I don't really want to get into the whole what is GTO thing and whether it's a good or a bad thing.

So here are my assumptions when asking this question:

• The AI players NLHE.
• This GTO AI will play completely unexploitable.
• It will not adjust to opponents in any way.
• If matched against another perfect GTO AI they will be dead even after playing an infinite amount of hands.

Now would this GTO AI make money playing against random people?
If so, from which plays or situations would this money be made?

The whole point of the AI is to play unexploitable, or perfectly balanced.
When making a bet, it will have the value/bluff percentages perfectly balanced.

So against someone who calls too often, it's going to lose EV when bluffing, but regain that EV when value betting?

Against someone who folds too often, it's going to gain EV when bluffing, but lose that EV again when value betting.

So where does the EV come from? Or would this GTO AI just be dead even against any random player after an infinite amount of hands?


I'm not asking if GTO is useful or not. I'm just wondering if and how it would make money while playing unexploitable or completely balanced.

I also realize it's not possible for a human to play perfect GTO and I'm pretty sure there are no AI's that play perfect GTO atm, though I could be wrong there.


Comparing this to a rock, paper, scissors AI makes it really obvious.
I'm not sure if the same logic applies to poker, because the game is much more complicated.

If you have an AI that plays perfect GTO, it will randomly play rock, paper and scissors 1/3th of the time.
And you can immediately see how this wouldn't win against even the worst players who play rock 100% of the time as an example.
The AI will win 1/3th of the time, it will lose 1/3th of the time and it will draw 1/3th of the time.

No matter what strategy is used against this AI, it will win, lose and draw the exact same amount.
If we were playing this for money, we would be losing, since we pay rake.

How is poker different? Is it different?

Search for strategic dominance on Wikipedia.

Poker gives people the option to play many strictly dominated and weakly dominated strategies. Whenever someone takes these strategies there is a possibility that GTO would exploit that.

E.g. 1. using small sizings at too high a frequency when you should be overbetting.
2. Calling rivers with hands that look good, but are garbage vs the blocker strategy the bettor is using.


Some non GTO strategies won’t lose to GTO. Like in a nuts or air game without blocker effects, the caller should be indifferent to calling or folding if the bettor is playing GTO.
If the caller is indifferent he can play 100% fold and he will still make the same amount of EV compared to if he played GTO.

Yes the GTO-bot would make a lot of money. This actually works by definition in game theory:

GTO (Game Theory Optimal) is actually a term that is only used regularly in poker. In other non-cooperative games this is called the Nash-Equilibrium.

So alright we're applying our NE strategy, but our opponent isn't. Does that mean we that we gain extra EV? Yes.

Poker is also a zero-sum game (without rake, but it's not very relevant to your question) which means that each player's loss or gain of a player's EV is balanced by gains or losses of EV by other players. So if we sum up all winnings and losses we get zero.

Now if we add these definition up we get that by deviating from the Nash-equilibrium, the non AI players give-up EV, which will be gained by the GTO AI.

Or consider this toy game:

All stacks: 100
Pot: 100
Hero's range: AA, QQ
V's range: KK
Board: 33322
Action is on hero and he can bet 100 or check.

In nash hero bets 100% with AA and 50% of his QQ.
V calls KK 50% of the time.
Hero's EV is 75 and V's EV is 25.

Now try manipulating some frequncies and see where EV is gained.

Lol. That’s the exact toy game that I said GTO would not gain EV in vs an exploitable opponent...

This is all a bit complicated for me.
I'm not good with complicated logic and math.

Is it possible to demonstrate your points with a simple poker hand example?

The strategic dominance article is pretty interesting, but how do you prove GTO is a strategic dominant strategy?

Oh right only works if you change the frequencies of the better.

@Im Nacho Friend

has hero 50% AA and 50% QQ in this toygame?

The only simple examples I have are extreme examples. Do you think someone who VPIPs only AA will have the same EV vs GTO than a tough player would? Do you think someone who VPIPs 100% will perform as well as a tough player?
These errors occur on a more minuscule level for every player, and sometimes GTO takes advantage of these errors. If you want something concrete you would have to get a solver. I have one and I can’t put it into words.

To your 2nd question, I dunno lol. If you know how an exploitable opponent plays then GTO is not a strategically dominant strategy since an exploitative strategy would perform better.

So GTO makes money when opponents miss value by betting too small?
Wouldn't GTO widen it's calling range against the small bets?

I guess this works for betting too large when bluffing as well?
A simple example is maybe open-shoving for 500bb with T9s, GTO is probably only going to call this with AA, but it will gain EV in these spots.

Not sure what a blocker strategy is exactly or how that would work, could you explain?
(I do know what blockers are.)

Hmm, I understand what you're saying and I think you're probably right.
I just have a very hard time translating this to actual situations.

Sizing errors are just one set of easy to understand examples. It would widen its calling range yes. That’s not the point though. Switch the cards. Now GTO is the bettor, and he picks the larger sizing. This let’s him bet more hands profitably = more money.

GTO is complex mate, it can do things like fold flushes and call sets, because a GTO bettor could bluff with hands that block flushes but not sets. So whenever you have a flush, the bettor is less likely to be bluffing. Because he’s bluffing with flush blockers only. This is an extreme example to illustrate blockers OTR, I’m sure no practical situation exists that would have GTO pure folding flushes and pure calling sets.

But wouldn't this again balance out to 0EV when adding in the amount of times the AI is bluffing?

If it's playing GTO then any deviation from GTO when playing against it would result in an EV of equal to or greater than 0.

I understand the first part.
But I find it very hard to find real situations where the EV would be larger than 0.

I know it must be true, but I fail to understand how it works.

It only does that if you’re in nuts/air no-blocker toy games. In real games, bluffs will have 0.1 EV or something like that, because blockers. Or equity if you’re not OTR.

If you use a big sizing you can bluff with 10 combos.
If you use a small sizing you can bluff with 5 combos.

10 x 0.1 is greater than 5 x 0.1.

My poker knowledge does not run deep enough to understand this.
Isn't the whole point of GTO to balance your value/bluff to exactly 0EV?
Why would a bluff have 0.1EV? I know you said blockers and equity, but why would it not account for those when balancing?

If you bluff more often when sizing big, isn't your EV going down against players that call too much? (Which seems to be pretty much everyone I play against.)

Yes 6 combo's of both.

Zenith Poker has some free courses on Game Theory. Might be useful to check those out OP.

That’s not the end goal of GTO at all, the end goal is to keep your opponents EV under a certain threshold no matter what they do.

Your own EV is irrelevant to this equation.

There are a lot of opportunities for someone to lose EV against a GTO opponent. When a balanced range is constructed only the pure bluffcatching portion of the opponent's range becomes indifferent. If the opponent folds a hand that can beat value bets or calls a hand that loses to bluffs then they lose EV vs. a balanced range. Also, within the bluffcatching region, not all combos are equal. Some combos of bluffcatchers are better than others and will be pure +EV calls, while others will be pure -EV folds, due to blockers and/or equity. The same applies to bluffs. You won't balance all bluffs/bluffcatchers to be 0 EV because some combos are just much better than others.

Another example is sizing, and we can use a simple toy game to illustrate. IP on the river of 22233 has a range of {AA, QQ}, while OOP has {KK}. Stack size is 2 pots. If the IP player bets pot with a balanced range, he'll bet 100% of AA and 50% of QQ, for a value:bluff ratio of 2:1, offering KK a 0 EV call. Since IP is effectively winning the pot 75% of the time he offers a 0 EV call, he has 3/4 pot capture with his river range using this strategy. So IP appears balanced, and there's nothing his GTO opponent can do to gain EV.

However, GTO requires more than being balanced. A different bet size is better here, so betting pot loses EV compared to GTO. IP should actually be going all in. When he does, he will bet 100% of AA and 2/3 of QQ, for a value:bluff ratio of 3:2, offering KK a 0 EV call. This time IP gets 5/6 pot capture, which is greater.

There are many other situations where non GTO can lose EV vs. GTO.

@ToiletBowler

this seems wrong.

Example: 100% rake game

if you fold vs opponent he gains 1 BB, if you call he loses, but you lose too!

If the population bluffs too much ---> the bluff catcher region would gain in EV (along with also any value range that played passively)

If the population under bluffs too much ---> hands that would have otherwise folded flop/turn/river get to realize their equity more than they should have

Pure nash equilibrium would print

It would own itself a lot snapping rivers too wide bc limp-dick humans do not bluff enough at all but it'd more than make up for it preflop by opening more (humans are nits), 3betting more frequently (humans are nits) AND more correctly (more appropriately polar when necessary) so as to have not just wider flatting ranges but also more balanced flatting ranges, and postflop bluffing way way way more than a human (humans are nits) which is doubly +EV because humans generally overfold in all spots (humans are nits) and using better sizing choices at all points.

Wasn't there a dude who sucked at NL100 or something who then started cheating with a RTA and raped nosebleeds left and right? that'd be your answer.

Essentially, even the strongest players have leaks in their game that will lose money over time to a GTO bot. The baseline EV for the AI is 0. It is much lower for a human.

Example:
Lets say we have a good winning reg, a total fish and a GTO bot

GTO bot vs fish -> GTO bot wins 8bb/100
Reg vs fish -> Reg wins 20bb/100
GTO bot bs reg -> GTO bot wins 3bb/100