ha yeah. with some people you just have to acknowledge there is no point continuing to engage with them. he will prob keep writing for no reason regardless

Lol ya seemed like he chose just that. Easier to ignore and halt the discussion then argue with 2 close minded clowns.

Stopped reading, due to all the silly back and forth about deserved livelihoods, so this may already have been covered, but I don't want these point to get lost.

1) Liberatus' strategy is proven to work. It is not proven to be GTO. It may be, and probably approximates, but there's no mathematical proof that it even does that. It just maths HU poker better than humans.

2) GTO does not automatically win the most. Anyone saying that does not know what GTO actually means. It doesn't even automatically win, given Vs who don't use dominated strategies (good luck finding any of those at our current understanding of the game) since raked poker is a negative sum game. There are good threads written by mathematicians in both Poker Theory and LLSNL that explain this.

3) (and this is the most important), no one has shown that a multi-way GTO strategy even exists, much less figured out what it might be. Many, many multi-player games do not have a GTO solution. Yes, HU (limit or NL) has a GTO (I haven't seen a mathematical proof of this, but it shares all the features of games that do), but it does not follow that 6-max even has such a solution. This doesn't mean that an AI couldn't learn to beat the best 6-max regs in the relatively near future, but it would not be doing it because the game was solved.

John Nash? loosely speaking all you need is finite players and finite action choices in order for there to be at least one equilibrium, doesn't matter if there are 2 or n players. can you please point me to some multi-player games that share theses properties but do not have at least one equilibrium?

Nash showed that an equilibrium exists, even in multi-player games. It has also been shown that GTO (minimax) and Nash Equilibrium are the same in 2-player zero-sum games. After this we get over my head mathematically, but my understanding from discussions with a math PhD is that they are not always the same in multi-player games because "In multiway games in particular, you can play a NE strategy and still be -EV if more than one other player is deviating from the NE you are playing for."

One reason for this problem is that "it's possible to have strategies in the game that are dominated by admissible strategies, but only because the admissible strategies outperform the dominated strategy only against inadmissible strategies (and are equal against the admissible strategies). When you have such a scenario you have a dominated strategy that functions exactly like an admissible strategy unless the other player deviates from GTO."

Also, I misspoke above. I should not have said that many multi-player games don't have a GTO strategy. I should say that they have not been shown to have one.

GTO is not the same as minimax, GTO implies that players play equilibrium strats (nash); it‘s just the case that in 2-player zero-sum games minimax is the same as nash.

your first sentence is a contradiction to what you said above; as for the last paragraph: ‚not been shown to have one“ - what are you saying? you know there‘s at least one equ, it doesn‘t matter whether anyone has found it yet.

yes, a nash equilibrium in a 3+ player game doesn‘t have the same guarantee or robustness compared to HU as a nash strat might become -EV if one or more players deviate - that doesn‘t mean there‘s no GTO solution to the game in the first place.

I don't know about the semantics as to what is what. But I do know that in multiplayer poker games where the rules are the same for everyone, there need not be strategy that guarantees that you will do no worse than break even no matter how the others play, even if they are not cheating. That should be common sense.

yes, being guaranteed to at least breakeven is simply a property of a nash equ in a 2-player zero-sum game, not a general property of nash. not exactly common sense imo, but has been said plenty of times in various subforums.

it‘s not really a matter of semantics, GTO means game theory optimal, and that always means nash in non-cooperative games. minimax is a way to find nash in HU, that doesn‘t mean that a game that hasn‘t got a minimax solution also doesn‘t have an equilibrium aka a game theory optimal solution.

yeah, you basically have no clue wtf you are talking about. but great job polluting the thread with your wisdom and trolling ppl

It's true that the optimal strategy is not guaranteed to maximise EV in a multiplayer game (because opponents do idiotic things that can harm your expectation). But that theoretically optimal strategy still has to exist. It would be pretty weird if we were all playing a game where there wasn't a "best" strategy, dontchathink?

Can you please enlighten us what's wrong about what he said instead of just ****posting "you don't know ***** bro lol"?

And I don't understand why it should be common sense that a GTO strategy with 3+ players isn't always at least breakeven in rake-free environment. I always thought GTO was some kind of unbeatable holy grail.

^ I guess you've never made a GTO shove with 66 and been called by 3 players with KQ, JTs and A6o. :/ In such cases, the non-GTO overcalls are calamitous for your EV, since the opponents' hands are accidentally 'colluding' against yours.

No I don't. What is "best" supposed to mean? (Notice that if you try to bring the proclivities of opponents into it, GTO isn't even the "best" head up strategy.)

He said that the strategy is "100% fixed". But he didn't make it clear that some hands might be played differently and it is only the random played chances for each tactic. that are "fixed". That makes others misconstrue.

This is where we are losing each other. I think we agree on the math but are just using the term GTO differently. When I studied Game Theory, the GTO solution was defined as the minimax solution. It's made confusing by the fact that minimax and Nash are the same in all the example games (because they are all two-player).

As for "justDgmt," step away from the keyboard, dude. Wolfram clearly knows more about game theory than you. I suggest you google "indifference principle."

Much confusion over the years is due to the fact that the people who originally popularized the term "Game Theory Optimal" in poker used the term as meaning "Nash Equilibrium".

It is an unfortunate historical accident but the poker community is now stuck with that terminology and all the confusion that goes with it.

Using that terminology, a GTO strategy (set of strategies) exists for all poker games in which explicit collusion is not allowed. Be they 2-player or N-player games. Be they zero-sum or non-zero-sum.

There are special "theorems" which apply to the 2-player zero-sum case based upon Minimax and other related aspects. Not only does an equilibrium pair of strategies exist in this special case, von Neumann and others developed algorithms to derive those strategies.

But these theorems in general do not extend to the N-player case or the non-zero-sum case. In general, even though we know that Nash equilibrium strategies must exist (in a purely non-cooperative setting), there is no easy way to derive them. In fact, there may be multiple Nash equilibria in the general case.

The Poker Theory forum is a good place to learn about and discuss these issues.

I honestly can't figure out how it can even remotely be true. This isn't chess, your opponent matters in chess the better move is always the same. Same with the game of Go but poker is different

A simple example would be 6max when the AI raise in the sb with x%. A fixed range can't be correct vs a guy who steal 18% of the time and vs a tighter guy who almost always 3bet for value.

Even it rock paper scissors the GTO strategy for an AI would be to document the opponent tendencies and exploit them not just pick a random choice

In game theory terms, a poker strategy is what action to take (call, bet, raise, fold, etc.) and the bet amount (if betting or raising) in every conceivable situation that could arise at the poker table. A strategy in these terms can also involve probabilities (fold 10%, call 60%, raise 30%) of all the possible actions available to you.

Nash proved that there is a set of strategies, as defined above, one for each player that is "best" for each player where "best" means that it cannot be profitable for any player to unilaterally change their own strategy in order to try to improve his/her EV given that all the other players continue to employ their "best" strategies.

Thus, at this Game Theory Optimal (Nash Equilibrium) collection of strategies, one for each player, each player should play its "fixed" strategy.

GTO is the "opposite" (in some ways) to the "best" exploitative strategy. If you knew that your opponent in the big blind is an over-folder, you can exploit that by "over-raising" from the small blind, etc.

Of course, exploitative strategies are subject to being exploited by other players at the table which is not the case for a GTO strategy.

So, again, any confusion in these areas is usually due to terminology.

"GTO is the "opposite" (in some ways) to the "best" exploitative strategy. If you knew that your opponent in the big blind is an over-folder, you can exploit that by "over-raising" from the small blind, etc." So, again, any confusion in these areas is usually due to terminology. -whosnext"

and brought on by You


GTO would never care about how opponent is playing as it's playing GTO Maybe relearn terms . . .

it's not a matter of semantics or definition, no matter how you spin it. (ELI5 mode now) GTO is an abbreviation, it stands for game theory optimal. when you put out a statement like no one has shown that a multi-way GTO strategy even exists then what you are saying is that there is no game theory optimal strategy (or set of strategies for all players) for the game. this means nothing less than saying that there is no nash equilibirum, and thus no game theroy optimal solution. minimax is completely irrelevant in this context, as is whether or not a nash strategy for a certain game guarantees you to breakeven.

you are a 11-year old green account with 17k posts and "do you even math, bruh?" as location who is missing basic knowledge in game theory and is putting bs statements on the internet -- better take it easy on telling other ppl to step afk and in assessing who has more GT knowledge buddy. i suggest you google "nash equilibrium", wiki will actually do.

@whosnext: what a mess.

I'm very (by forum standards, not by professional mathematician standards) familiar with game theory, and I have not said that there is no Nash equilibrium in multi-way NL poker. I have not even said that there is no minimax strategy. I've said that there has not been shown to be one.

As I said before, I am not going to argue over whether "GTO means minimax" or "GTO means Nash." I'll just stop using GTO in the discussion if people are using it differently.

I think that you'll agree that Nash has been shown (by theorem, not by solution) to exist for multi-way NL, and minimax has not. I think that you'll likely also agree that most people don't realize that these are different things, because even if they know a little game theory, they are the same in 2-player games.

As for your comment at whosnext, I think that's actually a pretty good summation of game theory vs exploitation.

2:30

Just want to bump this for the lulz, the mods moved my posts from the challenge thread to this for some reason (told em to delete me but no) and after so many heroes were like "omg you're like totally wrong" while not debating anything that I said, literally ONE OF THE BEST PLAYERS IN THE WORLD says the exact same thing that I was saying.

not quite the exact same thing lulz

does it make you feel better that you are in good company in not getting the point of the experiment? although seems his point was more about whether we need to worry about libratus level bots in online poker and why this isn't currently a problem.

in contrast to your brilliant OP asking whether libratus actually beat humans. lulz. And then your other points that it is not fair that a computer uses computing power in the match against humans when humans don't have computing power. also (as far as i heard) he didn't make any stupid comments about different bet sizings being "unfair" in NO limit like you did

lulz

Oh yes, I was unaware of whether Libratus actually won or not, I wasn't implying that the conditions of the challenge were ridiculous, you totally got me. Reading comprehension, not even once.

He more or less echoed my point about what a ridiculous gongshow the match was, then again for someone that lacks the ability to understand what I'm getting at, I'm not surprised you cling on to sidepoints as if my main idea relies on them.

Libratus's sizings were another BS gimmick that it needed to use against humans to add a layer of confusion which has very little to do with the totality of a poker challenge unless you think the future of poker is deciding between 1/8 or 2/19.

My point stands and he further corroborates it (the match was a total farce), so LULZ @ YOU.

Toad the reason no one understands what you are getting at is that it makes no sense. From the minutes I saw he certainly didn’t say the experiment was a farce, just that the conditions were different than in current online poker (and did he have a dig at the standard of the players involved?)

The parameters of the experiment were clear and within those parameters and the rules of Holdem, AI clearly beat the humans at HU NL. And this is the conclusion of the experiment. No more no less

Your rabbit hole about sizings still makes no sense. Everybody is free to use whichever sizings they think is best. If the AI can calculate sizings that are more effective than the human then that is exactly the type of thing the experiment is trying to establish. Which goes to my point that you seem to think an AI computer should try and compete without using its computing power, but without computing power what is left and what is the point of the experiment?