pre flop ambiguity.

I'll try and get it started. Minimum defense frequency is defined as: Pot / (Pot + Bet). Here, UTG 5x vs BB, all folds, at 2-3, ignoring rake, it should be 5 / (5+15) or 25%.

So, (assuming I didn't botch this) we have to defend 25% of our range, ignoring things like being OOP, IO, etc... You said you are wanting to tighten up. I don't see anything wrong with tossing all three hands then.

If you did want to defend, I'd consider 3!'ing, not calling, the ATo hand (blocking the ace). This is mostly a bluff.

At 400 effective, calling a 15 open, means SPR will be 12 to 1. Not deep enough for me to mess with 53s or Q8s, honestly, esp OOP. QTs, sure, though I'm sure it's a leak.

We're supposed to fold the blinds, mostly.

I’m folding all 3 of these without a second thought.

The bit about MDF above is very wrong. The idea behind MDF is that if you fold more than MDF dictates your opponent can print money by bluffing. But this is an UTG raise. This guy isn’t thinking just about exploiting you because there is a full table of other people who are also reacting to this raise. They will not always fold around to you. That means you can continue much tighter than MDF with no worries.

"I know there are solver approved ranges but these assume you are playing against perfect playing opponents."

To be clear, those ranges represent the maximum you can earn while losing the minimum to the worst possible case scenario of opponent strategies. It is safe to assume, then, that any hand that is a pure raise (ie: +EV and not just breakeven at a mix) for a given size in that scenario, is a profitable raise regardless of who your opponents are. They become much more profitable facing live bozos.

The question is what exploitations you can make beyond that. One of the most consistent leaks in live games is the passivity, and raising for a larger size with the same range is one simple exploitation of that. (Whereas against the aggression seen at equilibrium, your biggest liability when raising large is running into a top hand from any of the many players remaining to act.)

"Some sites say to open UTG with any pair. Some say to open down to TT's+. Others suggest down to 66's+. Some sites include T9s, 98s etc in ep. Others do not."

I think bar none the least helpful thing you can get out of looking at solved hand charts is looking at specific combos. The overall frequencies, the proportions of different hand types, the ways they get coverage, and how each of these change given different factors are going to be much better broad lessons to take away.

"Nobody opens for 2.5x in cash games. Is there any information regarding a basic 100BB game where the opening sizes are more realistic? It's rare that I see an open size less than 4x."

Solver study is a lot of triangulation. How much do frequencies and compositions change facing a 2.25x raise versus a 2.9x raise 100bb deep, and how much do they change facing a minraise versus an open jam 15bb deep, etc, and how do you extrapolate from there?

Mathematical study is also helpful here. How much do you "need" to defend against those different sizes in theory? How wide can they sustainably raise for those sizes? What's the hot-and-cold equity of different hands facing those ranges?

"Many times the open is 5-7x."

Spoiler: At these extremes, you kind of just stop flatting. Ez game.

Taking the MDF math above, at least one player acting after UTG will show up with a top 5% hand 33% of the time, so they are never getting direct odds on a pure bluff.

There are some specific combos and ranges that still defend the BB and maybe flat the BTN, but the most important thing in the whole wide world to figure out when people at a live table are opening for 7x is how wide is their range, and so what range can you 3b against it from different seats. The like 0.07 EV defenses are both rare and inconsequential relative to the EV hemorrhages going around most the time.

"Hand 1) Tag UTG opens for 15. I am in the BB. This is a bigish raise size. I realize I should be playing tighter. Assume I am the effective stack with 400 in a 2/3 game. Assume the UTG is a solid winning player. Assume I have a tight image. It's folded to me. What am I doing with these?

ATo
35s
Q8s"

These are all folds for 3x, much less 5x with murderous rake.

"Are we only 3 betting AK+ AA, and KK's?"

No. Sizing is everything when it comes to your flatting range, but not nearly as important for 3bing. Obviously an opponent's size may affect my assumptions about their range width, which will proportionally affect my frequency, and the changes to my flatting range have knock-on effects on my 3bing range (3bing some hands that would have otherwise been stronger calls).

"Is there a standard defending percentage we have here?"

Yes, and that's where I'm saying your inquiry should start when looking at these situations.

Fold all those hands. What you 3bet depends on rake and how v responds to 3b. You should 3b QQ+, AK. AKo and QQ can flat sometimes if the game does not have rake, but you want to continue more with a 3b if the game is raked. KQs is also probably a 3b, and then sometimes with hands like 65s and A5s. This is where you just have to consult preflop charts. GTO Wizard does have sims for 5x open sizes.

So you basically never "squeeze" except with premiums...even against a TAG, who is the player type most likely to fold to a 3-bet?

Regarding preflop, I would basically concentrate on getting yourself in situations that *you* are confident/comfortable in (not the expert, not the computer, not the YouTuber, not the forum poster, etc., because it will be you playing out the rest of the hand, not them).

Personally, against a solid winning player who is opening UTG and us OOP in a raked game, I'd simply ask myself what hands I think are likely going to be profitable for me in this situation. None of the ones you listed make the cut for me. There is pretty much no reason to "defend" our BB at a typical LLSNL table in this spot. IMO.

GcluelessNLnoobG

Face. Palm. You're absolutely right. Oh well, this is how I learn.

Still playing with the idea, maybe tied to a model of MDF with multiple defenders, but yep, definitely not the way as I stated. Thanks!

Is 3! ATo mostly burning money with the 1-2->2-5 contingent, given how sticky most openers are, esp if opening in EP, they've waited all day for JJ-KK and they don't want to fold it, plus the large typical open sizes?

If they're tight though, are they opening a lot of stuff in EP that's going to fold to a 3!?

At risk of derailing this thread, MDF with multiple defenders is incredibly tricky. The “burden of defense,” so to speak, is not spread evenly among the remaining players in the hand because of relative position considerations. In fact, in some cases where the OOrP players are capped, they can sometimes be folding 100% of the time. However, in this example preflop this is not the case since everyone can still have anything when this raise is made. The UTG raiser is naturally checked by the possibility of someone waking up with a playable hand behind him, and in that case someone else will enter the pot before it gets to you.

Most populations underfold to 3bs across player types and stakes both online and live. I have my explo-strats for players who overfold to 3bs locked and loaded at all times and sadly I don’t get to break them out much.

There are lots of caveats to that, but EP raisers in particular tend to underfold. (Myself included, by the way, it’s just soooo hard to find enough folds with gorgeous hands.)

In any case, 3bing frequencies are so narrow in this configuration that you could use a maximally polar strategy, and ATo still wouldn’t make the cut of hands to pull out of the muck and re-raise with.

I'm going to note that if the UTG is raising 5 BB pf, they aren't a solid player. The factors involved include whether this is their standard raise size when opening or do they vary it. If this is their standard raise, most likely they have a tight raising range. They won't be able to be a winning player raising this much pf and having to fold a significant amount of the time when they miss on the flop. If they vary, is this higher than normal or lower. Most likely it will be higher, meaning their hand isn't AA but a hand they prefer to play HU or just win the blinds. That is likely a range of high pocket pairs and AK.

I agree with the others that none of the hands you listed should be playing pf regardless in the situation described.

Answering your question about why the starting hand charts are different for different creators, it has to do with the underlying assumptions the creator makes about their villains. In a GTO scenario, the assumption is that you want to play an unexploitable game and the villain is doing the same thing. For a player at low stakes, your villains are going to play an exploitable game and more profit can be found by exploiting their mistakes than just making yourself unexploitable.

With various charts that aren't GTO, the creator is assuming a certain level of skill for the Hero and the various villains. Some creators will tell you about their assumptions (this is for a novice player). Others will simply say, this is how you should play, meaning this is how they play. The less skilled a player, the tighter the range will be. The reason is that a skilled player might be profitable with a hand like 88 in an earlier position while the novice would lose money. In many cases, hands are marginally profitable. Eliminating or adding those hands at the margin are going to make little difference. So the creator's bias with certain hands is going to play a role. As the founding mod KurtSF of the low stakes forum wrote, most winning players net profits come from being on the button or having AA.

Why would we want to play low pocket pairs UTG? Are these low frequency raises just for balance? Are we playing these hands or not based on how agro the players behind us are? Are we playing these lower pairs only if we have a deeper stack? If I start with 100BB should I be cutting out the mid to lower pocket pairs? What is the worst pair you guys usually open with UTG?

Continuing with the original example of a 15 raise UTG. How tight should our BB range be? I've seen examples where the button opens big and the solver suggests a mostly 3 bet strategy. Obviously we can't be getting too out of line against an UTG raise. We have established that the hands I presented are folds. What do we call with?

AQo+

3 bet AA, KK, AKs?

Are we calling broadway suited hands? Are any of these being turned into 3b bluffs?

Are we calling any suited connectors? Are any of these being turned into 3b bluffs?

Are we calling with any pair and any Ace suited?

How does your strategy change based on having a 300 stack or having a 600 dollar stack? Assume villain covers. This is in a 2/3 game.

Okay this "section" of the post alone ended up being massive, so I'll just post this standalone:

When non-broadway cards mix a raise or fold preflop, it is essentially for board coverage. Against a maximally exploitative opponent who knows your exact range, you will make SO MUCH money with these hands on boards that miss the rest of our range that those become 0EV raises.

Of course, in theory, those hands can only be included at certain frequencies before A) creating imbalances in our range (eg: our ability to continue with enough hands to a 3b), and B) those ranks get represented enough in the range it defeats the purpose of board coverage in the first place.

It's interesting because these two things are in tension with each other when playing bad passive players. You'd think you can play more of these hands because imbalance doesn't matter and everyone's worse (so EV just goes up in general), but you'd also think the conditions that increased the EV of these hands in the first place (aggression and employing strategies that are sensitive to our range and tendencies) are diminished, so mixing these into your range isn't accomplishing much.

I have three things to say on this:

1) I've been playing this stupid game for long enough that I remember when people were first starting to phase OUT low PPs from EP raising ranges. The conventional wisdom at the time was that your bottom line comes entirely from sets, TPTK, and overpairs so open folding 55 because you were in bad position was kinda tantamount to folding AKo because it's just A-high. At that time, most people who open folded pocket pairs were young sharps who were analyzing real-world databases and empirically observing what hands were losers taking which actions in what situations.

I don't know *precisely* how a Party Poker table during the Moneymaker boom compares to relatively solid low-stakes live games now or how your typical LLSNL poster compares to a 2005 online crusher, but I'll just say it seems compelling enough a comparison that I will default to it in the absence of equally compelling data/theory/arguments.

2) The 3b frequencies against EP opens at equilibrium are so low, and low stake live fishes' frequencies are so static across configurations, that they actually kind of accidentally converge. My base assumption for an low stake live player's 3b frequency is 3-5% (with reads, some become higher than that, some become lower than that), which is essentially the range within which each seat should be 3bing an UTG opener in a 9 handed game (maybe it's closer to 4-6% for relatively aggressive ranges that implement all the mixes at a lower size). So this is one spot where I wouldn't really say you're facing less 3bs than you would at equilibrium, and so at least some of the problems of bloating your range with hands that are only contingently breakeven will materialize in the real world.

Of course, the opponents are still garbo and the EV of many hands goes way up in these games. The big leak is that players are cold calling waaaaay too much, which I think just means clear preflop value hands increase in EV (which is both to say AA gets fatter vbets postflop AND the value of bluffing KJs when it whiffs goes up).

And also, this is only relevant to this one particular configuration. By the time you get to the LJ (where 3b frequencies should be closer to 6-8%), and especially in even later seats (where the 3b frequency should be as much as 15%), the combined deficiency of the remaining players' 3bing strat is going to turn a lot of 0EV hands into clear opens.

3) Raise size matters so much. It matters for how much your range can withstand 3bs (which, again, do not even need to be "light" 3bs in this case), and obviously it matters so much for continuing frequencies. (In practice it probably doesn't matter so much for the ROI of scooping the blinds).

I would not be surprised to find that hands as good as 88 and KTs and A5s are a polarity error to raise for 5x in EP, but in the absence of databases or large enough samples for these relatively infrequent hands in just a couple configurations no one would really know. OTOH, I also wouldn't be surprised if raising 22 for 1/2p from EP is printing.

Again, for people who make enormous preflop raises and multiway bets, etc, I would consider the enormous size the exploit and would be skeptical of both raising 2x pot with 8 players LTA AND adding specious combos.

I wouldn't think so for two reasons:

1) Hot take: Stack depth* doesn't matter** for RFIs.

Okay, now for the caveats:

* Obviously, in the grand scheme of NLHE, stack depth matters a ton. My point is *exactly* how deep stacks are beyond the basic observation that we are a playing relatively deep-stacked cash game (ie: a tournament player would be like "Damn, we're deep-stacked") is of diminishing importance.

** Okay fine, it matters at least a little bit, but following the principle that stack depth doesn't affect RFI ranges will get you closer to the correct answer than most people who account (ie: overcompensate) for stack depth will. Or hell, compare it to something I discussed in the previous post: the effect of raises sizes on theoretical RFI ranges absolutely dwarfs the consideration of whether stacks are 100 or 300bbs deep, but you'll see a lot more people mention stack sizes in the justification of RFI decisions than you will hear people adapting their range given the raise size.

2) For pocket pairs in particular, the sweet spot for stack depth for low pocket pairs in single-raised pots is about 70-200bbs (well, that band is second only to AIPF). Less than that, and the potential payoff for sets starts to put serious downward pressure on the ROI of raising; more than that, and bottom set runs into RIO problems. But within that band, the variability isn't huge.

Don't get me wrong, low pocket pairs mix more at 200bb stacks than at 100bb (and opponents have to re-raise larger in order to get you to fold small PPs, etc). But again, we're talking nuanced changes that would be among the last adjustments you make after already having mastered everything else about that particular branch; not foundational changes to your strategy that make "how deep are we" a question that is asked very early in our mental flowchart.

I personally pure raise 88+ from any position and sprinkle the lowest pairs in like 10% just because I have a personal fetish for tilting people by showing up with either bottom set in seemingly impossible spots or top set when people think I should have raised.

I suspect there's been a non-zero number of times where I incorrectly raised 88-99 and there are some conditions where I pure raise 66-77.

I raise more PPs the later I get, obviously, until I'm pure raising all PPs from CO.

This is where I think talking about exact combos is going to kind of miss the forest from the trees. I would never fold QQ/AK, but beyond that there's a number of ways to construct your range.

If you're going with a pure linear 3b or fold strategy, I think your frequency should be no more than half of their raising range. You could literally just 3b the top 5-6%, or you could pure 3b QQ/AK and mix everything less than that at a rate proportional to its strength.

As you include more combos to flat, you will polarize a bit more and your 3b frequency will start to top out closer to 1/3 of their range.

Etc.

From there, do your own research.

Thanks for taking the time for all of your posts above. I will need to reread these a few times since a lot of this stuff is going over my head at the moment.

It doesn't help that I'm being coy in the post you quoted because I'm veering close to paid content territory.

Yes, a lot of the time..

Using the example hands, A10o I’m folding and Q8s and 35s I’d consider a mix of raise / call..

If the TAG 4 bets it’s a simple fold, and if they call then we get to play post flop being the aggressor

5x can be great when you get under 3bet and still get called wide by recreational players. The more aggressive regs that 3bet you a lot, the more you want to go smaller. Just adjust to what your actual game conditions are.

If you watch Mark Goone's vlog series he even goes straight 25 at 5/5 in unstraddled pots.