that was just an estimation on my part to illustrate the point. If you give your estimation, we can look at the MDF again, but it's for sure still going to include KK.

Villain doesn't need to jam ATC to exploit hero; the latter has already shown that they are folding KK (and 'exploiting themselves' as a result). Therefore villain can effectively safely 4bet with all hands that have 15/77 x100 - a mere 20% equity vs UTG+1's jamming range, which is pretty wide already. Villain would need to narrow that a little as hero is going to have AA some of the time, but it's still a wide range. Of course this depends on how wide we believe UTG+1 is jamming too, but I imagine at low stakes live poker this is going to be a wide and wonky range, including small pairs, raggy aces, offsuit broadways, etc.

Can you show your math? I see this simply as villain risking $140 to win ~$78. Hero is going to fold sometimes (but sure, when he continues, it will be as a jam).

Can you show me the calculation you would use? Just genuinely interested to see this and discuss, I'm not claiming that you're wrong or whatever.

When is UTG "shoving the bottom of their range"? Thus far I'm only looking at the part of villain's range that 4bets to $150.

I'm not sure what point you are making here. "Have to shove x" - in order to achieve what?

Correct, it is not literally a completely protected pot. So much of the pot is so protected that it pushes the MDF so low that we only "have to" continue with such a nutted range that it would not be reasonable for a non-clairvoyant player to assume they can profitably stack off with 77 because we will fold the second nuts 100% of the time. (Even a clairvoyant player could not reasonably surmise that we fold KK 100% of the time given the responses ITT, including my own which make no bones that I would not ever actually have the wherewithal to pure fold this hand in-game.)

Again, the tone of the post you're quoting would have been somewhat different if I'd first seen your post where you started to account for equity.

Assuming villain never folds once they put in $150, in theory the number is exactly $390. In practice, we are the OOP player, so we can make the number exactly $390 if we believe that is what's advantageous to us.

I will grant you that in the process of running the numbers I realized that IP COULD in theory r/f $150 as a bluff, so if you have any reasonable expectation that your opponent is capable of doing that, then ... well I'd personally see it as an honor to be exploited in such a gross way, but some people have mortgages to pay.

This is again fundamentally misunderstanding what the numbers in the calculation represent and what the formula is solving for. The numerator is amount won when we fold. The denominator is amount lost when we continue. That way, you solve for the continuation percentage (ie: 1 - fold%) that, when multiplied by the other side of the expression, gets you a 1:1 risk:reward ratio. The equation does not need to account for the fold percentage; that is the very thing it's solving for.

I'm concerned that you may have decent knowledge of some formulas, but a pretty tenuous understanding of what the inputs and outputs of that formula actually represent.

Let me be clear that my take on this hand entirely boils down to villain's 5b size. Making it significantly smaller or significantly larger would change my view, yes.

I don't know if I quite buy that villain is raise/folding $130-140 as a bluff either, but $150-250 is kinda peak "lol" territory for me, and every few bbs bigger or smaller his 5b is from there, the less explo my response will be. If he had shoved or made it $115-, I would not be playing exploitatively at all.

*All of the have to's in all of the last few posts are in scare quotes because you do not have to (nor should you) play unexploitably.

Yes, about 70% of the pot is protected, but that percentage drops significantly once villain 4bets to $150.

If villain knows hero is folding KK then he should 4bet with almost all of his range that has 20% equity or more vs UTG+1's 8bb jamming range.

Sorry but I can't agree that the number is "$390 in theory". Villain is risking $140 to win $78. This is why I'm asking you to show an EV calculation where $390 can be used, because I don't believe it's possible.

I'd also argue/agree that villain can have a raise/fold range for his $150 sizing. Yes, it's more than the classic 33% of stack threshold for getting it in preflop, but I think we can be a little flexible with that rule - especially in this hypothetical situation where we are expecting hero to overfold to the 4bet (and if he's folding KK to the 4bet then presumably his jamming range is exactly AA).

Sure, that makes sense and I understand what you mean.

@RaiseAnnounced

Another thing to note here is that if hero is only 5bet jamming with AA and nothing else (as appears to be the case) then villain can exploitatively fold range vs any 5bet, in which case the maximum villain risks at any point in this hand is the $140 preflop 4bet. This is another reason (and I think the best mentioned thus far) that only the $140 value should be used when calculating the EV of villain's 4bet.

Assuming this seems illogical, based on N=1.

You really struggle with this being an exploitative fold, don't you? Or do you not believe in exploitative folds?

The sample size is one hand in every post on 2+2. Obviously it's necessary to extrapolate or it's not possible to discuss anything.

It's perplexing and odd that you often turn these threads into attacks/assumptions on the character of the people making the posts, rather than discussing the issues/concepts at hand. This type of behavior in what should be a healthy debate is honestly quite childish and toxic, and I'm amazed to learn that you are in your sixties - during our first exchanges on this forum, I thought you were a teenager. "Debating" in such a manner (with ad hominems and other personal attacks, instead of responding to the points made) is how children behave in the playground, and how people with personality disorders (or just an outright lack of intelligence or social skills) behave in life. Frankly it smacks of a lack of formal education, and some form of unresolved insecurity/need to try and feed on other people - and it's pretty incredible that you don't have the insight to understand that at your age.

It's not an exploitative fold, it's an exploitable fold - as is clear in the discussion above. It's a clearly minus EV play that villain can exploit in numerous ways. Of course exploitative folds exist, but this is not a case that warrants one. You've described villain as a TAG and yet you're folding KK to him preflop in a situation where he's incentivized to go after the dead money in the pot. It's a bad fold, because you're scared of monsters under the bed (in other words, always putting villain at the top of their range) and as a result you're playing emotionally rather than using any modicum of poker logic or reasoning.

You're not making sense. We're talking about observations of human behavior. Stick with topics you know about.

We're getting hung up on the Janda math, so let's make this simple and rewind allllll the way back to Sklansky math. Let's just calculate some basic EV:

Let's say we're the UTG player and we hold JJ. Same action happens, and we are looking to solve the EV of r/c'ing when BB shoves an overpair 22.3% of the time.

So EV = Lucky number 0.777*(Net gain when BB folds) - 0.223(Net loss when BB shoves)

Let's say we have 60% equity against UTG+1, so we win 25+0.6*76-0.4*15= 64.6 78% of the time, which is $50.19.

For the amount lost when BB shoves, for simplicity's sake we'll say we lose the $390 of our remaining stack 80% of the time = $312 and we gain the pot+the remainder of BB's stack = $435 20% of the time = $87. Combined, we lose $225 22% of the time = $50.17

So we are losing two shiny pennies by r/cing JJ when BB shoves any overpair 22.3% of the time.

Okay, a couple of questions:

1. Why are we only looking at this from the point of view of when we have JJ? Shouldn't we look at the EV of the range in question?

2. I'd argue the amount lost when BB shoves is $140 because we know that he will fold KK to any 4bet and therefore we can fold everything except AA when he shoves. In other words, villain is not committed when he raises to $150.

3. Following on from the first point, I would say that any hand that that has 20%+ equity vs UTG+1 8bb jamming range should be 4betting (and folding to a jam).

I don't have time right now but can look at some math in relation to this later.

Honestly, I don't think you can infer that much information from villain's raise size, and I think doing so involves making some pretty clear and unreliable assumptions. I see players make sizing errors on a daily basis at live low stakes. And if villain was aware you were thinking that way, he could use it to exploit you.

How so? I'd argue that folding KK to a 4bet in this spot allows villain to bluff with *a degree* of impunity. The only thing stopping him really pushing the boat out is the UTG+1 player being all-in (as we've discussed). This is why my view is that villain can 4bet with the entire range that has 20%+ equity vs UTG+1 (which he obviously couldn't do if hero wasn't overfolding). And in addition to that, he can exploitatively overfold when hero responds with a shove, allowing him to lose the minimum when hero turns up with AA.

For simplicity's sake to demonstrate a point.

The idea behind MDF is that if we don't meet a certain threshold, then villain can bet their entire range with impunity. If villain's strategy is -EV even with a hand that's in the top 1/3rd of their range, then clearly we're not failing to meet the MDF.

That doesn't mean our strategy isn't problematic for other reasons. (It is.)

I'm kinda running out of ways to say this: if villain ever 5b/fs $150, then he his risking $140. If he does not, he is risking $390.

I genuinely cannot remember the last time someone that I so much as suspected to be a reg either online or live 4b+ 40% of their stack preflop only to shove to a fold, so entertaining the possibility feels a bit more like an interesting toy game than actual poker HH analysis. But I have been careful to caveat my posts nonetheless.

To be clear, the "sizing error" I believe villain is making here is picking a size that makes it apparent he's playing for stacks without trying to maximize his fold equity. The commonality of such a sizing error makes my assumption better tested, and so more reliable, not less so.

This is necessarily the case with any exploitation. We've kind of circled around this a lot in this back-and-forth and I'm still not clear on this: Is your position is that we should never deviate from GTO and that playing exploitatively is necessarily bad?

In any case, if it makes you feel better, it's an exploitation I would not actually make at the table any more than 50% of the time.

To be clear, the exploitation villain is able to make is that he's able to 5b/f 40% of his stack. Sure, if villain is able to pull off the poker jujitsu of forcing us from the pot for $140 without ever getting his $390 in with the worst of it, then he's printing.

Putting aside the likelihood of villain employing this counter-exploit (see above), I will point out that this exploitability is made possible by the fact that we are not shipping AKs more-so than it is from us folding KK. I've mentioned several times in earlier posts that KK is a better hand to ship than AKs here (precisely because I've assumed villain his committed himself to going AIPF with this sizing) and no one seemed to take issue with that statement then. No one was saying "Oh but RaiseAnnounced, you simply MUST shove hands other than big pairs lest villain will surely stop feeling committed to a shove and we won't get value from KK+ anymore!"

No, it was all well-and-good to assume villain was committing himself with this $150 5b when it was a factor in FAVOR of jamming the hand we happen to hold in the HH, but once that assumption allows us to play tighter overall well NOW it's a problematic assumption.

The problem is that, whenever kk goes all in against a weaker hand it is not posted. We only get the posts where it's as so we are biased to think the shove is always aa. Just watch the polk video. There's another video where polk folds kk correctly but that is some insanely deep hand not 140 bb

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1/3 is a limit where regs don't GII with worse than KK/AA, and as a result you have to be able to fold KK.

Most players at 1/3 will happily get the money in with QQ+ and AK at the bare minimum in my experience.

Instances where you fold KK pre are rare as a percentage of hands played, and they’re nonstandard insofar as any hand that involves a cold entry into the pot is somewhat nonstandard, but it is very easy to devise scenarios at a 9-handed table where KK should fold a non-zero frequency.

It just so happens that almost any 100bb+ hand that involves a positionally aware UTG and another tight EP player reraising each other and another sane player entering the pot cold, and then someone shoving after that will mean that at least one of the players should fold KK a non-zero frequency.

Only exception I can think of off the top of my head is like UTG raises, UTG+1 3bs, BTN cold calls, UTG overshoves <120bbs. UTG+1’s gotta just go broke with KK there and BTN shouldn’t really have KK in their range. Other than that you can pretty much write the second paragraph on an index card in black ink and use it as a flashcard.

Fun with numbers time!

Let’s see how often the above scenario would occur naturally in a live game:

First precondition is that we have to get dealt KK, which is 0.45% of hands (ie: every 200 hands, or 8 hours of live play).

For now let’s see how often all the other conditions will be met when we’re not in EP.

So next precondition is UTG is someone who is tight and/or positionally aware enough that a raise-first-in from them limits them to 10% of hands (let’s say this is 1/2 the population) and they raise. We meet this precondition 5% of the time. So far this already only happens once every 4000 hands, or 160 hours of live play.

Then, one of the other EP players needs to re-raise them, which should be 5% of the time. We’ll say there’s an average of 2 other EP/MP players who are sufficiently tight to meet this condition, so there’s a compounded probability about 10% that the UTG raise will be reraised by someone with a sufficiently tight range.

We’ll assume once the above preconditions are met, we will cold 4b KK 100% of the time. So we’re cold 4bing two tight/positionally aware EP players once every 40,000 hands or 1,600 hours. We’re already at about once per year for a full time player, and no one has come back over the top yet.

I’m sorry to say my IP 5b over a cold 4b heuristics have not yet been developed so this paragraph is speculative, but sufficed to say KK+/AKs is 1.25% of all hands (so top 1/8th of UTG’s range and top 1/4 of the 3bettor’s range) and they should not be 5bing anywhere near 100% of those hands. I think saying they have a compounded probability of 5bing about 1/4 of the time is fair. So we get 5b in this scenario once every 160,000 hands, or 6,400 hours, which is about once every 3+ years for a full time player (and obviously much more than that for anyone playing less than 2000 hours per year).

(The probabilities just happen to be quite similar when we’re dealt KK in EP. Say were the UTG player, the “tight EP open” condition is met 100% of the time, but then we need to add a “cold 4b from same player” precondition. A player should cold 4b a 5% 3b range about 1.67% of the time from most seats, and we’ll assume there’s on average 3 players at a table who are sufficiently sane for us to give them that tight of a range when they cold 4b. 0.983^3 is 0.951, so it ends up being pretty much the same 5% number as the “tight EP opener” precondition that we’ve replaced. When we’re dealt KK in EP/MP, then all of the conditions are actually met LESS frequently because we’re replacing the 10% “tight 3bettor” condition with the 5% “sane cold 4bettor” condition.)

And allllll of that being said, KK still won’t necessarily fold 100% of the time and it could be dependent on sizing or live tells, or quite frankly, whether hero is playing well enough to even notice that they should be considering a fold.

There are of course other scenarios where you’d consider folding KK, like an extremely nitty opponent or being very deep-stacked.

So yeah, the numbers line up with “even the pros who are grinding thousands of hours a year only fold KK once every couple years.”

I haven’t been put in the spot live yet, but it crops up like once a year online.

This has been bothering me since I posted it, but I just wanted to say that the number of professionals who actually play 2000 hours of live cash game poker is so low as to functionally be zero. Anyone who has a big enough platform for you to know how many times they've folded KK preflop in the last 5 years is almost by necessity not living at the tables 40 hours per week, 50 weeks per year.

Doug Polk is spending enough time streaming bankroll challenges, running Upswing Poker, playing in tournaments, etc, and even the cash game hours he does book are often going to have so much nit button/7-2 side bet/bomb pot shenanigans and can only spread 7-handed most the time and have an expectation that nit-folding KK preflop will get you uninvited from the private game that I feel confident it takes him many many years to book 160,000 hands of "normal" live 9-handed poker.

This is no knock against him, by the way, he's STILL probably booking more live hands than I am even with all those poker-related side hustles.

There's like some random guy who did an AMA here recently who actually plays 2000 hours a year who commented on the number of times he's folded KK preflop (I think it was like twice in his 10-year career), and even he said his cash game hours have lagged some years due to playing MTTs.