Let's advance the GTO vs Exploitative debate today.

Exploitative poker: Assume you know your opponent’s strategy. How do you win the most money against it? How do we maximize the ceiling?

GTO poker: Assume your opponent knows your strategy and max exploits it. How do you lose the least? How do we maximize the floor?

These are complementary frameworks. How are you gonna exploit without a baseline from which to recognize imbalances? How can you understand GTO without studying at the exploitative threats that shape it?

You need one to understand the other.

The Deeper Problem

The deeper problem is this: Both frameworks rely on this abstract object we call a "strategy".

In game theory, a strategy is a complete map of how one would play every possible hand in every possible spot.

And that's critical. To find the best move with your hole cards on the flop, you need to know how your opponent plays every hand in their range on every future node. And to find the least exploitable strategy, you need to know your entire strategy. What you do with one hand in a vacuum doesn't matter in terms of the exploitability of your strategy.

The issue is, this "strategy" does not exist in reality.

I promise, you cannot write down your full strategy. It is an unfathomable amount of information. It changes with the runout, formation, betting line, stack depth, and so on. Even if you could, it's a fuzzy ever-changing thing that swings with your mood and blood sugar.

So any framework that needs a well-defined strategy to operate, is operating on fiction.

This is why I believe the best (and only real) framework is Bayesian. You need a hybrid approach that can make fuzzy reads, perhaps using Nash as a prior and leaning towards best response after updating with population/player data.

Every top pro is already doing this intuitively. But you'd be surprised just how little quantitative work has actually been done to map this out. Even basic questions like "what makes a strategy exploitable, and for how much?" are barely explored.

And once you get into this area, things get weird. Ceiling/floor are no longer the only objectives. There are valid strategic ideas like exploratory moves that seeks to uncover where their response adjusts poorly.

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

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.

Blockers are often explained backwards in solver outputs.

GTO (Nash Equilibrium) is fundamentally defensive: It's working out how to lose the least vs the best response. Every move is a consequence of exploitative threats.

Good players understand this. But with blockers, people suddenly start talking offensively, "GTO calls this hand because it blocks value or unblocks bluffs" or whatever the rationale is.

But really, a solver is aware of these tactics and builds its strategy to minimize its own blocker weaknesses. It is trying to make the opponent’s blockers less effective.

Once you see this, you start noticing features like value/bluff mirroring, bluffing with hands that are harder to block, spreading out calls so the clairvoyant opponent doesn’t have easy bluffs, and so on.

The correct GTO explanation is defensive, not offensive.

Example

Here's an example. 100bb CO vs BTN 3BP, B-X-B line.

Why does CO spread calls across TT, JJ, KQ, and QT? Why not just call KQ and fold the rest?

The naive answer is "oh because it blocks/unblocks such-n-such"

GTO Solution: 100bb CO vs BTN 3BP, B-X-B

The defensive explanation is that if BTN *knew* that CO calls KQ and folds QJ, QT, JJ-TT, then BTN could just bluff with a K and not with a J or T.

Let's prove that. Here I've nodelocked CO to defend in this simpler more human way:

Nodelocked defense

Here's how BTN exploits it. You can see a bunch of Jx Tx bluffs moving down to 99, 89. And Kx bluffs becoming more common.

BTN's exploitative response

Are Blockers Important?

To be clear, I’m not saying blocker effects should dominate your in-game thought process. In fact, I feel they should often be low on the priority list.

This is mostly a lens for understanding solver outputs. Why does the solver do the thing? Because if it didn’t, the best response would exploit it somehow. That's the key to understanding GTO.

The irony is that solver strategies are designed to make blocker effects look as inconsequential as possible. So when we measure blockers, we see the effect is almost nothing. But that's by design. This probably leads us to underestimate its practical importance against imbalanced, real opponents. But an exploit is only as valuable as it is detectible, and other exploits are likely much higher on the priority list.

Was having a normal conversation with GPT and all of a sudden it started outputting random nonsense.

Full chat: https://chatgpt.com/share/69f0f23b-f900-83e8-aca5-38222320aeea

No custom instructions just some crazy bug.

https://preview.redd.it/3skw5ww1wyxg1.png?width=934&format=png&auto=webp&s=343be451e8f7fa447685aa8c58dc2c43a5fde2d9

This is a famous thought experiment that has deep ties to decision theory (and ultimately how one thinks about poker).

You walk into a room with two boxes:

-Box A is clear and has $1,000.

-Box B is solid and contains either $1 million or nothing.

You may choose to take box B, or both box A and B.

Here's the catch: Before you walked in, a near-perfect supercomputer analyzed you and predicted your move. If it predicts that you would be greedy and take both, it left box B empty. If it predicts that you would only take box B, then B contains $1 million dollars.

You know nothing about the predictor other than it's remarkably accurate, having correctly guessed the decisions of hundreds before you.

The money is already placed in the box before you enter the room.

Do you take one box, or two?

View Poll

I’ve come to believe the most important question in poker is this:

>What makes a strategy exploitable, and for how much?

GTO tries to minimize exploitability. Exploitative poker tries to capitalize on it. Whether you're trying to play balanced or exploitative poker, ultimately every strategic framework is built on that central question. It is the bedrock of poker strategy.

But there's almost no work on this topic. Sure, everyone has intuitions about it, and poker wisdom is largely directionally corrrect, but no one has really measured it or designed a taxonomy of imbalances.

The Node-Level Problem

Poker tools are built to examine node-level decisions, so modern poker theory naturally focuses on node-level explanations. Why does this combo bet? Why does this hand mix? Why does this suit matter?

These are largely explained by micro effects, things like blockers, backdoors, board coverage, scarcity, suits, and so on. These micro effects can strongly influence which combos the solver chooses, so naturally they get all the attention.

However, I suspect most exploitability comes from bigger line-level things that are harder to measure in a solver:

• How much money gets contributed to different lines
• How much money gets put in now and folded later
• How hand classes are broadly allocated across lines
• Whether bluff ratios are roughly coherent

That list is obviously incomplete, but if any of those are off, the strategy becomes exploitable in broad, obvious ways.

Experiment Idea

So how should this question be addressed?

In theory, you could use any solver that supports nodelocking and MES measurement. Start with a GTO strategy, introduce a specific bias, then measure how much the best response gains. Repeat across a flop subset and different formations in a systematic way.

So the question I’m interested in is:

How would you categorize the main ways a strategy can be imbalanced in a human-readable, measurable way?