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Old 06-18-2021, 10:31 AM   #76
Yeodan
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Re: In theory, GTO cannot win

Cool, thanks for the info!
As a total chess newbie it's interesting to read the view of an IM
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Old 06-18-2021, 10:55 AM   #77
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Re: In theory, GTO cannot win

GTO does try to balance. That s the one and only point of mixing frequencies.
It does inherit the properties of MES in equilibrium, but thats besids the point
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Old 06-18-2021, 11:13 AM   #78
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Re: In theory, GTO cannot win

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Originally Posted by Yeodan View Post
GTO is balanced and unexploitable as a result of trying to maximally exploit a GTO opponent.P
This isn't accurate, you can maximally exploit Nash Equilibrium without playing GTO. GTO is Equilibrium MES+Balance
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Old 06-18-2021, 10:05 PM   #79
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Re: In theory, GTO cannot win

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I think the chess comparison is kind of flawed as we are comparing a perfect information game vs imperfect information. Mixing is most likely required in poker GTO, in chess it is definitely purely optional.
Well, I did say that is the main difference (no mixing). Thus the comparison is not perfect but I just think for the vast majority of people with questions about GTO on this forum, thinking of it the "strategy that a computer would play" is much closer in chess to poker than lots of these other comparisons that come up, most notably RPS.

So thinking of GTO as "computer strategy", the key points that apply to both chess and poker are:

1. No human can possibly replicate computer strategy because of it is too complicated.
2. Computer strategy will beat every human... very badly.
3. If you study very hard and play much closer to the computer strategy compared to your opposition, you will crush them.

In my experience these are the most commonly misunderstood points about GTO in poker, but fairly easy to conceptualize in chess which is why I recommend thinking of it more like that even if there are no mixed frequencies.
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Old 06-23-2021, 09:51 AM   #80
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Re: In theory, GTO cannot win

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Originally Posted by soda_grapesoda View Post
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.
Hello. Just watch this video. He even uses the rock-paper-scissor example to explain why GTO can win money on poker.

https://www.youtube.com/watch?v=OMEH01MN87g
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Old 06-23-2021, 10:47 PM   #81
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Re: In theory, GTO cannot win

[QUOTE=Aesah;57166998]Ya there are no are mixed strategies unless its like "ok if i choose option A, its a draw, and if i choose option B, its a draw" and the computer random picks one in that case

If I open 50% 1.d4, and 50% 1.e4, that's a mixed strategy. In higher level chess where your games are public and players prep against you, it becomes important not to play a predictable opening.

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Originally Posted by Yeodan View Post
...

From what I understand there are hundreds if not thousands of openings available to the currently top rated human players.

I'd imagine at least a few of those, if not quite a lot, would be capable of forcing a win with white in a GTO match.
It's easy to decimate players that are much worse than you at chess. Check out this lichess skill distribution graph. A player that's 400 points higher than their opponent will statistically win 90% of the time.



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There's no "higher EV" in chess GTO in that sense, it's purely deterministic. Any given position either results in a win, a loss or a draw for white if both players play perfectly from that point forward. It's just one single outcome 100% of the time.

If there is any opening that can force a win with white then all openings that can force a win with white (against a perfect opponent) are also GTO and any mixture of these openings is also GTO.
Chess moves definitely have an expected value. Here's what it looks like:



The numbers in the top right represent the computer's evaluation of different moves as an expected value. 1 point is roughly equal to a 1 pawn advantage. Note that this is an estimate (28 ply deep) since calculating all the way to mate is practically impossible from most positions.

The win probabilities at the bottom are based on a library of human games, not computer games, so it's more exploitative.
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Old 06-23-2021, 10:49 PM   #82
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Re: In theory, GTO cannot win

[QUOTE=Aesah;57166998]Ya there are no are mixed strategies unless its like "ok if i choose option A, its a draw, and if i choose option B, its a draw" and the computer random picks one in that case

If I open 50% 1.d4, and 50% 1.e4, that's a mixed strategy. In higher level chess where your games are public and players prep against you, it becomes important not to play a predictable opening.

Quote:
Originally Posted by Yeodan View Post
...

From what I understand there are hundreds if not thousands of openings available to the currently top rated human players.

I'd imagine at least a few of those, if not quite a lot, would be capable of forcing a win with white in a GTO match.
It's easy to decimate players that are much worse than you at chess. Check out this lichess skill distribution graph. A player that's 400 points higher than their opponent will statistically win 90% of the time.



Quote:
Originally Posted by plexiq View Post
There's no "higher EV" in chess GTO in that sense, it's purely deterministic. Any given position either results in a win, a loss or a draw for white if both players play perfectly from that point forward. It's just one single outcome 100% of the time.

If there is any opening that can force a win with white then all openings that can force a win with white (against a perfect opponent) are also GTO and any mixture of these openings is also GTO.
Chess moves definitely have an expected value. Here's what it looks like:



The numbers in the top right represent the computer's evaluation of different moves, given perfect play, as an expected value. 1 point is roughly equal to a 1 pawn advantage.

The win probabilities at the bottom are based on a library of human games, not computer games, so it's more exploitative.

Lastly, to put things into perspective, a chess computer on my phone will beat the world champion 99/100 times, even though the evaluation is more or less just a 28 ply guesstimate.

Last edited by tombos21; 06-23-2021 at 10:57 PM.
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Old 06-24-2021, 02:44 AM   #83
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Re: In theory, GTO cannot win

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Originally Posted by tombos21 View Post
[Chess moves definitely have an expected value. Here's what it looks like:



The numbers in the top right represent the computer's evaluation of different moves, given perfect play, as an expected value. 1 point is roughly equal to a 1 pawn advantage.

The win probabilities at the bottom are based on a library of human games, not computer games, so it's more exploitative.

Lastly, to put things into perspective, a chess computer on my phone will beat the world champion 99/100 times, even though the evaluation is more or less just a 28 ply guesstimate.
Today's engines use EVs, yes.

I was talking about an actual full solve of chess though. In that context this kind of EV no longer makes sense.There's no randomness in a full chess solve, you select a position and the solution can tell you the deterministic outcome if both players play perfectly from that point on.

White winning a position 95% is not a possible scenario in a full solve. It's either 100% white, 100% draw or 100% black.
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Old 06-24-2021, 05:36 AM   #84
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Re: In theory, GTO cannot win

Fully solved chess would look like this:
https://en.m.wikipedia.org/wiki/Endgame_tablebase

You'd just have to cover the entire game, instead of the 6-7 pieces remaining subgames that are covered by today's endgame solutions.
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Old 06-24-2021, 04:12 PM   #85
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Re: In theory, GTO cannot win

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Originally Posted by tombos21 View Post
If I open 50% 1.d4, and 50% 1.e4, that's a mixed strategy. In higher level chess where your games are public and players prep against you, it becomes important not to play a predictable opening.
It's technically a mixed strategy but there's no reason to do it at optimal. The reasons for mixing it up are purely exploitative. I'm not a really strong player, but even then I'd think it's more important to further develop what you already know and (at the top level) discover novelties than to mix it up with dramatically different openings. Learning a bunch of different openings is splitting the time you can devote to each one.

In theory any move which doesn't change the value of the position would be part of a NE.
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Old 06-24-2021, 06:01 PM   #86
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Re: In theory, GTO cannot win

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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
It's an interesting question. I think that is correct that it is about the relative strengths of hands. If we just simplify that problem and think about a game of poker that was pre-flop all-in or fold rules, we would not play 72o as much as AA. Essentially, if our range pre-flop is stronger than our opponents, then we are +EV. In rock paper scissors, the ranges for each player are essentially the same. We can't pick a stronger range than our opponent without exploiting their tendencies. 3 scissors is as strong as 1 scissors, 1 paper, and 1 rock. That is why it does not matter how the villian plays RPS if we play GTO.
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Old 06-24-2021, 08:07 PM   #87
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Re: In theory, GTO cannot win

Quote:
Originally Posted by tombos21 View Post
If I open 50% 1.d4, and 50% 1.e4, that's a mixed strategy. In higher level chess where your games are public and players prep against you, it becomes important not to play a predictable opening.
yes of course but I meant in the context that GTO chess results in a draw for both players, it isn't necessary to mix in highest level chess
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Old 06-24-2021, 08:44 PM   #88
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Re: In theory, GTO cannot win

I get it, you could imagine some perfect tablebase chess strategy that would never have to mix between moves, although it could mix if it wanted to.

Realistically though, chess is far too complicated to solve. EV estimation is much more efficient. The best we've got in 2021 are 7-piece solved tablebases, the game starts with 32 pieces.

Also there is the added advantage of being able to choose between multiple strategies when studying. Sometimes it's worth it to give up a little EV to make the position more playable or give you better long-term chances. We don't have a good public system for studying alternative lines in poker.
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Old 07-10-2021, 07:51 PM   #89
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Re: In theory, GTO cannot win

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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.
I've been looking for an explanation this clear for days. Thanks!!
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Old 07-12-2021, 03:37 PM   #90
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Re: In theory, GTO cannot win

I don't know GTO poker or too much game theory, so I not mean this post as if I do. I'm just trying to understand it better.

Poker isn't RPS nor does it involve blinds. But what if it did?

I got a simple game of preflop push/fold. Each player has 100 chips before posting blinds. Hero BU villain A SB for $5 and villain B BB for $10. They only can push or fold. Player A is on the button with R,P or S. I think GTO play would be to shove 100% of the time. Villain B's GTO would be call 100% as well as villain C's. I'm not sure where I'm going with this other than to say if villain A or B folds any % of the time hero would profit. Is this right or am I missing something? And if the rake was 10% hero should fold correct?
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Old 07-14-2021, 01:57 AM   #91
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Re: In theory, GTO cannot win

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I got a simple game of preflop push/fold. Each player has 100 chips before posting blinds. Hero BU villain A SB for $5 and villain B BB for $10. They only can push or fold. Player A is on the button with R,P or S. I think GTO play would be to shove 100% of the time. Villain B's GTO would be call 100% as well as villain C's. I'm not sure where I'm going with this other than to say if villain A or B folds any % of the time hero would profit. Is this right or am I missing something? And if the rake was 10% hero should fold correct?
^ ya that all sounds right to me except the bolded part- the player on the BTN can shove or fold, it doesn't matter either one is 0 EV (if not rake). but everything else looks right.
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