How exactly would you exploit it once you know the BOT's stand pat calling frequency? I believe the idea is that the bot will randomly choose hands with different strengths, nutty and bluff catchers, at such a frequency that it doesn't matter what you do. The randomization of the hands (achieved by choosing specific bluff catchers in their ranges that will occur randomly) as well as the unexploitable equity of the nutty hands they call with will prevent you from exploiting them.

There's actually information that changes between those situations without assumptions - the bot's range. It would play differently postflop not because of the opponent's actions but because of its own range which in turn changes its optimal frequencies.

It is very easy to describe GTO strategy to the layman but I guess it is left to me to do it.

Imagine if you are forced to tell your opponent how you will play every hand in every situation. But with the stipulation that the strategy you are divulging includes some randomizing. But the randomizing probabilities have to be divulged also. So perhaps you will divulge that playing limit holdem you will, with aces in the big blind reraise 85% and flat call a raise 15%.

Armed with this information your opponent can guarantee himself a break even game. By matching your play. And he can guarantee a win by usually matching your strategy, the one you divulged to him, except when he is sure there is a better alternative.

The only way that your expert opponent doesn't have the nuts is if somehow your strategy is clearly "perfect" game theory wise. In that case any time he tried to improve upon your strategy he would cost himself money (or in some cases do equally). An example might be if he tried to improve on your calling strategy on the river when he could easily be bluffing. You call a pot sized bet half the time. If he doesn't mimic you he will cost himself money if your bluffing strategy is good.

But most decisions are far more complicated than that. And it is reasonable to assume that if you have to go first in divulging your strategy he will be able to come up with one that beats it. Think picking the best all in hand from 22 AKoffsuit and JT suited. Not a perfect analogy but you see what I mean. Similarly it might stand to reason that If I have to come up with a strategy that I am forced to divulge, there are head up games where this onus is going to allow a smart opponent to exploit it no matter what that strategy is. Even with randomizing my being fordced to divulge means the other guy can find a counterstrategy that wins. It would seem that n some head up games there is no divulged strategy that is immune.

Except that John Nash suppsedly proved that all symetrical head up games, by their mere headupness, ARE immune. There is a strategy, according to him that exists for everyone of them whereby even if you divulge it to your opponent, he can't use this information to get an edge. That strategy may take a supercomputer a trillion years to find but it is out there somewhere. His logical proof of this helped him get a Nobel Prize

fyp

First of all, durrrr-

If you were right and could prove it, you would win the Nobel Prize in Economics for disproving a proof that already won the Prize in 1994.

I know you're from NJ. Next time you're home with your folks, why don't you take a ride down to Princeton. Doctor Nash can often be found in his office and will chat to curious folks.



Your explanation shows a fundamental misunderstanding of game theory and Nash equilibria.

I would be happy to book an 100k bet with you right now that you're wrong. I bet I could prove it to you pretty fast as well.

The reason GTO play can fold more often vs a larger bet is not because their range is stronger but because the optimal frequencies for defense are going to be much lower based on the odds being laid. GTO does not have the privilege of acting on assumptions as that opens your strategy up to exploitation when those assumptions are known and acted against.

so much fail in this post I don't even know where to begin. Seriously, before posting about game theory, please take a class or read a book. Applies to lots in this thread.

You probably don't know where to begin because you're wrong.

See I can add just as much the conversation as you did. Ain't it fun?

I'm sure you understand this but maybe were just careless in your post. He doesn't always cost himself money in this situation. He just never gains, so he [weakly] costs himself money.

Okay well, let's start with some definitions. The idea of NE is you both know each other's strategies and are best-responding. Therefore the second part of your post is nonsense.

EDIT: I may have misinterpreted what you meant as I've only read 2 of your posts ITT but my position overall is there is a NE and durrrr is just completely wrong/a fish.

The idea of knowing assumptions and acting against them is nonsense when it comes to NE. If you act against them, your opponent knows that. It's not like you're duping him. The idea of NE is you know the other person's strategy and are best-responding given their strategy. This goes both ways for 2 player game.

I fixed it, thanks.

I understand this and it's not the argument I was making. My point is that opting not to draw is a risk or an expense in the same way that a larger bet is and that for that reason the optimal defense frequency against pat and bet is lower than against draw and bet.

Consider the following game:

We each get five random numbers 0-100. Round of betting. Discard as many numbers as you like and get new ones. Second round of betting and showdown. Highest sum wins. Do you think GTO play is the same regardless of how many draws each player takes in this game too or do you think this is not conceptually analogous to a real draw game?

Let me simplify the game even more.

Dealt a random number 1-3. Round of betting.
Discard/replace or not. Round of betting + showdown. Highest wins.

Is this a fair simplification?

One hand = one game. Strategy can adjust if there are many hands? http://en.m.wikipedia.org/wiki/Repeated_game

Were Mayan astronomers subconsciously doing integral calculus in their heads? The results were as if they had been for some calculations.

And if they were so good at predicting things why didn't they predict Schrodinger's cat?

I believe this is fine, too. If it's not we'll see in a minute I think

I would call myself a layman but what you write does nothing for my understanding. I am clueless and probably hopeless. This has not stopped me from reading every post ITT. Hope springs eternal.

As far as a trillion years goes, I believe the universe is only 16 billion years old.

Hahahah, oh boy. In starting to write everything out I'm suddenly fearing I might have just gotten Monty Halled but I'm still not certain that applies. Thinking on it for a bit now.

There are no 'occasional spots' where you can exloit a GTO HU NL bot! This is the very definition of Game Theory Optimal Strategy. Assuming a fixed stackdepth and each player having to both play from the SB and BB and a finite number of betsizes, by Nash's Theorem there exists a mixed strategy that will not lose in expectation.
I dare durrrr to come up with one hypothetical spot where he could exploit the GTO strategy. Since he did already in the 2011 thread I will use that one to show why he is wrong, but he is free to come up with another example. http://forumserver.twoplustwo.com/sh...&postcount=200

On the river with a Th9h8hxx board given the action durrrr's range will consist of Jh6h X percent of time and he will shove 50,000 times the pot 100% with it.
And with positions reversed (i.e. the GTO bot on the button) and the same board and action till the river the bot will have Jh6h Y percent of time.

Now durrrr makes the assumption that - mostly given preflop 4bet, since one would expect Qh7h not to fold too quickly on Th9h8h - does have Qh7h with exactly 0%.
He does never state how often he would have Qh7h in the same spot! I will come back to this later, since it can be used against durrrr's argument.

The bot has Jh6h with the optimal frequency of Y percent and will shove it with a Z percent frequency, if this optimal frequency was 100% then durrrr would not exploit the bot since he plays this spot exactly the same. If this frequency is lower then durrrr is bluffing away his 100,000,000bb too often.

Also the bot will call a 50,000 times potbet on the river with his bluffcatchers with a frequency that is (roughly) proportional to the inverse of the size of the bet. So when he bluffs for 50,000 times the pot he will win 1 potsize 49,999 times and lose 50,000 times the pot 1 time vs the hands that would've called a potsized riverbet (clearly these numbers are not exact but just an indication since I don't know the GTO strategy for 100,000,000 HU NLHE and furthermore they are based on a comparison to a 1x potbet for simplicity where is it conceivable that optimal betsize is much larger). Winning 1 unit 49,999 times and losing 50,000 units one time equals losing 1 unit one time, which is (again roughly) the same as losing to the better hands at showdown when checking.

Also note that Qh7h is not the only bluffcatcher that the bot will have in his range. If he would only bluffcatch with Qh7h then his GTO opponent (and durrrr when he copies this strategy) could make twoway bets with {KhJh, AhJh} by shoving them, folding out the ace high flush, the 7h6h straightflush and boats (to which they lose), and get calls from Qh7h (which they beat). Hence these hands need to bluffcatch also.

But most importantly, by turning these strong hands AhJh, KhJh, Jh6h into a bluff will lose expectation compared to the strategy of the GTO bot. durrrr thinks he can do something special that the bot cannot do (i.e. shoving some combo's in a certain spot with a certain frequency) but once you write it out for what it really is you don't even need to understand Nash's Theorem to see that durrrr is mistaken here. Everything durrrr can do the bot can do also.






Back to how often durrrr calls the 4bet with Qh7h. If durrrr does have Qh7h with the same 0% frequency as the bot, then clearly the bot can do the same to durrrr (i.e. bluffshoving Jh6h with a 100% frequency when this has a higher expected value than playing it for value).

But it is not impossible that there are spots where the bot never has the nuts and durrrr's range is stronger to the point where durrrr can shove a wide range or even his entire range and the bot has to fold everything. Once you understand this you will understand that any such example spot that you can come up with is just as useless as the Jh6h on Th9h8h spot.


This does not prove that durrrr could exploit the bot since the bot can always do the same. And furthermore these situation will come up very infrequent (if ever).

One example would be that durrrr 2x potbets the turn and the bot calls, and on 70% of rivers durrrr will shove and the bot must fold and when the bot hits his 30% good rivers he has exactly 0 implied odds. The bot must win the pot 40% of times to make up for the 2x potbet call on the turn but only wins 30%, a contradiction since the bot only makes optimal calls on the turn.

We can conclude that against a GTO bot there will be no such spots where you can bluff him of his entire range without a cost. The cost will be either money lost in expectation on previous streets by playing too loose or too tight and losing more in common spots than you can make up with the very rare spots.

This is likely the same situation as the Qh7h call preflop, say it loses 5bb on average when you call. And 1 in 1,000,000 times (the Th9h8h runout with given action) you lose a 200bb pot on the river to a shove that you cannot call since you don't have Qh7h does not mean you got exploited since 5bb >>>>> 200bb/1,000,000.

http://forumserver.twoplustwo.com/sh...&postcount=212
This is clearly wrong, if you always fold anything but QhJh to a shove the bot can exploit you by bluffshoving any Jh in this spot. Which in turn would be highly exploitable since you could then call with any hand that has over 50% equity against his {JhX | not a valuehand} range on the river. So he will bluff with a much lower but optimal frequency.

If you only get paid off 0.002 percent of the time with your straightflush against his bluffcatchers that would've called a 1x potbet 100 percent of the time you don't make any money by shoving, at least not in expectation!


This logic would've been correct if you had an edge in just one spot.
His calling frequency of x percent is optimal against your optimal range. Note that the GTO bot implicitly 'knows' your range since it knows it's own range in the same spot and how to play against it. Deviating from the optimal range (for example calling too many 4bets with Qh7h) will by definition not make you any profit, at least not in expectation.

It is very likely that with 100,000,000bb stacks the bot will have combo's that can make or block the nuts on even the rarest spots to protect itself from 50,000x potbets. Qh7h has this property but it is not even the best bluffcatcher in this rare Th9h8h example as I've explained with the twoway bets.

If Qh7h was a hand that could win 100,000,000bb more than X/100000000 times by calling Xbb at a certain point then for sure the bot would make that call with a positive frequency.

• cliffs:
• durrrr thinks that whenever his range is stronger than his opponent to the point where he could shove his entire range to get 100% folds in a Xbb pot in a spot that occurs with frequency Y will always weigh up to the cost of building your range up in a way that deviates from the optimal mixed strategy, when in reality the cost of building your range up like that will be always >= X*Ybb by the very definition of optimal strategy;
  
• durrrr makes the mistake by thinking in terms of hands in a vacuum and not in terms of expected winrate of a certain mixed strategy against another mixed strategy;
  
• durrrr owes me at least $5k for all the propbetfish action that he is not gonna give to other HS regs after reading my post.
  

too simple.

in this example your nut hands, your bluffs and the meaty center all act the same (or at least can act the same without there being a cost) whereas in stud, it would just be the two extremes standing pat.

obviously you COULD stand pat with your medium strength hands in stud, but it would be the lesser option to drawing.

the other persons response to you standing pat is to basically assume that (for a pot sized bet) you're bluffing about 1/3rd of the time, and they're going to call with the top half of their range.

so it doesn't matter to the bot whether you choose to flesh out your stand pat range. he would prefer that you do.

People who speak broken english because it is not their first language do not think in broken English and are not incapable of deep, rational, sophisticated thought.

In other words: no, that is not his thought process. That's just how he would communicate it in English.

I would play the proposed 1-3 toy game all day long against an opponent whose strategy included bluffs. Maybe you guys are assuming the (unstated) antes and/or blinds, though.

obviously we're assuming blinds/antes, it's just not very important to state the specifics. bluff frequencies would change depending on the pot size but the basic character of the game wouldn't (except that obviously no poker game works without some sort of blinds/antes).

Most players who are striving for GTO wont usually try to make these adjustments. They also dont believe any of the spots they put themselves into are exploitable.

Why GTO is unobtainable. For every player that you're playing, you don't know
how many hands you'll be playing with him in the future. Because he could go
broke and leave poker, or you could go broke and leave poker.

The GTO play where you "know" that you'll be playing him for 300,000
more hands is different from the GTO play where you "know" you'll
have only 250 more hands against him.

Just an idea.

ike i'll play a lhe bot thats setup in a way where it can't be adapted from the start. 500-1k or 1k2k lhe 100k hands? (I'm bad so need a bit to learn how to beat bot). ideally id wanna play on ftp/stars b/c don't want any chance of bot gaming a new site if rng is fkd up etc