I've been thinking a lot about the marginal value of extremely high-resolution solutions.

GTO Wizard has "complex" solutions that use between 8-19 bet sizes per node postflop. That's actually ridiculous.

The thing is, aren't they already highly abstracted by using 1 sizing preflop and solving to 0.4% accuracy post? It seems like zooming in on a 1080p image with an electron microscope. Would you simplify a flop spot to one cbet size, then include 30 sizes for turn and river? No, because that would be crazy. But that's essentially what they've done here.

Now, some solve libraries use higher accuracy or multiple preflop sizes. But there's another, more fundamental issue. Modern postflop solvers completely ignore the bunching effect.

This thread fascinated me. Players' strategies influence the deck. You're more likely to flop low cards than high cards, because players prefer to hold higher cards when they pay to see a flop. The difference between tabling an ace and a deuce can be as high as 1% in some spots, and that card removal magnifies as ranges narrow towards the river.



Furthermore, wouldn't this significantly affect change the correct weighting for flop subsets? These weights are fixed so they completely ignore bunching effect. (brokenstars comment in the above thread made me think of this)

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There are groups spending literally $thousands$ every month on high-powered supercomputers, solving 20 sizes post to super-high accuracy. Yet the equity/EV of individual hands will often be off by a good half percent or more, just due to ignoring card removal.

There is a fundamental limit to the resolution we can (currently) achieve with heads-up postflop solvers like GTO+ or Pio. The thing is, this is actually a very solvable problem. @whosnext managed to calculate the effect in two different ways with simulation and analytical calculation. From a developer's perspective, this is a very doable feature, so long as you provide a default preflop tree. One day I think people will recognize how significant this effect is on the overall quality of their solutions, relative to adding a 3rd, 4th or 20th bet size.

There is definitely some EV to be gained taking into account card removal effects, but the amount of EV to be gained is likely only relevant in a bot vs bot match up to be honest.

The whole idea of a bunching effect only really seems to be relevant, in theory, for two things, though possibly very important things:

1. In the design of flop subsets to feed into preflop sims.

2. Adjusting observed frequencies for the purpose of deducing a range, especially preflop ranges. If someone opens or 3bs a pot, their open range and bb range, conditional on it being deployed, is just their open range or 3b range. But if card removal effects change how likely they are to be dealt an opening combo, you'd need to adjust observed empirical frequencies to get a better idea to what their true open frequency

In practice, it's tough enough to deduce a real-world best response strategy in 20-30secs+timebank and adding in another layer of complexity like worrying about a 40 basis point difference in seeing an ace peel (something I'm still not really convinced is even a thing, though admittedly I haven't seen the methodology used for the above analysis) seems like 0ev additional at best and a huge distraction at worst.

If the bunching effect is significant, I'd guess the time it is most relevant is when action folds to the button, or SB, and that the deck is richer in high cards than otherwise.

It's easy to underestimate this effect. Poker players like to think in terms of their own EV. But think about this; all of your solves, all of your outs, all of your flop subsets, your equity calculations, your training software, almost every solve library out there is gonna be off by a significant amount. Even a half-percent error in the probability of individual deck cards can make a huge difference on the final solution.

I had thought the same thing. But card removal may actually be even stronger heads up. Calling/betting ranges have a significant effect on the flop cards you see, apparently. @Whosnext calculated this graph, based on a simplified heads-up tree:

Card removal by active ranges should be taken into account by every solver, if a solver cuts corners here that'd be quite concerning. Maaaybe some implementations are sloppy with removal when using flop subsets, idk about that.

But in general, the "card bunching" that is ignored by many solvers refers to the card removal effects caused by folded ranges, these wouldn't be a problem for HU though.

And yeah, bunching can definitely sway the ranges of late positions to the tune of a few percentage points, especially for full ring. It's probably not a huge effect in terms of overall EVs, but also not negligible.

Cross-posting from the other thread in the Beginners forum:

It's probably fair to call it non-trivial

And I think even if we somehow knew it were true, it's even MORE non-trivial to quantify the magnitude

And as competitors there are pretty much endless other decisions that almost certainly are far far far more impactful to winrates

But it's something to keep in the back of your head, I suppose.

Other narratives are also intuitive to me (e.g.--an Ace is most often dealt with a shitty sidecard, and there's only 4 Aces in the deck, so even removing 1 Ace is super impactful vs. removing 1 of the much-more-numerous "low" rank cards)



(My buddy's words, not mine--though I wholeheartedly agree with his sentiment)

Put real EV #s to it, then. That's all that matters. Anything else is just being hand-wavey. Using words like "significant" here is a HUGE leap beyond what you've shown.

Also, it's a zero-sum game: assuming this is even something that matters, then it's not really a problem if no one else is considering it, either.

Which they're not, and for good reason--any sort of model for this is impossible to implement in limited time under the rigors of competition.

If these are MTTs were talking about--I'm gonna go out on a limb and say it's possible to achieve a 30% ROI without ever once considering anything related to a supposed "bunching effect", and I'm gonna go further out on a limb and say that there isn't a single crusher who gives a **** about this, instead focusing their time on much more fruitful sources of EV extraction.

I'll gladly eat crow and tip my hat if you can find one person who crushes and claims they actively alter their ranging and strategy creation based on supposed (and let's be clear: extremely non-trivial to quantify) card removal effects.

And lastly: unbelievably strong Location to thread topic synergy ITT with OP

I ran a quick sim with bunching vs no-bunching if anyone is curious about the magnitude of bunching effects.

Setup:
Full ring, 9 players w/ stacks 30bb+antes (1.5bb total antes in pot)
Sizings: 2.25bb opening / 3-bet all-in, SB can complete
Postflop: 0.75pot or all-in (2 + 3 way pots)



BU Opening (bunching):


BU Opening (no bunching):


I don't have a strong opinion on whether or not that's super significant in practice.

Some observations, probably all somewhat expected:
*) No bunching solution shows much higher EV for pockets 55-KK(!)
*) Bunching shows considerably higher EV for opening high Ax
*) BB is defending a lot wider against BU opens w/o bunching

Save files can be found here:
https://www.holdemresources.net/misc...30bb-bunching/

You can't just say "I ran a quick sim with bunching vs no-bunching if anyone is curious about the magnitude of bunching effects" and then just wave away an explanation of whatever model you used to quantify the applied "bunching effect"

What specifically are your assumptions?

One sim uses the displayed opening ranges for the UTG-CO players. That means for a sample that reaches the "folded-to-BU" subgame, the card distributions will be skewed by the folding ranges. The other "no bunching" sim simply folds everything to the button, this is what solvers effectively do when they ignore bunching.

Here are the full opening ranges for reference, didn't think it matters tbh:


Bunching isn't a hard thing to consider when you calculate by Monte Carlo sampling, you just have to play out the early position ranges and drop samples from the simulation that don't get there because earlier positions would open.

Why isn't this supported by some main solvers? The 2-player solvers don't usually work by Monte Carlo sampling, because there are more efficient alternatives for two players. But these alternative algorithms can't easily deal with bunching.

Those computed BTN open ranges are so nitty that it's impossible for me personally to accept those results.

Also don't think they're internally consistent: I don't think here's a chance in hell that K6o is ever a higher-EV open than 76s.


There isnt a game in the world where folding 76s OTB 30bb deep w/ antes is not an objective error.


Then why wouldn't BTN, knowing BB is defending less, start opening more instead of less? I'm only seeing 34 extra combos off a >40% freq range that BTN is opening in that no-bunching solution. BB defense ranges are not supposed to be anywhere near that sensitive to open range widths.


If bunching is a thing, why are we not seeing ALL combos containing "low" cards (whatever "low" means--it's not like anyone has even defined that, which is important here) monotonically losing EV in the bunching solution? Shouldn't we expect all "low card" combos to be worse off if there are fewer "low" cards left in the deck? I turn your attention to 72s and 22 as just two examples? Why would these lose less EV--is this just the solution not being solved to full unexploitability?

Why would Kx LOSE EV due to bunching? Whatever your definition of low is, a King certainly will never satisfy it.

Especially if BB is defending narrower under the bunching scenario. Turning your attention to KJs,KQs for example.

Is BTN winning more EV overall in the bunching scenario? It would make no sense otherwise given what you've said about BB defending narrower in the bunching solution.




I think the people implementing those Monte Carlo models would beg to differ.

The bolded part is especially troubling to me.

If we're talking about BTN opens, wouldn't it require an assumption for player's responses for EVERY SINGLE possible confrontation between ALL players from UTG through CO?

I would hazard a guess that at the very least, a model would have to include flats, and 3bs, and 4b-or-fold to be considered valid.

I'm not gonna pretend like I can do the combinatorics on that one--if you allow players to flat, and 3b+, couldn't there be hundreds of thousands of confrontations between all players UTG through CO? Maybe a lot more.

You've basically just very casually said: "It's not hard to do: just make a few hundred thousand assumptions about how humans play poker, no big deal"

Also, I'm not sure if the open ranges matter that much either, but for example opening A3o from HJ is silly, as is folding 44 from the same position.

I'm not sure what those ranges are supposed to mimic, but they are definitely not equilibrium open ranges and for that matter they are DEFINITELY not representative of the uber-nitty population.

Does "bunching" exist in the scenario when a nitty UTG player opens and everyone folds to the BB?

I personally would nary even defend my BTN with AJo vs some ultra-nitty UTG openers and I'm like 99.999% positive I'm correct in folding a bunch with that combo specifically vs a lot of member of the population when they open UTG.

I actually think you'd see the distribution of folded cards be pretty symmetric wrt rank in that kind of scenario.

I think another problem here is no one has actually defined the scenarios in which bunching is supposed to be relevant.

Is anyone here claiming that getting 5 folds pre produces the same "bunching effects"--if they exist at all--no matter what happens intervening or preceeding those 5 folds?

The latest version of Jesolver (an alternative "engine" for PIOSolver) has support for changing the probabilities of the cards in the deck. See https://jesolver.com/cmdref.html#set_deck_distribution.

(pio 2.x support is coming soon)

On second though, of course the opening ranges matter.

To the extent these effects may exist, you've assumed ranges that would basically magnify them to the fullest.

In theory and in practice, opening ranges are not nearly as "rank-linear" as you've assumed.

Suited connectors are gonna be higher-priority opens than A-rag offsuits, for example. You assumptions imply the opposite. I don't think its valid--at all--to assume, for example, LJ opens A5o and K9o, but not 98s.

You are focusing on all the wrong things, the exact hand selection of those ranges doesn't matter when we just want to gauge the rough magnitude of the effect. I just locked the EP ranges after a few iterations, they are not close to fully converged.

Let's break down a really trivial example, step by step:
Just a simple 10bb (no antes) push-or-fold scenario, so we don't have any unnecessary complications. Let's look at SB-vs-BB.

The no-bunching solution looks like this:


SB push 58.2%:
22+, A2s+, A2o+, K2s+, K2o+, Q2s+, Q7o+, J3s+, J8o+, T4s+, T8o+, 95s+, 97o+, 84s+, 87o, 74s+, 76o, 64s+, 53s+, 43s:0.51

BB calls 37.4%:
22+, A2s+, A2o+, K2s+, K5o+, Q7s+, Q6s:0.45, Q9o+, J8s+, JTo, T9s

The bunching solution looks like this:



SB push 52.5%:
22+, A2s+, A2o+, K2s+, K3o+, K2o:0.99, Q2s+, Q8o+, J4s+, J3s:0.30, J8o+, T6s+, T5s:0.80, T4s:0.04, T8o+, 96s+, 95s:0.30, 98o, 85s+, 75s+, 65s, 64s:0.12, 54s

BB calls 32.9%:
22+, A2s+, A2o+, K5s+, K4s:0.99, K3s:0.01, K7o+, Q9s+, Q8s:0.63, QTo+, J9s+, JTo

Original SB pushing EVs within the no-bunching game vs BB calling 37.4%:


Not lets plug the ranges from the non-bunching solution into the bunching sim and see how the EVs for these ranges look like with the skewed distribution.

SB pushing EVs against the same 37.4% BB calling range, this time with bunching from the early position ranges:


Those are some pretty sizable mistakes if you play the nobunching ranges on a table that opens anything like the bunching solution,...

Just catching up with the rest now, thread was moving too fast.

Maybe skario can chime in, I think he's doing that for a living as well.

No, the interactions after an earlier open occurs are irrelevant to the folded-to-the-button subgame. All that matters is that a particular deal won't be folded to the BU and we already now that much after an open occurs.

seems like a pretty big leap to first say you're just trying to gauge rough magnitudes, and then shorty thereafter declaring it's a big mistake not to adjust strategies

I ran the initial sims to gauge the magnitude. I only ran the second batch after your initial objections and I was actually a bit surprised by the size of the mistakes. I knew ranges are shifting around a bit but never made that EV experiment before. Hope that clears up that leap.

plus, seems really dangerous to use a push-fold 10bb BvB spot for this demonstration

giving SB no limping range isn't reasonable at all

If your hypothesis is that the bunching effects would be insignificant once we introduce a SB limping range then I think you should show some work on that, because it certainly isn't obvious why this would be the case. If that's not your point then I don't see how it's relevant to this discussion at all. We are not trying to perfectly solve 10bb games here. This is just exploring whether or not bunching has the potential to significantly affect strategies and I chose a simplified example to do so.

Clearly the skew in card distribution is enough to sway hands from slight +EV to sizable mistakes. Nothing about this is specific to push/fold. As long as the opening ranges are top heavy you will see some effect on hand frequencies & equities and that's going to apply to all sorts of scenarios.

Anyway, I don't want to spam the thread with more examples.

set_deck_distribution 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1