A shortie. There may be a flaw in that GTO is "best" vs unknown. If we know how an "average" player deviates from GTO (tighter and more passive probably), then a different strategy may have higher EV versus an unknown too. 
Why not...?
/Johan = 
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Originally posted by mattisks
Originally posted by madorjan
Damn, I can't disagree with anything in that post, please rewrite!It's also an interesting point that we should treat an unknown opponent as a GTO-player. Will have to think about it a bit, but that sounds a good abstraction I haven't thought of.
So yeah, truce, and GL at the tables.
Dunno man. I play lower stakes for about 2 months now. I don't count previous lenghty experience with poker as lot has changed.
Ppl play about the same so you can exactly figure out what they doing. Does it count as GTO as well if you learn how to exploit them little motherfathers? ♠_evil:
No, it does not. This is precisely the sort of thing you cannot do. It would render you exploitable.
/Johan =
Originally posted by YohanN7
Originally posted by mattisks
Originally posted by madorjan
Damn, I can't disagree with anything in that post, please rewrite!It's also an interesting point that we should treat an unknown opponent as a GTO-player. Will have to think about it a bit, but that sounds a good abstraction I haven't thought of.
So yeah, truce, and GL at the tables.
Dunno man. I play lower stakes for about 2 months now. I don't count previous lenghty experience with poker as lot has changed.
Ppl play about the same so you can exactly figure out what they doing. Does it count as GTO as well if you learn how to exploit them little motherfathers? ♠_evil:
No, it does not. This is precisely the sort of thing you cannot do. It would render you exploitable.
/Johan =
so if I exploit the other guy I will become exploited? This sounds like yet another quantum theory. Who will exploit you if you exploit the other guy ♠_confused:
Wrong. There is only one quantum framework, that of quantum mechanics itself (though not axiomatized successfully yet). 
I have no idea about who is going to exploit you. The point of GTO is that nobody will if you stick to GTO because they can't.
/Johan =
Originally posted by YohanN7
Wrong. There is only one quantum framework, that of quantum mechanics itself (though not axiomatized successfully yet).
I have no idea about who is going to exploit you. The point of GTO is that nobody will if you stick to GTO because they can't./Johan =
so GTO pretends to be ideal play against any or random opponent?
How many players play GTO? Some ppl are complete noobs, some ppl didn't figure out ranges yet and some ppl even though very skilled yet might be lacking some key points of it.
We all have leaks but pretending we play GTO everytime won't fix them, will it?
so if I exploit the other guy I will become exploited? This sounds like yet another quantum theory. Who will exploit you if you exploit the other guy shark confused
Ok Yohan, I have to take back everything I said. THIS guy doesn't get GTO at all.♦
Originally posted by mattisks
Originally posted by YohanN7
Wrong. There is only one quantum framework, that of quantum mechanics itself (though not axiomatized successfully yet).
I have no idea about who is going to exploit you. The point of GTO is that nobody will if you stick to GTO because they can't./Johan =
so GTO pretends to be ideal play against any or random opponent?
How many players play GTO? Some ppl are complete noobs, some ppl didn't figure out ranges yet and some ppl even though very skilled yet might be lacking some key points of it.
We all have leaks but pretending we play GTO everytime won't fix them, will it?
It is s too much to answer for me to even attempt it. For one thing it will take a while to pin down that "ideal" you use.
/Johan =
Originally posted by madorjan
so if I exploit the other guy I will become exploited? This sounds like yet another quantum theory. Who will exploit you if you exploit the other guy shark confused
Ok Yohan, I have to take back everything I said. THIS guy doesn't get GTO at all.♦
I am just asking. You can try to look smarter that you know some definition of something. I am just saying that something "new" doesn't have to be the best. I am actually glad that all those new theories take place.
Then ppl are confused enough and make -EV calls with JTs in spot where old theories would say: toss, toss, toss you idiot. This is not the right play. Toss toss toss.
So you can keep your insults for the friend next door, who doesn't know what pocket pair is 
Its about as valid as my wife laughing to me that my project doesn't work after two days I am running it.
It's short sighted people that will never learn. Remember that my buddy..
okay, some notes for the discussion so far
1) in order to define a strategy, you must list what you'd do in every possible situation that may occur in the game. that list is your strategy. there's no strategy that isn't like a big ass chart.
2) if you play a nash equilibrium strategy (NES) in a finite zerosum symmetrical two-player game, then you cannot possibly lose, not matter what the other guy does. so in poker, if you play a guy heads up, and play NES in a no rake environment, you will at least break even. if your opponent deviates from NES in any way, you will win money.
if you play NES in a more than two-player game, then unfortunately there's no guarantee that you won't lose (because of the possibility of implicit or explicit collusion against you)
3) in practice you can't play NES in a complex game like fixed limit heads up. a person cannot store enough bits of information in their head to remember a NES strategy (or indeed any strategy. this is why poker requires thinking while you play. if you could remember your entire strategy as a list, you'd just 'look up' what to do in a given situation)
4) optimal play (the idea of using Nash equilibria) is nothing new, it's been around for decades. John Nash himself experimented with applying optimal strategies to the game of poker in like the fucking fifties
5) i haven't yet seen a proof for this anywhere, but it seems intuitive that for a game as complex as fixed limit holdem, there are likely to be several different optimal strategies. and when i say several i mean like fucking millions.
i have some experimental evidence for this, that comes from searching for optimal strategies for some simplified limit games. in these toy games you routinely end up with multiple optimal solutions. generally all these strategies can be then divided into classes of strategies, that differ from each other only in minor details, or are otherwise equivalent in some sense.
of course the fact that these toy games often end up having a bunch of similar optimal solutions doesn't necesseraly mean that we would get similar results with the full game. perhaps there's only a single solution, who knows... i'd be shocked though.
On note 5.) I haven't seen a proof either. Nor have I seen a precise statement (by a mathematician) about what has actually been proved. Those collusion conditions are new to me. I strongly doubt the non-uniqueness though. I recall statements to the effect that it has been shown that the equilibrium is unique.
On note 4.) I object to the unqualified use of the word optimal. You obviously mean GTO. Optimal, by itself is, in my world, not a standard term with precise mathematical meaning . Much confusion arise from this. [In fact, the statement "GTO is never optimal" is true (provably so) with most poeples interpretation of the word optimal ?(. Now I had you confused ♦]
We need a real mathematician.
/Johan =
Originally posted by YohanN7
On note 5.) I haven't seen a proof either. Nor have I seen a precise statement (by a mathematician) about what has actually been proved. Those collusion conditions are new to me. I strongly doubt the non-uniqueness though. I recall statements to the effect that it has been shown that the equilibrium is unique.On note 4.) I object to the unqualified use of the word optimal. You obviously mean GTO. Optimal, by itself is, in my world, not a standard term with precise mathematical meaning . Much confusion arise from this. [In fact, the statement "GTO is never optimal" is true (provably so) with most poeples interpretation of the word optimal ?(. Now I had you confused ♦]
We need a real mathematician.
/Johan =
^^^^^^^^ perhaps with all my words out there this is what I meant. Yet we keep arguing and then am being called noob. It is not as hard to list some topics and find some wording behind it.
here for example is interesting discussion about it: http://www.deucescracked.com/forums/34-Small-Stakes-Shorthanded-NL/topics/556691-GTO-ranges-OTR
Originally posted by redskwerl
okay, some notes for the discussion so far1) in order to define a strategy, you must list what you'd do in every possible situation that may occur in the game. that list is your strategy. there's no strategy that isn't like a big ass chart.
2) if you play a nash equilibrium strategy (NES) in a finite zerosum symmetrical two-player game, then you cannot possibly lose, not matter what the other guy does. so in poker, if you play a guy heads up, and play NES in a no rake environment, you will at least break even. if your opponent deviates from NES in any way, you will win money.
if you play NES in a more than two-player game, then unfortunately there's no guarantee that you won't lose (because of the possibility of implicit or explicit collusion against you)3) in practice you can't play NES in a complex game like fixed limit heads up. a person cannot store enough bits of information in their head to remember a NES strategy (or indeed any strategy. this is why poker requires thinking while you play. if you could remember your entire strategy as a list, you'd just 'look up' what to do in a given situation)
4) optimal play (the idea of using Nash equilibria) is nothing new, it's been around for decades. John Nash himself experimented with applying optimal strategies to the game of poker in like the fucking fifties
5) i haven't yet seen a proof for this anywhere, but it seems intuitive that for a game as complex as fixed limit holdem, there are likely to be several different optimal strategies. and when i say several i mean like fucking millions.
i have some experimental evidence for this, that comes from searching for optimal strategies for some simplified limit games. in these toy games you routinely end up with multiple optimal solutions. generally all these strategies can be then divided into classes of strategies, that differ from each other only in minor details, or are otherwise equivalent in some sense.
of course the fact that these toy games often end up having a bunch of similar optimal solutions doesn't necesseraly mean that we would get similar results with the full game. perhaps there's only a single solution, who knows... i'd be shocked though.
A 
A
Originally posted by redskwerl
2)...
if you play NES in a more than two-player game, then unfortunately there's no guarantee that you won't lose (because of the possibility of implicit or explicit collusion against you)
If your strategy is the Nash equilibrium and all the players have the same subset of information (i e, they only know their own hole cards and the board) you will at least BE. Implicit collusion does not play a role here, if I understand correctly what you mean by that.
Wow this got out of hand really quicklyL
OK let's quantify the terms I use:
GTO - Game Theory Optimal - The perfect strategy to use in the case you are up against an opponent also using a GTO strategy or, in more realistic terms, a strategy you cannot yet readily exploit. GTO-based play is by definitition unexploitable, however it doesn't take advantage of your opponent's errors to the maximum potential
Optimal - When I use the term "optimal" on its own, I essentially mean "Max EV", i.e. the best play to make under the current circumstances
I like to this of it, in a way, as the defensive side to your game. Everyone talks about GTO and Exploitation as if you have to either have your entire game defined by one or the other but that's completely not true.
Game Theory and Balance are your shield. They are what stops your opponent exploiting you. However to make the most off an opponent eventually you are going to have to adapt to his/her tendencies but attempting to do so without data/experience of his play is akin to leading an attack on a castle when you've no idea what's defending it.
If you try to play an exploitative game without data all you are doing is guessing and it's not like you're up vs a static strategy, you're opponent should also be adapting to ou and it's this lvelling war which balanced-play seeks to avoid. If your opponent isn't adapting, sure throw the kitchen sink at him.
To answer an earlier question, all exploitative strategies are, in themselves, exploitable. If you spot a guy being a nit in the blind and decide to open up more than what is usually advisable he could counter-act by 3-betting you, at which point suddenly now it's YOU being exploited. So you adapt again....and so does he...and then you do....
Additionally an understanding of GTO/Balance play can actually vastly improve your exploitative game. Now you don't just know that someone's making an incorrect play, you know WHY. And additionally knowing the inflection point in many situations will allow you to start teeing off on the TAGs certainly at lower stakes as well as the fish and allow you to crush not only drooling 70/0 types but the guys who are more regularly in teh games too
Is it something to aspire to?
Well put it this way, Polaris beat the best players in the world at the time in a HUHU competition in 2008 and the GTO/Equilibrium bots ahve only gotten better since then, the Hyperboolean Model which replaces Polaris can address 10 times as many games states as Polaris could.
When I chatted w/ Phil Newall about the results of a bot competition briefly he basically said the only hope against something like that is that you're in a game where you can exploit another player at the table better than the bot can, similar to the example Yohan gave earlier.
As far as GTO in Multiway situations that is LIGHT YEARS away, and will probably never be solved
In HUHU Limit Holdem with a 4-bet cap there are approximately 10^18 different game states. Even moving the game to 3 hands would exponentially increase the possibilities making it impossible to solve.
Originally posted by Boomer2k10
Game Theory and Balance are your shield.
Following that logic Exploitation is our sword.
And in order to take a stab at our opponent, we have to lower our shield which could lead us being stabbed horribly if he's exploiting us (counter-act 3-bet example).
Don't worry though, we're respawning in every hand.
Playing against an unknown is like going into a duel at night in complete darkness and we don't know if the opponent will swing, stab, slash or defend, so we should defend and look for holes in his shield instead of swinging blindly and risking losing a heads. And if there are no holes in neither of our shields (both playing GTO), than we have an awkward standoff with two guys circling each other, defending perfectly and unable to hit one another until they die of rake.. err.. old age.
[x] unnecessary metaphor to complicate things even further
Originally posted by Tarhonya
Originally posted by Boomer2k10
Game Theory and Balance are your shield.Following that logic Exploitation is our sword.
And in order to take a stab at our opponent, we have to lower our shield which could lead us being stabbed horribly if he's exploiting us (counter-act 3-bet example).
Don't worry though, we're respawning in every hand.Playing against an unknown is like going into a duel at night in complete darkness and we don't know if the opponent will swing, stab, slash or defend, so we should defend and look for holes in his shield instead of swinging blindly and risking losing a heads. And if there are no holes in neither of our shields (both playing GTO), than we have an awkward standoff with two guys circling each other, defending perfectly and unable to hit one another until they die of rake.. err.. old age.
[x] unnecessary metaphor to complicate things even further
I like
Also update your blog!! 
Can someone point me to a rigorous*) statement and proof, preferably detailed, and specialized to poker, of the existence of GTO in FL HUHU and FL multi-handed.
*) Rigorous = Hardcore mathematics by a hardcore mathematician published in a journal of mathematics. (At Wikipedia they would say "sourced".)
/Johan =
Can either the guy with the shining horse, or the guy with the clumsy bronze horse, or any horse owner for that matter, explain what goes into GTO when actually determining a strategy for one particular situation. (Even a measly physicist will do.)
One could assume that we are allowed to do this:
1,) We are allowed to look at our hand.
2.) We are allowed to look at the board.
3.) We are allowed to look at the size of the pot.
4.) We are allowed to remember the betting sequence that got us thus far.*)
It probably ends there. Having a HUD (let alone using it) is a big nono.
*) Point 4 is already shady. We'll perhaps be making assumption about the opponents holding here (because we could (because, (in turn) we are allowed to remember the action)). Is this allowed? We are clearly allowed to be paranoid and suspect that the opponent is trying to exploit us. Then we must defend against the opponent exploiting us with any holding. Can we in any sense weigh the probabilities for each of his possible holdings (aside for counting combos)? I'' guess "no", we can't.
More:
- We must bluff with the proper frequency
- We must call down bluffs with the proper frequency
The only sensible definition of what constitutes a bluff is to run through every possible combination of hole cards in the opponents range. Then take a (not weighted) average. This is very very much in the spirit of the unfashionable fundamental theorem of poker. (That I like, because FTP is correct.)
Before I make a further fool of myself, please give some clear exposition of what GTO looks like in more detail than not being exploitable.
/Johan =
Originally posted by YohanN7
Can someone point me to a rigorous*) statement and proof, preferably detailed, and specialized to poker, of the existence of GTO in FL HUHU and FL multi-handed.*) Rigorous = Hardcore mathematics by a hardcore mathematician published in a journal of mathematics. (At Wikipedia they would say "sourced".)
/Johan =
Yes it's called Nash Equilibrium which has been around for years and has been proven to be correct for non-cooperative 2-player games and has been explored for multi-player games but is seen as ridiculously hard which is why when you see range building exercises they are almost exclusively for 2-player hands (i.e. postflop) as multi-player Nash is impossible for even a super-computer to calculate in poker (even modern day bots are a factor of almost 1,000,000 short of HU Game Theory Optimal Play)