This chart compares BB's preflop defense facing an open in Pot Limit Omaha & No Limit Texas Hold'em.

BB defends a bit wider in PLO despite facing much larger open raise sizes. We can see a tendency to 3-bet less in PLO, which I attribute to calling being more attractive, plus 3-bet sizing being restricted making it less attractive.

Check out the difference vs SB btw. This is the one spot where open sizes are identical. This really shows off the magnified positional advantage in PLO.

https://preview.redd.it/3lanzlb4h52h1.png?width=848&format=png&auto=webp&s=6ec4ff2d32e4f16a267a8ce3ce549f20f49b8dec

Offering hand history reviews. Drop a hand you've been thinking about and I'll give you my honest read on it. I'm a professional MTT player & coach, just want to look at some interesting spots.

I've been grinding NL100 for about a year and I'm hitting a wall. GTO study has plateaued for me - I know my ranges, I know the solver outputs, but I feel like I'm leaving money on the table against the regs in my pool who clearly have specific leaks.

Curious how others approach this:

1. Do you actually do opponent-specific study, or just play GTO and hope?
2. If you do study exploits - what's your workflow? PT4/HM3 stats? Manual review? Solver node-locking?
3. How much time per week does it take you?
4. What's the most frustrating part of it?

Not selling anything, just trying to fix my own game and curious what's working for people.

I've always been frustrated looking at library solutions that suggest mixing a whole bunch of bet sizes starting from the flop. It feels impractical to try to implement such a strategy, and solutions on later streets become less realistic as the ranges we're working with stray from our pure sizing strategies.

On my journey making my own solver, I've come across an interesting finding: some bet sizes are strictly dominated, and completely disappear as solutions converge. Here is the c-bet strategy in a BTN vs. SB 3bp. As you can see, we have a little B75 mixed in:

https://preview.redd.it/78769rosnr0h1.png?width=3836&format=png&auto=webp&s=267a1727e4b46d069d39c869eb3d45d150af75c8

Here are how the global action frequencies vary by exploitability:

dEV	Check	B25	B50	B75	B125
1%	32.5%	48.3%	16%	2.9%	0.3%
0.5%	31.5%	50.4%	16.1%	2%	0%
0.2%	32.3%	51.8%	14.1%	1.8%	0%
0.1%	30.1%	55.6%	14.3%	0%	0%
0.05%	29.7%	56.9%	13.4%	0%	0%
0.01%	29.3%	58.3%	12.5%	0%	0%

As we can see, the industry standard of 0.2% to 0.5% that solver libraries solve to may accidentally capture convergence noise that could disappear if they converged closer to equilibrium.

If we take a look deeper in the solve, the noise becomes more prominent. Here is data from the same solution, but on a turn:

https://preview.redd.it/8prm4z2snr0h1.png?width=2558&format=png&auto=webp&s=4271af6d254bb97052f4b16c95b2ea62ea437ded

And global action frequencies:

dEV	Check	B25	B50	B75	B125
1%	23.4%	60.9%	6.2%	4.6%	4.8%
0.5%	27.8%	60%	3.5%	3.2%	5.4%
0.2%	29.4%	58.1%	0.7%	2.6%	9.2%
0.1%	34.2%	52.9%	0.1%	0.2%	12.6%
0.05%	36.9%	49.3%	0%	0%	13.8%
0.01%	37.6%	48.4%	0%	0%	14.1%

What's Going On?

I can only speculate, but it seems like the solver doesn't care to use all the complexity it's given. Particularly on "less important lines" that don't affect global EV as much, the solver seems to be more relaxed about converging to certain bet sizes. In the first example, B50 may very well be a dominated line (although we should test this ourselves) but if the EV loss of using it is very little, the solver won't feel pressured to optimize that area.

Can We Get Better Library Solutions?

What can we take away from this? Maybe if libraries could solve to tighter tolerances, we could minimize the amount of "ghost" ranges (e.g. B75 due to solver noise) that impact the ranges of future streets. This seems like it would make studying the pre-solved libraries more effective, if only a little.

As proven experimentally, we can tweak bet sizes, force pure sizing, range bets, and whatnot and still maintain EV. So the practical method of GTO strategy-building still seems to be defining your own strategy, verifying the EV difference vs. a fully-enabled strategy, and nodelocking with your strategy and re-running the solve.

Anyways, a solve is only as good as its inputs, and I suspect card bunching from preflop action may move the needle quite a bit, especially at ultra low dEV%, but that is something I will have to test.

The other day I posted on X saying "equity wasn't real", giving some example of how equity is often a poor predictor of pot share.

DeathDonkey (A high stakes mixed game specialist) responded with something interesting:

https://preview.redd.it/6xwyr0mhhe0h1.png?width=591&format=png&auto=webp&s=d323f053b65fa4b0e8f8179117a05cc72dd5b7c1

This is a really interesting observation. We can empirically observe that in PLO4, equity more strongly correlates with EV (preflop anyway)

But why? I'm not sure his explanation is complete.

Why Pure Equity Is Incomplete

You could imagine a [0,1] version of PLO where the middling hands were more dense (less spread). In this case, I think equity would still be a very poor predictor of EV because it's so easy to create a purely polarized range with unbeatable nuts. A toy game calculator shows that as soon as one player can do that, they can make the opponent indifferent with a small amount of nutted hands.

The thing is, pure bluff-catchers (like in 0,1 game) are very hard to defend because their only path to EV is getting to showdown vs a bluff.

As it pertains to our question, I suspect the reason is less about equity, and moreso about draws.

First Principles

If there's no more action, then it doesn't matter how many hole cards you have, EQ = EV. Doesn't matter if you're playing PLO6 or whatever. When there's potentially more action, villain can condition their range on the amount of money going into the pot. Strong hands tend to put in more money than weak hands.

So the juice is somewhere in how your hand's equity holds up as your opponent's range narrows.

Compare a made hand and a draw each with 50% equity on the flop. The draw will either be nuts/air by the river, while the made hand only beats air and doesn't improve (for our thought experiment). Now imagine we remove the bottom half of villain's range. The draw's equity hasn't changed, but our made hand is now worthless.

That equity retention is the key difference.

Draw Equity and Hole Cards

We often think of hands as monotonic, A > B > C.

But in poker that's not really the case. All-in preflop, 22 > AKo > JTs > 22.

That kind of rock-paper-scissors relationship cannot exist in a clean [0,1] game. It exists in poker because hands win in different ways. Some hands have pair value. Some have high-card value. Some have straight potential, flush potential, and so on.

This gets more important as you add hole cards.

• A NLHE hand is basically one two-card hand.
• A PLO4 hand is a portfolio of 6 two-card hands.
• PLO5 is a portfolio of (5C2) = 10 two-card hands.
• PLO5 is a portfolio of (6C2) = 15 two-card hands.

It's very hard to have a purely dominated hand preflop in PLO, because there are more ways to outdraw each other.

Just like our draw vs made hand thought experiment, adding more cards makes hands more drawish (especially preflop).

Anyway, I'm still working out my hypothesis here, but wanted to get your guys' thoughts on it.

GTO solves are based on clairvoyance (knowing villain’s exact ranges). In the practical scenarios where we can only assume/deduce other player’s ranges, I’m trying to understand if there’s a EV difference between these different scenarios -

1. Villain is tight/lose but we assume he is GTO
2. Villain is GTO but we assume he is tight/lose

Let’s say we are opening UTG and BTN 3bets in a 6 max cash game 100 bb effective.
We know that most players are not as aggressive as the solver. So should we reduce our 4bet %? If we continue to assume villain is GTO and play the “optimal” strategy do we -
- Do we actually gain EV via implicit exploitation
- Do we lose EV (Intuition points in this direction)

What is the way to go about answering questions like this? Most resources have me believe that GTO strategies are this perfect defense which cannot lose. If this is indeed true, then a perfect GTO bot that assumes everyone is playing GTO should never lose, right? (Assuming no rake)