[0,1] makes sense to me, I can see the lines and see the equations for FL/potbet-distributions. But when I see solutions for 52cards even just one street they start to not make sense in many cases. Sure I can see that some card has a blocker here for that combo there most of the times. But that is one street with one betsizing for the solver. But then add the turn, flop and preflop and different betsizings and future actions etc and I am pretty sure that I as winning NL2k player would be totally lost and that even Matt would be lost. Just keeping track of all different lines will be close to impossible.

I think you misunderstood me. Obviously you cannot understand all precise reasons for every bet size for each individual hand. Truly understanding every detail would mean understanding GTO play perfectly. But I'm saying that the strategy, viewed from a high level, will still roughly fit with most of the heuristics you do understand. You'll be able to see portions of the range being used as bluffs, bluff catchers, balancing hands, etc. Whereas I don't think there is any such high level understanding to be had in those chess videos (I'm not a chess player though).

Exactly. Understanding the correct theory of what to do vs. a range doesn't help much if you can't accurately estimate another player's range, etc etc.

You have to be correct. Chess is like chaos theory but poker isn't.

I disagree.

Some of the ideas behind GTO play are very basic and many people apply the idea without even knowing it.

In the case where someone is playing a hand without the initiative, the idea behind GTO is to defend enough (by calling or raising).

Anytime someone says something like:

• I can't fold this hand. I have ace-high, but the board is so dry, and I most of the time I won't even have a pair. I need to defend here. I could call or raise, let me think about it.

Or something like:

• I'm near the bottom of my range, so I am okay folding here.

... they are basically thinking GTO in that they are making sure their villain isn't exploiting them, and the GTO approach is all about playing unexpoitatively.

So you are looking down at K7s in our solution for poker. We check for the branch Kh7h:r2.5r10 and see that it's call. Why is it a call? We looka bit more and see that the tree moves into 117600 different branches. Sure we can analyze a few of them and some of them we hit our hand, some of them a draw, some of them we get a nice blocker and some of them we fold. But why didnt we 4bet? "Because the EV is higher calling" will be the answear for tons of questions, not "we use it as a semibluff because the king has a blocker for KK, AK, KQo and 7 for A7,76s,75s".

same in chess, we see the complex position and see that Nxd4=1 Ba6=0 and 0-0=1/2. We just dont understand it. It is the same for both game's solutions.


Try out a GTO for chess position solver:
http://www.k4it.de/index.php?topic=egtb&lang=en

Please point out if something of the following is wrong.

The way I see it there is nothing to guarantee us that at the Nash equilibrium the strategy that is played is not a function of the other players frequencies of making certain actions. Thus, the Nash Eq strategy of how to play against 3-bets could be a function of the 3-betting range of the opponent, which means that different amounts are being lost against Aces depending which other hands opponent 3-bets.

Ofcourse in poker when both players are at a Nash Equilibrium, having the Nash equilibrium strategy to be a function of opponents actions would be pretty useless as other players strategy is known and hence the result of this function is known. However, when opponent deviates from his Nash Equilibrium strategy then the value of this function is no longer known and is opponent dependent. Hence, it is possible that the reaction to opponents 3-bets are opponent dependent, hence possible that different amounts are being lost against Aces depending on opponent when we are playing our Nash Equilibrium Strategy (I guess that' s what you mean by GTO?).

source: this thread, about a gazillion times.

i mean wtf, did you still not get what a NE is but prefer to keep guessing itt instead of reading the ****ing definition?

It's quite clear from this thread that there are some counterexamples.

"So you are looking down at K7s in our solution for poker. We check for the branch Kh7h:r2.5r10 and see that it's call. Why is it a call? We looka bit more and see that the tree moves into 117600 different branches. Sure we can analyze a few of them and some of them we hit our hand, some of them a draw, some of them we get a nice blocker and some of them we fold. But why didnt we 4bet? "Because the EV is higher calling" will be the answear for tons of questions, not "we use it as a semibluff because the king has a blocker for KK, AK, KQo and 7 for A7,76s,75s"."

Exactly. Toy games are useful because they translate reams of information into a few principles which we can apply with human imprecision to many different game states. As a human trying to play GTO, we need to make heuristics for ourselves which capture the most information possible. For instance, the principle 'bet all your value bets and add an appropriate amount of bluffs,' does a good job capturing near optimal play even if we size our bet somewhat conventionally.

I know several people who understand all this game theory stuff and can't beat 50nl. I also know several people who beat 5/10+ and their knowledge of game theory stops at just the basics of exploitability/balance. I'd guess in general there is a positive correlation between understanding game theory/nash equilibriums and poker, but in general since it's a game where the goal is to maximize how much you win by (as opposed to chess where you get a win if you win in 5 moves or 50 moves, so gto will always out-perform any strategy), you generally see much better returns working on figuring out strategies of opponents and exploiting them rather than trying to play gto, especially given there's a rake (aka it's possible gto would actually lose post-rake).

Bots win by forfeit apparently.

Good game humanity.

Ya I think you didn't understand anything of what I wrote.. I obv know about Nash Equilibriums. There are a lot of ideas in my previous post but I don't want to overwhelm your brain so for a start focus on the main idea which is simple:

How can you guarantee that the NE Strat (of our bot) doesn't contain instructions like "If he 3-bets x% call cx%", where c is constant say?

Kisses

...because then it wouldn't be the nash equilibrium strategy.

Hi.

Yea, lots more to poker than game theory - tilt control, accurate range estimation, game selection...

nah thats wrong..

So you've excluded a bit of strategy therefore the definition of a game theory game has not been fulfilled since you need to be able map every possible combination of strategy to determine specified pay offs.

I think the only practical semi-solution for solving heads up holdem is to feed the computer trillions of session histories (and regularly update) and build an algorithm based upon the winning positive expectation moves.

What if a certain opponent actually never checks behind with King high, but does with A high ? (which is very possible as some players check behind a high expecting it can win showdown but has no value to bet, and bluff there K high hands so that opponent might fold A high or bottompair)
Then doesn't the "gto" strategy, get it wrong? I guess I am saying that the nash eq strategy would not make an assumption like this that the opponent will check behind more often with K high. It cannot make these kind of assumption on player ranges in specific spots, if it did, it would be exploitable. The "bot" cannot assume that K high is more often in the range of a player checking behind in this spot then A high.

I realize i probably misunderstood something along the lines of the first player is doing that because it is playing optimal against what the second player "should" do. It is interesting to note though, that if the GTO is doing as you say and making plays like the one you detail, by using what the "optimal" range of the opponent is, it seems that it could be making "mistakes" against someone NOT using those "optimal" ranges, and therefore calls into question whether or not the bot would even make plays like this.

You don't seem to have made any moderately convincing arguments that HUNL strategies are not a finite set. Millions, billions, trillions, whatever, it's theoretically countable and mappable, ie. there is at least one GTO solution.

Re: last sentence 1st paragraph:
Yes, the bot can "assume" that if it is the best response. A GTO/NE bot is playing the best response to itself, thus if doing something w/ range x is the best play vs the bot then the bot is also playing the best response to that something. The bot doesn't care whether it is right or wrong, because when its opponent deviates from GTO strategy the bot gains.

Re: 2nd paragraph:
If by "make mistake" you mean use a less profitable strategy than one that is purely exploitive, then yes a GTO bot can "make a mistake" in any given scenario.

The whole concept of an equilibrium is that nothing changes. In a Nash Equilibrium, nothing changes because neither player has strict incentive to change. Therefore, the Nash Equilibrium is where both players are playing a best response to their opponent. Because of this unchanging equilibrium, a NE player would never have a varying 3bet % - his strategy is set and he has no incentive to change it. Because a NE player would never have a varying 3bet %, his NE opponent would not have a 4bet % using the 3bet % as an input variable (a varying 4bet %) - he is already playing a best response to the best response.

You are thinking more about creating a maximally exploitative bot, and I think your point could be valid. It does not apply to a Nash Equilibrium bot, though.

Ya I understand and agree with everything you say. Obv when both of them are playing their NE strategies they will not vary their frequencies based on other player frequencies because they already know the other players frequencies!!! My point is that there is nothing to guarantee that our bot's NE strategy doesn't contain an instruction line like "If he 3-bets x% call cx%" that would simply be "asleep" when the other player plays his NE (would be "asleep" because we would know his x due to knowing his strategy). BUT at the moment that the other player stops playing his NE strat then this line "wakes-up" and starts to vary depending on opponents x value!!

I don't doubt that when the other player plays NE strat our strategy is set I just question whether the instructions that have it being set could unset it when opponent stops playing his NE strat. Think about it.. its definitely not something obvious.

Yes there is....NE must play exactly the same against all opponents. The strategy is static....so every hand is played as if it was it's first hand against a totally unknown opponent.

You're somewhat right in that GTO, at least in some games, has exploitive plays 'written in', even though they would never be used vs a GTO opponent. If you have quads on board in stud and the other player keeps calling bets, clearly there's no way to act 'as if' the opponent is playing GTO. However the GTO strat doesn't 'think' it's switching into explo mode at that point; it's just maximising vs the nemesis like it always does.

Opponent's frequency of taking any action doesn't come into it though.

yeah im going to disagree and say a lot of top players dont and play more by feel. As long as their feel doesnt get "off" they're good, but those sorts of players can be a little more streaky and can get stuck in ruts. I mean I watched a bunch of PoorUser videos and I never thought the theoretical side of poker was his strength, but he had a good sense of where he stood in a hand.