people been saying if hero plays GTO, then hero can make money when villains make mistakes, I used to believe it, but here is the question:

In the game of rock paper scissor, the GTO play is to do each one 33.333% of the time, randomly. but if hero plays GTO, then there is no way villain can make any mistake. no matter what villain do, 100% rock, 50% rock 50% paper. hero cannot win.

My point is, if hero plays perfect GTO, villain cannot make mistakes at all.( assuming hero does not exploit), and therefore, GTO cannot win.

any thoughts? also, if you disagree, please tell me the difference between rock paper scissor and poker, because I think in the core, both games are the same.

you can clearly see this is false if I play GTO and you play a strategy of folding 100% of your hands, I will win

That is how it works in RPS, but poker is much more complicated. It's easy to come up with some examples in poker to show that it's not true here. For one that is silly but very clear, imagine someone who folds every hand playing HU with a perfect GTO player. They must lose at the rate they are forced to pay the blinds, minus the walks a GTO player would give them when they fold the BU. An exploitative approach can do better by raising 100% of hands vs. the always folder, when GTO will fold stuff like 72o as the BU. However clearly GTO is still extremely profitable.

Generalizing, whenever the GTO strategy mixes actions, it is not a "mistake" to take any of the actions that are mixed. At the NE mixed actions have the same EV. "Mistakes" happen when a player takes an action that GTO would never take, and which is lower EV than the alternatives at equilibrium. Using improper frequencies can still be exploited, just not by a GTO opponent.

yes, and I know if I shove 27 preflop, GTO will make money in the long term.

I just dont know what makes it different from rock paper scissor

is it possible you can add some rules in RPS and make non-gto player have a chance to lose? so that i can understand the difference better

Poker is not Rock Paper Scissors though? lol

In RPS all actions are solver approved and they are worth the same exact EV in equilibrium.

In poker this is not the case, some lines lose EV in equilibrium and they make you lose against GTO

So imagine in RPS there's Rock, Paper, Scissors and Excrement. Excrement loses to everything and beats nothing. So if someone is playing GTO and you throw Excrement even if it's only everyonce in a while, you are being beaten by GTO.
This is analogous to calling with bad blockers, bluffing with bad blockers, folding hands that are too strong at any point in the hand, etc, etc. obviously easier to make a mistake than in the Excrement game.

that example is very smart, thank you

so the differnce is that in the game of poker, the strength of every hands are difference.

Ive been thinking if the fact that in poker, there are 4 street is also a factor, what do you think.

Yes strength of hands is a big factor.
I don't think the amount of streets plays a role in this though

I don't think strength of hands has anything to do with it (at least in the long term, short term hand strength is critical). Unless your saying that people will misjudge the strength of their hand, then I agree. GTO wins when your opponent makes mistakes. If you both play GTO, you break even (minus rake).

Imagine Doug Polk playing a beginner in HUNLHE. It would be a bloodbath. Ask yourself why.

The beginner would make many "mistakes" such as:
- Folding too much
- Calling too much
- Raising too little
- Playing too tight
- Playing too loose
- Making bad bets (too large, too small, checking too much, etc.)

RPS does not provide a beginner with these types of "opportunities" as does poker.

Maybe a bit nitpicky but doing something "too much" or "too little" is not a fundamental mistake in poker, but doing it with the wrong hands is.

I think it does.

In RPS, all of the hands have the same exactly equity(im not sure if equity is the correct term) against villain's range. Rock has 33% equity as well as Paper and scissor.

But in poker, the equity of every hands against villain's range is different, for example, both players hold aces, kings and queens. the equity of Aces against villains range is 100%(or sometime tie to villain' aces, whatever), kings 50%, queens 0%. so in this case, even hero plays the perfect GTO, Idk what exactly, but let say betting aces all the time for value and bluff some of its queens. Villain can make mistakes by calling with all the queens, the reason why queens lose, but Rock/Paper/Scissor dont, its because the equity. you may think this is a stupid example and villains must not misjudge his hands like that in real life. but in reality, poker player often play 200-500 combos of hands, and its hard to judge some of the marginal hands, and thats where mistake come from.

Also, i think the position plays a big rule as well. in the game of AKQ, i believe IP can gain its EV(not equity), I learned it from a toy game, but Im not gonna explain it here, because its too complicated and i cant say i am fully understand it.

yea, so this is my point, hand strength and position are the reasons make poker different.

not sure if there is any other reason

maybe, also the fact that you can fold in the game of poker? which it gives up your equity.

if you can fold in RPS, then folding is a mistake and the GTO-player can make money out of it.

can I say the fundamental of poker is to realize hero's equity as well as deny villain's equity?

The better way to say it is maximize hero's EV while minimize villain's EV

BTW, if both players play perfect GTO, does it make the EV=equity?

Hand strength and position are factored into GTO. Sometimes, GTO will have you lose the minimum.

No

Yes this

No, you could just shove every hand and realize 100% of your equity. There's more to it than that.

RPS is kinda a unique game where it's essentially impossible to make a mistake. Most games, including poker, are not like this.

Consider something like Tic Tac Toe, you can clearly see playing GTO is better than playing badly

isnt it because if hero shove every hand, villain can deny hero's equity by only calling with a selected range? therefore, hero cannot realize 100% of his equity by shoving every hand

I'm not sure you understand what "denying equity" means. Hero will realize 100% of their equity, because they go to showdown with their entire range.

With GTO you must make the highest possible EV play with information given. You only start randomizing or "mixing" when the EV of certain actions is even. So if you notice your opponent is throwing 100% rock, maybe you go 40% paper instead of 33%. You could go higher, but then opponent can change his strategy. Stay at 40% and he never notices the difference and he keeps losing forever.

Rock,paper, scissors is also nothing like poker. A mistake in RPS costs you 1 point or set or match whatever you want to call it. While a mistake in preflop can compound to a lot more than the big blinds lost because of a loose pre flop call with J7o.

The main complexity of poker is that in poker you have to pay a blind. If poker were played without a blind, and as a Nash equilibrium strategy played against another player playing the same strategy in a zero sum game would have an ev of exactly 0, you have an obvious 0ev strategy without blinds: folding 100% of the time. So, if hero is playing at a Nash equilibrium for poker without blinds that involves folding 100% of the time (and this may not be the only Nash equilibrium for such a game, I don't know), then villain cannot make a mistake, which is the same situation you are referring to with rps. Introduce blinds, and the game changes considerably.

GTO always has blinds. Folding as a pure strategy always has the EV of losing your blind, or whatever you have invested in the pot for whatever reason. Folding as a mixed strategy is the GTO solution when continuing has an even larger negative EV.



Theoretical GTO versus multiple opponents means that Hero loses the least possible.

In heads-up this also equates to winning the most possible.

That's it. Statements beyond these two may or may not be true, or at least provably true.

No. Game theory, and game theory optimal solutions to games, aren't limited to poker. There are a lot more theoretical situations that game theory can be applied to than just poker, so clearly, gto would not always have blinds, as it would not always apply to poker. Poker, on the other hand, may well always have blinds, I don't know. That's why you can get a valid equilibrium strategy for rps, and you can get at least one equilibrium for a poker game without blinds. Which I correctly explained. You can even have any number of equilibrium strategies for choosing heads or tails for a coin flip. It's pretty pointless though, as any strategy you choose will be optimal.

For a game such as poker, assuming no rake, any equilibrium strategy will have an overall EV (when playing against any number of players playing an equilibrium strategy) of exactly 0. The only way that the EV of an equilibrium poker strategy Vs another equilibrium poker strategy (again assuming no rake) would have an EV different to 0 would be if the sequentiality of the game was changed, i.e. if players were at certain positions more frequently than others. So, for example, in hu, if one player was always the SB.

I felt my explanation as to why the gto solution to playing rps didn't really translate to poker (because poker is played with blinds) made intuitive sense, and helped to provide an answer to the question. Whether the theoretical point I made is useful (beyond the strictly theoretical) is up for debate, and it may even be incorrect (although I highly doubt it). If you do want to show it is correct or not, I'd consider looking into game theory for zero sum games (poker without rake is zero sum, with rake, negative sum, obviously), and not making wild statements which are just not true. I count 2 incorrect assertions in what you've written, and I'm not even commenting on your last sentence, and the one about losing the least possible in multiway settings is only true assuming rake. Actually, the hu statement is true assuming positive rake, I.e. the rake is paid to the players, rather than the players paying the rake.

Blinds have nothing to do with the difference between RPS and Poker.

You could play RPS with blinds similar to a HU match and each play would still be worth the same EV in equilibrium.

You could also play Poker with no blinds and you could make plays that lose EV against GTO (unlike in RPS), such as betting with anything other than the nuts.

I still postulate that the main reason why you can lose EV against GTO in poker is because some hands are weaker than others