Random Game Theory Stuff

Starting this thread as a place to talk about different game theory concepts without derailing other threads.

This seems to be a very developed field with right and wrong answers but most people in the poker world misuse or misunderstand the terms and concepts of this field (myself included). I'd like to use this thread to get the correct definitions of terms and to better understand game theory concepts in general.

On January 28 2015 12:02 Romm3l wrote: remember optimal strategy is defined as the strategy that minimises the expectation of a perfectly adapting opponent.

First of all, what is optimal play?

Is this just shorthand for "game theory optimal play"?

Because it seems "optimal play" could also be interpreted as the maximally exploitative play -ex. taking maximum advantage of a fish's weaknesses. I'm pretty sure we usually mean the former definition but wanted to point out it could be confused with the latter.

Right now I assume that "optimal play" is shorthand for "game theory optimal play" which is a strategy that is at "nash equilibrium"

http://en.wikipedia.org/wiki/Nash_equilibrium


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On January 29 2015 17:02 Romm3l wrote: because minimising a perfectly exploitive opponent's expectation is the strict definition of optimal play. http://en.wikipedia.org/wiki/Minimax

The creator of GTORB had this to say about defining GTO Strategy (I'm assuming we're using this interchangeably with "optimal play" in the way that you have:

"One of the most common misconceptions that people tend to have regarding GTO poker play comes from the idea that somehow the key element of a GTO strategy is its "unexploitability" or "balance" and the belief that any unexploitable strategy is inherently GTO.

The conditions required for a strategy to be GTO are much stronger than simple unexploitability (although of course any GTO strategy must be unexploitable), and in a practical sense, the elements of GTO play that are generally going to be the most valuable to try and use in real world poker games are the elements that have nothing to do with unexploitability. By focusing on unexploitability people minimize and miss what is actually the a huge part of the value of understanding GTO play." - http://blog.gtorangebuilder.com/2014/...-so-much-more-than-unexploitable.html

Interested to hear your thoughts after reading and if you would change your definition or not.

GTO = Optimal = Nash

I think "optimal" is a bit confusing because it doesn't necessarily mean "the best" in this instance, but whatever, we're stuck with it.

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I think much of the other confusion actually comes from different usages of "exploitable". It can mainly mean one of two things:

1. Exploitable means using a strategy that has weaknesses. In this sense, a weakness merely means "not perfect", and we usually define "perfect" or "optimal" as the GTO strategy. So when we use this definition, an "exploitable strategy" is actually just the negation of the GTO strategy by definition. This logically entails that all GTO strategies are actually unexploitable by definition. This does not mean that a strategy cannot be beaten or will never lose money on average.

2. Exploitable means a strategy that can lose money. This logically entails that an unexploitable strategy cannot lose money. For heads up rake-less poker, in which an even number of hands are played and starting stacks are reset, the GTO strategy is unexploitable. For multiway poker, or for hu poker with an uneven number of hands (one player gets the sb more often), the GTO strategy is not unexploitable. This should be intuitively obvious. No matter how good you are, if you play the big blind in a heads up game every hand you'll lose money.

I don't really think using either 1 or 2 is necessarily wrong or right. But I think I'm a bit partial to 2 since it seems to fit the more colloquial definition of "exploit". We just need to drop the notion that GTO play is "unexploitable" for it to fit. Definition 1 also doesn't quite work when we're playing multiway poker. The Nash equilibrium is the state where no one player can deviate and improve their expectation. But two players still can both deviate (collusion). So it doesn't seem right to say we're "unexploitable" when two players can be colluding against us and winning a ton of money against us.

That link actually clarified a lot of things to me I was confused about how could only be a virtually infinite amount of balanced shove ranges on the river by changing sizing yet only one GTO, good to know now.

2. Exploitable means a strategy that can lose money. This logically entails that an unexploitable strategy cannot lose money. For heads up rake-less poker, in which an even number of hands are played and starting stacks are reset, the GTO strategy is unexploitable. For multiway poker, or for hu poker with an uneven number of hands (one player gets the sb more often), the GTO strategy is not unexploitable. This should be intuitively obvious. No matter how good you are, if you play the big blind in a heads up game every hand you'll lose money.

From a math point of view, that's not what exploitable means. Whether a strategy can or can't lose money on average doesn't necessarily have to do with GTO (although if you are restricting it to a situation that is symmetric it should) . If we were playing a headsup poker game where the button didn't move, even though someone is stuck with the big-blind every hand they can still play in a way which is game theory optimal. That way would simply be the strategy that guarantees the highest EV if the opponent is playing in the best way possible to beat that strategy. The strategy is GTO (and also unexploitable, which is one of the necessary components of GTO) but in this case it can still be losing because there is an inherent advantage in the game that the button gets to take advantage of.

*EDIT*

Which was the point of your post. Sorry. That the mathematical definition of it is not how most people would usually toss around the word.

I don't think there's an official "mathematical definition" of exploit like there isnt an official definition for "game theory optimal". It's mainly just a word poker players throw around.

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Been reading the GTORB blog a bit and I gotta say it seems completely wrong to me somehow. Speaking mainly of the Brain Teaser #6. Seems like the author is arguing that we're unexploitable because our opponent can't adjust to us to make more money, even though we're not GTO because we can adjust. This however doesn't account for the fact that villain could already be using the best possible exploitative strategy.

On January 30 2015 02:00 NMcNasty wrote: I don't think there's an official "mathematical definition" of exploit like there isnt an official definition for "game theory optimal". It's mainly just a word poker players throw around. ------- Been reading the GTORB blog a bit and I gotta say it seems completely wrong to me somehow. Speaking mainly of the Brain Teaser #6. Seems like the author is arguing that we're unexploitable because our opponent can't adjust to us to make more money, even though we're not GTO because we can adjust. This however doesn't account for the fact that villain could already be using the best possible exploitative strategy.

Brain Teaser 6 is saying that on both cases, in the shove and the bet/bet scenarios we have a perfect balanced ratio of bluffs/value thus even if villian knows perfectly our range he cannot exploit us, however the bet/bet line results in better equity.

Nash Equilibrium (NE) means that players are playing best response to each other. So If I'm playing x, villain's best response to that is y, my best response to villain's y is again x. (x,y) is NE.

OP's link gives a definition of unexploitable which goes like this: If I play x1, best response to that is y, which is part of (x,y) which is NE, then I'm unexploitable. As the example demonstrates, the hero is better off by switching to x from x1, knowing that the villain will play y. That is, x1 is "unexploitable" but is not a best response to the best response of x1, which is y.
I don't know if this is the "correct" definition of unexploiatbility.

In 0-sum games like poker, NE is always also a minimax solution. That is, if I minimize my loss against the "best" strategy that my opponent can choose, that strategy x will be my part of NE.

It may happen that I am playing x, part of NE (x,y), villain is playing y1, so that y1 is a best response to x, but x is not best response to y1. That is, I'm playing my part of minimax/NE but actually pass on making money against villain. If I switch to x2, which is best response to y1, we will not be at a NE with (x2, y1), because now the villain can switch to y2 and start making money against my x2. So if I choose to "abandon" my NE strategy and try to exploit the opponent, I may open myself to exploitation. The cycle of adapting to each others' strategies may or may not bring us to NE, depending on how we adapt.

On January 30 2015 03:27 Baalim wrote: Brain Teaser 6 is saying that on both cases, in the shove and the bet/bet scenarios we have a perfect balanced ratio of bluffs/value thus even if villian knows perfectly our range he cannot exploit us, however the bet/bet line results in better equity.

Right, so he's a using weird third definition of exploit, where it specifically means changing your strategy. If we already have the best possible strategy against any given strategy, and given that our opponent's strategy is non-optimal, we're already exploiting our opponent. There's no need to change strategies in order to satisfy the definition of exploit if we already have the best one.

On January 30 2015 07:48 pluzich wrote: OP's link gives a definition of unexploitable which goes like this: If I play x1, best response to that is y, which is part of (x,y) which is NE, then I'm unexploitable. As the example demonstrates, the hero is better off by switching to x from x1, knowing that the villain will play y. That is, x1 is "unexploitable" but is not a best response to the best response of x1, which is y. I don't know if this is the "correct" definition of unexploiatbility.

It seems wrong. Its basically saying that if our opponent's best strategy against us is the Nash strategy, then somehow, our strategy, regardless of what it is or what its EV is, automatically becomes unexploitable. I mean if our opponent is both taking advantage of the fact that we're using a non-optimal line, and is making money off us, but we can still be unexploitable, I'm not sure what "exploitable" could possibly be.

gt course i plan to watch

On January 30 2015 09:10 NMcNasty wrote: Show nested quote + On January 30 2015 03:27 Baalim wrote: Brain Teaser 6 is saying that on both cases, in the shove and the bet/bet scenarios we have a perfect balanced ratio of bluffs/value thus even if villian knows perfectly our range he cannot exploit us, however the bet/bet line results in better equity. Right, so he's a using weird third definition of exploit, where it specifically means changing your strategy. If we already have the best possible strategy against any given strategy, and given that our opponent's strategy is non-optimal, we're already exploiting our opponent. There's no need to change strategies in order to satisfy the definition of exploit if we already have the best one.

I dont know whats your confusion.

That example is to demonstrate that an inexploitable play (balanced range) =/= GTO there are many inexploitable lines but they are not GTO because they yield lower EV overall

When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced.

On January 30 2015 17:31 NMcNasty wrote: When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced.

imagine c/r river with nuts to 'balance' your c/f when betting is more +ev (=putting hands in wrong ranges)

or even using 'non-optimal' sizing on any street


e: nvm what i said

:sitting here, confused:

On January 30 2015 18:07 dogmeat wrote: Show nested quote + On January 30 2015 17:31 NMcNasty wrote: When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced. imagine c/r river with nuts to 'balance' your c/f when betting is more +ev (=putting hands in wrong ranges)

The reason we do that is to prevent ourselves from being exploited by having a weak checking range. Its not that we have two unexploitable options but one is better. One option is clearly exploitable.

On January 30 2015 17:31 NMcNasty wrote: When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced.

i think you understand concept of exploitability wrong

imo one is exploitable if his opponent has incentive to change his strategy to gain ev
unexploitable strategy with highest ev is 'gto'

On January 30 2015 18:50 NMcNasty wrote: Show nested quote + On January 30 2015 18:07 dogmeat wrote:   On January 30 2015 17:31 NMcNasty wrote: When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced. imagine c/r river with nuts to 'balance' your c/f when betting is more +ev (=putting hands in wrong ranges) The reason we do that is to prevent ourselves from being exploited by having a weak checking range. Its not that we have two unexploitable options but one is better. One option is clearly exploitable.

here one could c/r w/ nuts to protect his range while it might be better to bet and c/c with some other hand etc. goal is to not allow our opponent to profitably bluff atc (and even this isnt true for some scenarios like if we get to ther river w/ polarized range and we are just c/folding our 2 street bluffs, etc)

On January 30 2015 17:31 NMcNasty wrote: When our "inexploitable lines" are yielding less EV, that means our opponent is gaining EV. In other words he's exploiting us, both in absolute terms (he's making money overall) and in relative terms (he's making more than what he would if we were playing GTO). So I'm not sure how hero would be unexploitable at all except for some vague notion of being balanced.

No, you are confusing unexploitability with GTO, thats what the example is explaining.

He has a perfect ratio between bluffs and valubets on the turn, a clarivoyant opponent who knows our range exactly to the last combo cannot exploit us on the turn, however a line that contains a bet on the turn and bet on the river also perfectly balanced yield us a better overall equity.

The opponent didnt exploit us, he didnt deviate from GTO play in order to increase his EV, that is exploiting

anyone can help me solve this simple toy gaming? I feel a retard lol

The pot is 1, my range is {As, 2s, 2h, 2c, 2d} Your range is {Ks} Highest ranked card wins You are forced to check I can either bet 2, or check behind What is my GTO strategy?

You guys seem to be using a definition where to exploit someone you are required to deviate from GTO. I suppose a definition of that sort isn't necessary wrong, but unlike 1, and 2 above I do think its really terrible.

Example:

You're playing HUNLHE with a GTO strategy. Your opponent is a fish who is shoving allin every hand. Are we exploiting them? Because we aren't deviating from GTO. My answer is very clearly yes, we're both taking advantage of the fact they're using a non-optimal line and we're making a ton of money against them (both 1 and 2 above). We wouldn't be maximally exploiting them, as in we won't be calling shoves with K9 offsuit, but I feel we're clearly exploiting them.

Also we can calculate the maximally exploitative strategy against any given strategy. It probably doesn't exist for full poker, but for toy games the maximally exploitative strategy and the GTO strategy can be equivalent. For example, if our range is only the nuts in a one street game, If its checked to us we'll be betting with both strategies. Our opponents range, whatever it is, doesn't automatically become unexploitable because we aren't deviating.

River play, dogmeat is correct. It is entirely possible that betting 100% of value + bluffs with a 100% checkfold range is better than dividing up ranges. You would only ever have a CR value range if it had the same value as always betting/cf. It could be entirely possible that having 100% check and balanced cr/cc/cf is better.

1 thing is for certain, GTO is not the maximally exploitable solution vs someone playing exploitable. It could be more profitable to CR a lot or never cr.

On January 31 2015 09:07 Highcard wrote: 1 thing is for certain, GTO is not the maximally exploitable solution vs someone playing exploitable.

For full poker this is likely true, but I just gave an example where it isn't true for a toy game.

On January 31 2015 08:29 drone666 wrote: anyone can help me solve this simple toy gaming? I feel a retard lol Show nested quote + The pot is 1, my range is {As, 2s, 2h, 2c, 2d} Your range is {Ks} Highest ranked card wins You are forced to check I can either bet 2, or check behind What is my GTO strategy?

i might have done this wrong but here's what i got. assuming that 'static strategy that gives a logically adjusting opponent over infinite hands the lowest EV' is a good enough definition of GTO, at least for this example. not even sure if that's right anymore lol.

pot = 1
optional bet = 2

1. you check 100%, i have 4 EV (no adjustments)

2. you bet A and check all 2's, in a vacuum gives me the lowest initial EV but once i adjust by folding 100% when you bet, it gives the same result as option 1, but i suppose it's better since it allows for initial adjustment error.

3. you bet 100%. i adjust by calling 100%. i have 10 EV ((4 * 3) - 2)

4. you bet the A and 3/4 2's, i adjust by calling 100%. i have 8 EV

(2's: 1 check = 1 EV, 3 bets = 9 EV. A: -2 EV) = 8 EV

5. you bet the A and 2/4 2's, i adjust by calling 100%. i have 6 EV

(2's: 2 checks = 2 EV, 2 bets = 6 EV. A: -2 EV) = 6 EV.

6. you bet the A and 1/4 2's, i adjust by calling 100%. i have 4 EV.

(2's: 3 checks = 3 EV, 1 bet = 3 EV. A: -2 EV) = 4 EV

even though options 1/2/6 get the same EV, i think 6 is the best because it takes a bigger sample for me to verify your strategy and adjust optimally, so there's a bigger chance for initial adjustment error on my part. also makes me the most indifferent to calling out of all the options.

On January 31 2015 08:30 NMcNasty wrote: You guys seem to be using a definition where to exploit someone you are required to deviate from GTO. I suppose a definition of that sort isn't necessary wrong, but unlike 1, and 2 above I do think its really terrible. Example: You're playing HUNLHE with a GTO strategy. Your opponent is a fish who is shoving allin every hand. Are we exploiting them? Because we aren't deviating from GTO. My answer is very clearly yes, we're both taking advantage of the fact they're using a non-optimal line and we're making a ton of money against them (both 1 and 2 above). We wouldn't be maximally exploiting them, as in we won't be calling shoves with K9 offsuit, but I feel we're clearly exploiting them. Also we can calculate the maximally exploitative strategy against any given strategy. It probably doesn't exist for full poker, but for toy games the maximally exploitative strategy and the GTO strategy can be equivalent. For example, if our range is only the nuts in a one street game, If its checked to us we'll be betting with both strategies. Our opponents range, whatever it is, doesn't automatically become unexploitable because we aren't deviating.

GTO range for calling a 100bb shove doesnt change with villians frecuency thus being MUCH more tight than an exploitive range that should be 50% and ridiculously more profitable

Really interesting article. doesn't change how i understand optimal (NE) play but it does make you think about how to define and understand exploitability. the key insight is that weakly dominated lines exist in full poker and they're very hard to tell from gto lines.

In a 2p2 thread ages ago ike made a great post with an easy to understand analogy: imagine rock-paper-scissors-shitrock. shitrock is the same as rock except it loses instead of draws vs a throw of rock, so rock weakly dominates shitrock and one should never play shitrock, even if one can perfectly balance a shitrock-paper-scissor strategy. similarly in the example one should not build a strategy around shoving turn because it is weakly dominated by an unexploitable two-street bet strategy with the right sizing. and indeed in full-poker, it is extremely difficult / impossible to tell a strategy involving rock from a strategy involving shitrock or how shit the shitrock is.

As for how you define exploitable, i agree with what has been mentioned in the thread that it can be a matter of semantics - meaning being determined by how people use it. the article defines exploitability in an unambiguous and precise way, and according to that definition unexploitability is indeed not as strong as optimal play. But under some other definition (e.g. exploitable is anything that doesn't net the minimax game value) unexploitable == gto. Overall it doesn't matter how you use the words as long as you have the concepts right. There's a fine line between arguing trivially over definitions of words and arguing productively over possible fundamental misunderstandings of the concepts.

On January 31 2015 08:29 drone666 wrote: anyone can help me solve this simple toy gaming? I feel a retard lol Show nested quote + The pot is 1, my range is {As, 2s, 2h, 2c, 2d} Your range is {Ks} Highest ranked card wins You are forced to check I can either bet 2, or check behind What is my GTO strategy?

if you bet, villain has to call 2 to win 3, so he needs to be good 40% of the time to call (2/(2+3) = 0.4).

You minimise his maximum possible EV by making him indifferent between calling and folding, so your ratio of value to bluffs has to be 60:40, or 3:2. Always bet the ace for value - you have an ace 20% of the time so 20% of your river actions will be valuebets. That means 13.33% of your river actions have to be bluffs (3:2 value/bluffs ratio), leaving the other 66.67% for checking back.

You have a deuce 80% of the time and your overall required riv bluff freq is 13.33%, so you want to bluff 16.67% of the time you have a deuce (0.133/0.8) and give up the remaining 83.33% of the time. A practical way to get to that frequency might be to pick a suit - let's say spades. You will bluff two thirds of the time when you have the 2s and never with the other deuces. Look at your watch and bluff if the second hand is between 0-40seconds.

This is what the article linked in op refers to as using the indifference condition to solve a simple toy game. It's interesting to know that solving real poker is far less simple, when there are multiple streets, multiple possible betsizes and the possibility opponent can raise.

thanks Romm3l,
I wasnt understanding why I had to bet one deuce 66% of the time, I knew I had to be bluffing 40% when Im betting but didnt know how to get to that number lol

There's no such thing as deviating from GTO in order to become unexploitable.

The only thing a GTO strategy guarantees is that you won't lose money.

On February 05 2015 04:28 MARSHALL28 wrote: There's no such thing as deviating from GTO in order to become unexploitable. The only thing a GTO strategy guarantees is that you won't lose money.

Well you will lose rake/2 if both play GTO, right?

On February 05 2015 04:28 MARSHALL28 wrote: There's no such thing as deviating from GTO in order to become unexploitable. The only thing a GTO strategy guarantees is that you won't lose money.

wat?

GTO is always unexploitable, but there are an infinite (or finite by sizing amounts) number of unexploitable non-GTO plays

I guess I just disagree with the author of the blog.

Maybe I'm completely wrong but here's how I see it...

The purpose of a GTO strategy is to breakeven at worst against every other strategy possible. If the goal is to breakeven, how do we improve on it? By becoming more break-even ?

Baal,

You and the article seem to be saying that there are multiple unexploitable strategies and that GTO is the strategy that is completely unexploitable while at the same time being the most exploitative...

Do you see the logical contradiction here? (you can't have an exploitative strategy and be unexploitable)

Maybe I don't know what I'm talking about, if somebody is sure I'm wrong please go ahead and explain to me.

considering abusing mod status and changing the title of this thread to "Smart People Nitpicking Over Semantics"

On February 06 2015 18:14 Daut wrote: considering abusing mod status and changing the title of this thread to "Smart People Nitpicking Over Semantics"

dont think thats what im doing at all. i think there's an actual argument here.

didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not?

isn't that enough to prove you wrong marshall?

On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not?

No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

On February 06 2015 16:13 MARSHALL28 wrote: The purpose of a GTO strategy is to breakeven at worst against every other strategy possible.

That isn't what a GTO strategy is, but it is a characteristic of the sum of GTO strategies for a rakeless, hu, FLHE game with resetting stack sizes.

For asymmetrical starting conditions, ie one player has an immediate advantage over the other, for example sb vs bb, there still exist GTO strategies, but one those (the bb's), will lose money.

So a player playing optimally (GTO) from the bb can still lose money to a player playing sub-optimally from the sb (due to starting conditions).

On February 06 2015 21:16 NMcNasty wrote: Show nested quote + On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

How is there a counter strategy to GTO?

On February 06 2015 21:45 NMcNasty wrote: Show nested quote + On February 06 2015 16:13 MARSHALL28 wrote: The purpose of a GTO strategy is to breakeven at worst against every other strategy possible. That isn't what a GTO strategy is, but it is a characteristic of the sum of GTO strategies for a rakeless, hu, FLHE game with resetting stack sizes.

There is a GTO solution for every game of poker.

On February 06 2015 21:16 NMcNasty wrote: Show nested quote + On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO.

On February 07 2015 04:32 MARSHALL28 wrote: Show nested quote + On February 06 2015 21:16 NMcNasty wrote:   On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy. How is there a counter strategy to GTO?

I meant counter-strategy to mean a strategy that does the best against another strategy, not necessarily a strategy that beats it EV wise. But I'm in agreement with the gist of what you're saying. For a rakeless symmetrical HUFLHE game the most our opponents can exploit us for is 0$. The blogger is implying that strategies exist where we're "unexploitable" even though the amount our opponents can make from us increases above zero. I think the main mistake he's making is that he's solving an isolated single street toy game of poker and thinks that solution is a window to the overall solved GTO solution for that street. But it doesn't work that way because play on previous streets affects ranges and stack sizes on later streets.

On February 07 2015 05:03 Baalim wrote: Show nested quote + On February 06 2015 21:16 NMcNasty wrote:   On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy. I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO.

It doesn't matter if your opponent has no options to improve if he's already taking an advantage of a defect in your play (you are shoving instead of betting smaller).

On February 07 2015 05:00 MARSHALL28 wrote: Show nested quote + On February 06 2015 21:45 NMcNasty wrote:   On February 06 2015 16:13 MARSHALL28 wrote: The purpose of a GTO strategy is to breakeven at worst against every other strategy possible. That isn't what a GTO strategy is, but it is a characteristic of the sum of GTO strategies for a rakeless, hu, FLHE game with resetting stack sizes. There is a GTO solution for every game of poker.

Agreed, it just doesn't mean what you think it means. A player can be playing GTO in some forms of poker and still lose money.

huh if you're losing this isn't GTO, unless 2 players are playing GTO then they're both losing the rake

Or if one player starts with advantage such as getting to post less as the small blind and having position. Heads holdem is really two imbalanced positions being added together which makes them seem balanced. One player has the advantage as the small blind even while both play optimally, which means they gain EV for that hand while their opponent loses EV. For the next hand this situation is reversed and the EV advantage is wiped out, bring our total EVs for both players to zero. Point is being unexploitable (in the not losing money sense) isn't something that's inherent to GTO play its just something that happens to games with even starting conditions.

Mcnasty I just don't know where you're coming up with all this because it really makes no sense.

I'm a bit confused about the article myself, as a quick Google search yields the definition of exploit as:
1. a bold or daring feat.
"the most heroic and secretive exploits of the war"
synonyms: feat, deed, act, adventure, stunt, escapade; More

Can someone clarify? Thx!

On February 07 2015 06:22 NMcNasty wrote: Or if one player starts with advantage such as getting to post less as the small blind and having position. Heads holdem is really two imbalanced positions being added together which makes them seem balanced. One player has the advantage as the small blind even while both play optimally, which means they gain EV for that hand while their opponent loses EV. For the next hand this situation is reversed and the EV advantage is wiped out, bring our total EVs for both players to zero. Point is being unexploitable (in the not losing money sense) isn't something that's inherent to GTO play its just something that happens to games with even starting conditions.

On February 08 2015 13:31 n0rthf4ce wrote: I'm a bit confused about the article myself, as a quick Google search yields the definition of exploit as: 1. a bold or daring feat. "the most heroic and secretive exploits of the war" synonyms: feat, deed, act, adventure, stunt, escapade; More Can someone clarify? Thx!

that is exploit used as a noun. people are discussing the verb 'to exploit' here

On February 08 2015 19:13 PoorUser wrote: Show nested quote + On February 08 2015 13:31 n0rthf4ce wrote: I'm a bit confused about the article myself, as a quick Google search yields the definition of exploit as: 1. a bold or daring feat. "the most heroic and secretive exploits of the war" synonyms: feat, deed, act, adventure, stunt, escapade; More Can someone clarify? Thx! that is exploit used as a noun. people are discussing the verb 'to exploit' here

The exploiter exploited the exploitative players in his exploits?

yes

On February 07 2015 05:27 NMcNasty wrote: Show nested quote + On February 07 2015 05:03 Baalim wrote:   On February 06 2015 21:16 NMcNasty wrote:   On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy. I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO. It doesn't matter if your opponent has no options to improve if he's already taking an advantage of a defect in your play (you are shoving instead of betting smaller).

But the shove is perfectly balanced and on a street/street basis unexploitable but not GTO since GTO accounts for multiple-street play

On February 09 2015 05:57 Baalim wrote: Show nested quote + On February 07 2015 05:27 NMcNasty wrote:   On February 07 2015 05:03 Baalim wrote:   On February 06 2015 21:16 NMcNasty wrote:   On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy. I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO. It doesn't matter if your opponent has no options to improve if he's already taking an advantage of a defect in your play (you are shoving instead of betting smaller). But the shove is perfectly balanced and on a street/street basis unexploitable but not GTO since GTO accounts for multiple-street play

For a single street solution we can solve both for exploitability (however you want to define it) and GTO (Nash equilibrium).

For an overall (multi-street) solution we can also solve both for exploitability and GTO.

If you want to discuss strategy in a meaningful way you should be using overall definitions of both exploitability and GTO. There's no sense in choosing a single-street strategy for a game with multiple streets. The author is correctly using the overall idea of GTO, but for some reason is still clinging to the street by street version of exploitability.

On February 05 2015 04:28 MARSHALL28 wrote: There's no such thing as deviating from GTO in order to become unexploitable. The only thing a GTO strategy guarantees is that you won't lose money.

A gto strategy ensures you make money versus any other strategy besides another gto strategy in which case you only won't lose money (breakeven).

I get what you are saying that a GTO strat might just not lose because it isn't actually actively taking advantage of any opponent mistakes. The truth is though any gto strat will likely crush for a huge winrate; i'd guess it wouldn't even be that far off of the winrate of the maximally exploitative strategy vs anyone reasonable.

and yea why would you deviate from GTO in order to become unexploitable that doesn't even make sense. GTO by definition is intrinsically unexploitable.

On February 07 2015 05:03 Baalim wrote: Show nested quote + On February 06 2015 21:16 NMcNasty wrote:   On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy. I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO.

Baal is explaining it here.

The turn shove is not GTO because while it leads to indifference on that one street for villain (thus an unexploitable turn shove by hero) it is not balanced as part of an overall strategy. When shoving an unexploitable range on the turn you may be opening yourself to exploitation elsewhere, for example by having to put too many of your hands in a shoving range so that when you check you are now imbalanced and villain can bluff you profitably or something. This turn shove opens up other vulnerabilities in your game for villain to identify while being itself "unbeatable".

I haven't read the example but the GTO line for example may be to bet turn for x size and to shove river for y size. This line will also be itself unexploitable; we will be betting with a certain size at a certain frequency with a certain balanced range of bluffs and value that will lead to indifference in villain whether he calls or folds. The difference between this GTO/Unexploitable line and the only unexploitable line in the first paragraph is that the GTO line maintains balance in the rest of your game. Now when you check the turn in this exact spot you will have a viable defense versus the ideal play from villain

On February 09 2015 20:55 traxamillion wrote: A gto strategy ensures you make money versus any other strategy besides another gto strategy in which case you only won't lose money (breakeven).

Wrong. It only guarantees that you will breakeven or better against other strategies, doesn't guarantee a win at all. Trivial example is rock-paper-scissors were all strategies break even against GTO.

So I haven't read the whole thread, but I have a question that always confused me.

Player A and Player B are on the river in a NLH hand.
Pot is 1k and Player A bets 1k. His range is completely polarized and Player B's range is bluffcatchers only.

If Player A bluffs 1/3 of the time and valuebets 2/3, his play is unexploitable. However, any of Player B's calling frequencies here will earn him the same EV of 0.

Shouldn't there be an optimal calling frequency that Player B had to obey in order to breakeven with Player A's optimal bluffing frequency, and then deviations from this calling frequency would make Player B lose money and Player A win?

How can a GTO strategy win in the long run against a strategy that makes many mistakes if Player B's mistakes won't cost him?
It seems like the unexploitable strategy is making it impossible for others strategies to beat it but at the same time making it impossible for itself to beat strategies that make mistakes.

My logic has to have a flaw here, can anyone explain where?

any other play that player A does can be countered by player B and player B will lose less/win more often based on Player A deviation from GTO of 2/3 value 1/3 bluff in this scenario

the whole point of poker is finding spots that Player B does not adjust to player A deviation from GTO

OR being Player B and being able to adjust to Player A's none GTO strat better than Player A can adjust to Player B

This is why, a long time ago, I told you that poker is a zero sum game and your "statistical" analysis of your winnings is purely conjecture of playing worse people. Once everyone is equal in knowledge, poker becomes a zero sum game. Being taxed on a zero sum game is ridiculous. Combine rake and taxes makes collecting bottles more profitable.

In the Twilight! Oooh, a UU in the Twilight!

On February 09 2015 22:49 player999 wrote: Shouldn't there be an optimal calling frequency that Player B had to obey in order to breakeven with Player A's optimal bluffing frequency, and then deviations from this calling frequency would make Player B lose money and Player A win?

No, there is no guarantee that a deviation from GTO will yield positive expectation for the other player. A deviation necessarily opens yourself up to exploitation for the opposing player, but that doesn't mean its achieved with the GTO strat. A common example is rock/paper/scissors where one player decides to throw rock 100%. Its a severe deviation from GTO, but still won't lose him money against a GTO opponent throwing 1/3 of each.

How can a GTO strategy win in the long run against a strategy that makes many mistakes if Player B's mistakes won't cost him?

GTO simply doesn't guarantee that you win in the long run. All it means is there's a strat where your wins/losses get capped at a certain amount.

It seems like the unexploitable strategy is making it impossible for others strategies to beat it but at the same time making it impossible for itself to beat strategies that make mistakes.

In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

On February 09 2015 22:42 player999 wrote: Show nested quote + On February 09 2015 20:55 traxamillion wrote: A gto strategy ensures you make money versus any other strategy besides another gto strategy in which case you only won't lose money (breakeven). Wrong. It only guarantees that you will breakeven or better against other strategies, doesn't guarantee a win at all. Trivial example is rock-paper-scissors were all strategies break even against GTO.

Yes I understand this is the theoretical definition when talking about GTO and Nash equilibrium in general. I am talking about as it applies to full size NLHE played in practical terms terms.

I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy. You would disagree with that as well?

unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time

Yep, this ain't rock scissor paper. I mean sure that game follows Nash by it's nature but that's about its only similarity to poker and I think it is useless to compare the 2.

On February 09 2015 20:56 traxamillion wrote: and yea why would you deviate from GTO in order to become unexploitable that doesn't even make sense. GTO by definition is intrinsically unexploitable.

You can't deviate from GTO in order to become unexploitable. That was my point.

On February 10 2015 07:37 drone666 wrote: unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time

But is that EV always 0? This is my question, how can GTO have a positive EV in a given situation?

On February 10 2015 03:11 NMcNasty wrote: Show nested quote + On February 09 2015 22:49 player999 wrote: Shouldn't there be an optimal calling frequency that Player B had to obey in order to breakeven with Player A's optimal bluffing frequency, and then deviations from this calling frequency would make Player B lose money and Player A win? No, there is no guarantee that a deviation from GTO will yield positive expectation for the other player. A deviation necessarily opens yourself up to exploitation for the opposing player, but that doesn't mean its achieved with the GTO strat. A common example is rock/paper/scissors where one player decides to throw rock 100%. Its a severe deviation from GTO, but still won't lose him money against a GTO opponent throwing 1/3 of each.   How can a GTO strategy win in the long run against a strategy that makes many mistakes if Player B's mistakes won't cost him? GTO simply doesn't guarantee that you win in the long run. All it means is there's a strat where your wins/losses get capped at a certain amount.   It seems like the unexploitable strategy is making it impossible for others strategies to beat it but at the same time making it impossible for itself to beat strategies that make mistakes. In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

I could see my error being that my toy game is too simple for GTO to have a positive EV on it, but if that's the case can anyone come up with a slightly more complex toy game in which GTO yelds positive expectation?

just think of a nuts or bluff spot vs a bluff catching range

IP player A 10 total combos/5 nuts/5air
Stack size 2

OOP Player B 5 total combos
stack size 2

Pot size is 3

Find Player A GTO river strat

Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

If one player starts going all in every hand. By the 3rd or 4th hand you would probably start widening your calling range in an exploitable manner to start including hands like A8o/55.

GTO ignores this information regarding the player going all in every hand and just calls whatever the correct GTO ranges would be. For the sake of discussion lets say they are AJo/77 ... GTO is still positive EV against your opponent's strategy, just not as positive EV as the exploitable one.

In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

Given we have precise knowledge of our opponent's strategy, there's no situation I can think of where GTO is more +EV than an exploitable strategy. I don't understand how anyone can think this unless my understanding of GTO is incorrect but I haven't seen any compelling arguments in opposition to what I've stated.

On February 10 2015 12:41 player999 wrote: Show nested quote + On February 10 2015 07:37 drone666 wrote: unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time But is that EV always 0? This is my question, how can GTO have a positive EV in a given situation?

this is incorrect the EV isnt always 0, i used to think this way until I watched Sauce series, Toy Gaming, really mind opening
as I said the balanced range usually have a higher EV compared to unbalanced ranges playing vs random unbalances, unless you know if villain is overcalling or overfolding in a spot ( this is really rare imo )

if you know the basics about CREV I suggest you to setup a simple Toy Gaming and play around with your bluffing/value frequencies and bet sizes and see how your EV changes

but if you talking about GTO vs GTO ( thats what u try to do when solving Toy Gamings ) then yea, obv the EV of the hand is going to be 0 for both

On February 10 2015 06:01 traxamillion wrote: I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy.

This is incorrect. We already have the ability to calculate a perfect counter-strategy (its nemesis) against any given strategy. The strategy we come up with against a GTO strategy uses pure strategies (there's no mixing). So its heavily exploitable, but has equivalent EV to GTO strategies.

On February 10 2015 12:45 player999 wrote: Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

As Marshall and I have pointed out before, using a GTO strategy against a player shoving allin will yield positive expectation, even if you aren't calling with hands that you should be calling with (say K9o).

For a toy game example, say instead of Rock Paper Scissors, we have Rock Paper Scissor Fish. Fish is exactly the same as paper except it only wins 70% of the time, otherwise it loses. Obviously, using Fish at all instead of paper is completely retarded. Its dominated by paper, so the GTO solution doesn't change at all, its still 1/3 Rock 1/3 Paper 1/3 Scissors. But if we now play against some idiot throwing Fish for whatever reason, we pick up extra value every time we throw rock. Poker is more like RPSF than RPS. Going allin preflop is like the "fish" move though not exactly since its still possible to exploit a player who folds too much vs an open shove).

On February 10 2015 15:36 MARSHALL28 wrote: Show nested quote + In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV. Given we have precise knowledge of our opponent's strategy, there's no situation I can think of where GTO is more +EV than an exploitable strategy. I don't understand how anyone can think this unless my understanding of GTO is incorrect but I haven't seen any compelling arguments in opposition to what I've stated.

I meant GTO strats will generally beat non-GTO strats that is all, not that GTO strats are the best option against non-GTO strats.

On February 10 2015 15:31 MARSHALL28 wrote: Show nested quote + Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible. If one player starts going all in every hand. By the 3rd or 4th hand you would probably start widening your calling range in an exploitable manner to start including hands like A8o/55. GTO ignores this information regarding the player going all in every hand and just calls whatever the correct GTO ranges would be. For the sake of discussion lets say they are AJo/77 ... GTO is still positive EV against your opponent's strategy, just not as positive EV as the exploitable one.

I'd say this precisely answers your question player999

On February 10 2015 21:40 NMcNasty wrote: Show nested quote + On February 10 2015 06:01 traxamillion wrote: I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy. This is incorrect. We already have the ability to calculate a perfect counter-strategy (its nemesis) against any given strategy. The strategy we come up with against a GTO strategy uses pure strategies (there's no mixing). So its heavily exploitable, but has equivalent EV to GTO strategies.

You can only create that counter strategy if I give you my bot's and I wasn't really talking about that but even then it doesn't matter. I was talking about any strategy developed independently of my bot. Again I don't think it matters.

it would literally be impossible to beat my bot by definition. If you developed a perfect counter strategy by analyzing my bot it would at best break even vs my bot. Your counter strategy and a co-optimal GTO strategy would have the same winrate vs my bot of 0. The question is does that make your counter-strategy also GTO? That I don't know.

What I meant by this was mostly trying to show Player999 that GTO strategies in poker are quite strong despite what he might have seen in some toy game examples. Look at the limit machines that were releases in Vegas take free. People thought they played weird and bad at first but really they were based on some GTO approximation and crushed virtually anyone. My GTO bot in the example would crush any human by a ton.

Unexploitable and balanced have nothing to do with being breakeven

McNastys example is right, if you open shove 32o for 300BB that against a GTO calling range will have a negative EV even if villian doesnt adjust to your ranges.


I think a lot of the confusion we are having about exploitability is how we define it as someone said earlier, I think the term is used in poker as a one-street perfectly balanced ratio of value/bluff, rather than a multi-street unexploitable line, which would be GTO.

So lets stop using the word exploitability and lets use balance... balanced play =/= GTO, but GTO is always balanced.


Also pragmatically GTO should have in theory small winrates against people making a lot of mistakes so we should deviate as most as we can from GTO but always coming from a GTO starting point

agree with all that baal except for the last paragraph. Do you have any evidence for that?

For example a guy who is bluffing way too much or calling way too much; well in practice we don't perfectly identify these spots but we try to adjust as much as possible. Guy bluffs too much you call a little more. GTO will still be making most of the same plays you are i would imagine. And what you gain over GTO with your adjustments is small compared to what i'm sure GTO makes up over you with generally perfect play. To find an example where GTO has a small winrate compared to an exploitative strategy I think you would need to find a strategy so bad that no decent human or most fish would even use it.

2 examples i have of what I am saying.

GTO High Stakes HU limit bots having the highest winrates in any games.

The Sauce vs WCGrider NLHE HU challenge where they played for 20k or 50k hands and wcgrider just crushed him. Of course there is a ton of variance in a match like that and wcgrider is by no means GTO but at that time he was considered to play probably the closest to it and a lot of people considered Sauce the #2 but close maybe +110 vs wcg or something at kickoff. They played 100/200 and WCG opened pre everyhand to 440 and claimed that his strategy was played independently of anything his opponent might do. He doesn't adjust to his opponent. It doesn't matter that he is playing Sauce. He feels he had a balanced strategy ready to go versus anyone. Sauce used a pre strat of opening 3x or openlimping saying he developed it using gto principles and just what he thought would be good vs WCG's game so he unlike WCG was styling his game after his opponent to some extent. After getting crushed early sauce even adjusted to opening 2x-2.4x only showing he made further adjustments to his opponent. Sauce got crushed for almost a million and the consensus was he was thoroughly outplayed. That match basically cemented WCG at #1 where he has remained since.

On February 11 2015 06:45 traxamillion wrote: Sauce used a pre strat of opening 3x or openlimping saying he developed it using gto principles and just what he thought would be good vs WCG's game so he unlike WCG was styling his game after his opponent to some extent. After getting crushed early sauce even adjusted to opening 2x-2.4x only showing he made further adjustments to his opponent. Sauce got crushed for almost a million and the consensus was he was thoroughly outplayed. That match basically cemented WCG at #1 where he has remained since.

If sauce developed his strat using GTO principles, then your following statement is flawed "just what he thought would be good vs WCG's game so he unlike WCG was styling his game after his opponent to some extent". Anyways, I am not sure if WCG already knew sauces button strat but his BB checkbehind/raise vs limp was extremely tailored to it. In fact it was almost as if he knew sauces limping range (unless I am remembering the numbers for wcg vs ike) and the numbers are extreme.

Either way, it is quite obvious WCG has a solid formula or a game tree program similar to CREV and was able to destroy the limp range using it. As for the theory of WCG open size, he varies that over time. For instance, he has been doing a lot of 2.8x, lately.

On February 11 2015 06:17 Baalim wrote: McNastys example is right, if you open shove 32o for 300BB that against a GTO calling range will have a negative EV even if villian doesnt adjust to your ranges. I think a lot of the confusion we are having about exploitability is how we define it as someone said earlier, I think the term is used in poker as a one-street perfectly balanced ratio of value/bluff, rather than a multi-street unexploitable line, which would be GTO. So lets stop using the word exploitability and lets use balance... balanced play =/= GTO, but GTO is always balanced. Also pragmatically GTO should have in theory small winrates against people making a lot of mistakes so we should deviate as most as we can from GTO but always coming from a GTO starting point

So it sounds like we're both in disagreement with the author of the blog then?

If sauce developed his strat using GTO principles, then your following statement is flawed "just what he thought would be good vs WCG's game so he unlike WCG was styling his game after his opponent to some extent". Anyways, I am not sure if WCG already knew sauces button strat but his BB checkbehind/raise vs limp was extremely tailored to it. In fact it was almost as if he knew sauces limping range (unless I am remembering the numbers for wcg vs ike) and the numbers are extreme.

It's possible for both to be true. This is how most players make in game adjustments nowadays. It's not often you see a huge call down with bottom pair (though obviously they still do happen), it's that players are using game theory principles in order to make slight adjustments to their game in order to take advantage of what this person thinks his opponent may be missing regarding game theoretical considerations.

An example of this would be to adjust away from a default strategy of 3betting the SB of say 10% of hands vs BTN and widening it to 15% if player in the small blind happens to think BTN is raise/folding too much. Or maybe SB might make his range consist of 10% value 5% bluff in order to take advantage of an opponent who raise/calls too much.

These are exploitable strategies, but it remains that they are made based on principles of game theoretically optimal play.

I suppose all I'm really saying is that your default game should be your best approximation of GTO and any adjustments off of it should be in relation to why GTO isn't the most optimal strategy given a particular situation or a particular opponent.

I think the author may be confusing these two concepts and thinking that the exploitation moving away from GTO play is what the true GTO strategy is which is completely false because I'm talking about an exploitable strategy.

I understand the concept that trax said for sauce, but if sauce was using a 'gto derived style best suited for wcg" than his tweak would not have been completely stopping his raise/limp range to a pure 2.x range. My point is Sauce was so far from GTO it was a complete disaster of a strategy and to even mention GTO in that case is a joke.

and rereading your post, I think we both agree on that

im saying exactly what marshall said.

its not like sauce completely disregards theory, i was just pointing out sauce made opponent based decisions and adjustments whereas WCG claims he did not in order to reinforce my earlier statement

and as bad as you wanna say sauce (ben sulsky) played he was playing the best and i'd imagine he still is a lot better and knowledeable about game theory than either of us. hes a confirmed genius/prodigy and was playing nosebleeds today. yes he self-admittedly fell behind the curve for a while and got humbled by rider (and some of the 6max regs afterwards)

thing is that Sauce plays lots of different games while WCG was only focusing on HUNL
right now I dont see how WCG can sustain his #1 NLHU player for long since he's playing lots of PLO and there's lots of crushers learning NLHU lately

It's you saying sauce developed his pre strat via GTO principles and then applied an exploit strat vs wcg. That semantic is what I am telling you is incorrect given the rest of your statements about sauce. Furthermore, the results of the match dictate that he was far from GTO foundation principles, otherwise he would not have stopped limp/raise and instead modified it from "exploit" to "GTO".

My point is sauces strat was very far from GTO principles otherwise he wouldn't have had to switch it so drastically and then still get crushed after switching.

im saying he used both; they are not mutually exclusive. You can build a strategy using GTO principles and then make adjustments or even huge changes to it based on opponent or ingame adjustment. The two aren't mutually exclusive. I don't get it why are you nitpicking that; it isn't even an important part of what i said. If you please ignore i said Sauce even knows what GTO is and my point still stands.

And I mean sure you can say Sauce was far from GTO but what are you basing that on? I only said Sauce was less GTO than Rider not completely clueless because of what the players themselves said and a few other observations that when considered alone have little meaning. Seems you base your theory on the fact Sauce switched up his pre sizing mid-match and that he lost? Rider is good and there was a lot of variance; Sauce's final bb/100 probably does not reflect his expectation. I didn't see EV graphs and even those only tell part of the story. I just don't see whats hard about conceptualizing that Sauce may have had a game theory oriented strategy but frequently diverged from it during his match with Rider because he didn't think Rider was GTO (or he wouldn't play him) and felt exploitative strategies at times had higher expectation than default.

On February 10 2015 21:48 NMcNasty wrote: Show nested quote + On February 10 2015 12:45 player999 wrote: Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible. As Marshall and I have pointed out before, using a GTO strategy against a player shoving allin will yield positive expectation, even if you aren't calling with hands that you should be calling with (say K9o). For a toy game example, say instead of Rock Paper Scissors, we have Rock Paper Scissor Fish. Fish is exactly the same as paper except it only wins 70% of the time, otherwise it loses. Obviously, using Fish at all instead of paper is completely retarded. Its dominated by paper, so the GTO solution doesn't change at all, its still 1/3 Rock 1/3 Paper 1/3 Scissors. But if we now play against some idiot throwing Fish for whatever reason, we pick up extra value every time we throw rock. Poker is more like RPSF than RPS. Going allin preflop is like the "fish" move though not exactly since its still possible to exploit a player who folds too much vs an open shove).

Yeah I guess my flaw there must be that the toy game is too simple and ends up falling into the RPS level. I just wish I knew about a very simple poker toy-game in which GTO would show profit against faulty strategies so I could draw some conclusions about it. Maybe drone's suggestion will work for that.

And I already knew all of this, like what Marshall said, instintively, but I wanted toy-game mathematical evidence of it. But thanks all for the explanations.

GTO doesn't adjust. It makes the same play with the same ranges every time.

There's no way GTO can ever be -EV against any play. It can only at worst break-even. We have no idea what the EV would be at best but we can think about it like this...

Given any spot, the GTO play is one that does well against every possible strategy, therefore it's likely not going to be massively +ev against any given play since it has to make sure it never loses to any other strategies that an opponent might employ. It doesn't make any money by exploiting it's opponent's strategies. It makes money whenever it's opponent's strategies deviate from GTO as the imbalance in it's opponents' plays that cause GTO to make money. This is why the only way GTO can lose (to the rake) is if it's playing against an opponent also employing GTO.

Basically, if you were somehow able to play GTO, you would profit every time your opponent makes a slight imbalance away from GTO in his play. If your opponent is making massive imbalances, then obviously the GTO strategy will be doing even better, but still not better than a maximally exploitative strategy.

On February 12 2015 12:20 MARSHALL28 wrote: There's no way GTO can ever be -EV against any play.

I'm going to be a bit of a stickler here and again point out that the above is only true for games with equal starting conditions. In a single hand of heads up poker (an unequal starting condition) both players can be playing GTO while one of the strategies is -EV (the big blind's).

On February 12 2015 02:25 player999 wrote: I just wish I knew about a very simple poker toy-game in which GTO would show profit against faulty strategies so I could draw some conclusions about it.

Mathematics of Poker is a really good book for all of this sort of thing and there are several examples in it. You could also do a google search for "AKQ game" since a few of the variants have been posted online.

before discussing all this stuff, how about we first figure out what the GTO preflop is for 100bb?

On February 12 2015 21:19 NMcNasty wrote: Show nested quote + On February 12 2015 12:20 MARSHALL28 wrote: There's no way GTO can ever be -EV against any play. I'm going to be a bit of a stickler here and again point out that the above is only true for games with equal starting conditions. In a single hand of heads up poker (an unequal starting condition) both players can be playing GTO while one of the strategies is -EV (the big blind's).

I don't necessarily think that this is true. I don't know the correct answer, but maybe it's the case that GTO never loses more than the initial bb investment.
Because if what you're saying is true, then GTO is an impossibility in HUNL poker based on it's definition.

On February 13 2015 03:57 AndrewSong wrote: before discussing all this stuff, how about we first figure out what the GTO preflop is for 100bb?

let me know if you have any ideas

for 100bb poker hu?

do u think it would be similar to limit since the basic odds are the same pre or does the possibility of different betsizes change thinks. If its limit we can reference the Alberta GTO bot.

it opens like 85-90% otb and defends 100% in the BB. GTO says never fold the big blind in hu limit even 27o; you get 3:1 meaning you need 25% equity which you have with everything.

obviously being nl is going to change some things. i think with the ability to bet any size position becomes more important. It was shown by the limit Alberta bot that position had little importance at the GTO level for the computer. The sb winrate was .1 bb/100 higher than the bb or something like that. So if position is more important this may mean tighter play from the BB. The sb can open larger than 2x. We are not sure what exactly is optimal here yet. In heads up play i have been seeing a lot of 2.4-2.9x raising from the sb. Obviously the larger the sb bets the worse odds the BB has and this may tighten the BB calling range as well. Is limping the sb potentially a part of a GTO strat? hasn't been answered yet.

I haven't been playing with tracker software for some time but if I had to guess at my current stats (which i base on what I imagine GTO to be) I open raise to 2.5x pre (was minraising a long time before that and still do sometimes but when everyone minraises vpips get close to 100%) at maybe 80-95% and defend only slightly tighter. I used to play some ridiculous 80%sb open and 30%bb defend as did a lot of people until this was discovered to be terribly imbalanced. I will admit I am still probably too tight in the BB vs 3x opens.

What do u think gto pre is HU? iono if 6max is even worth talking about but we can try that too. What % do you defend vs a 3x open in nlhe

Minraising the button I think is pretty likely to be GTO. How often I don't know.

A lot of people aren't doing it right now but I think that's just a trend that people happen to be playing fairly well against a minraise and people tend to be playing on average relatively poorly versus larger sized opens. If we had a computer that could play GTO, I just doubt it would ever open anything greater than min OTB as it would be able to use every possible bet sizing postflop and better utilize it's position. Humans aren't able to perceive the slight differences in range interactions on flops that computers can. If we raise the button larger, it slightly diminishes our positional advantage.

This is all assuming 100bb tho. If we assume fewer bb's then minraising obviously becomes better.

On February 13 2015 07:01 MARSHALL28 wrote: Minraising the button I think is pretty likely to be GTO. How often I don't know. A lot of people aren't doing it right now but I think that's just a trend that people happen to be playing fairly well against a minraise and people tend to be playing on average relatively poorly versus larger sized opens. If we had a computer that could play GTO, I just doubt it would ever open anything greater than min OTB as it would be able to use every possible bet sizing postflop and better utilize it's position. Humans aren't able to perceive the slight differences in range interactions on flops that computers can. If we raise the button larger, it slightly diminishes our positional advantage. This is all assuming 100bb tho. If we assume fewer bb's then minraising obviously becomes better.

My gut feeling is that GTO would have a range of opening raise sizes, with different probabilities. Cannot imagine sb raises being 100% minraise. The hand ranges would largely intersect, so the raise size would give up little or no information about the range.

On February 13 2015 12:44 pluzich wrote: Show nested quote + On February 13 2015 07:01 MARSHALL28 wrote: Minraising the button I think is pretty likely to be GTO. How often I don't know. A lot of people aren't doing it right now but I think that's just a trend that people happen to be playing fairly well against a minraise and people tend to be playing on average relatively poorly versus larger sized opens. If we had a computer that could play GTO, I just doubt it would ever open anything greater than min OTB as it would be able to use every possible bet sizing postflop and better utilize it's position. Humans aren't able to perceive the slight differences in range interactions on flops that computers can. If we raise the button larger, it slightly diminishes our positional advantage. This is all assuming 100bb tho. If we assume fewer bb's then minraising obviously becomes better. My gut feeling is that GTO would have a range of opening raise sizes, with different probabilities. Cannot imagine sb raises being 100% minraise. The hand ranges would largely intersect, so the raise size would give up little or no information about the range.

you could be right

On February 13 2015 04:31 MARSHALL28 wrote: I don't necessarily think that this is true. I don't know the correct answer, but maybe it's the case that GTO never loses more than the initial bb investment. Because if what you're saying is true, then GTO is an impossibility in HUNL poker based on it's definition.

I meant before the bb investment. After bb is posted, yeah bb's play will certainly be +EV, even more so than sb.

On February 13 2015 07:01 MARSHALL28 wrote: Minraising the button I think is pretty likely to be GTO. How often I don't know. A lot of people aren't doing it right now but I think that's just a trend that people happen to be playing fairly well against a minraise and people tend to be playing on average relatively poorly versus larger sized opens. If we had a computer that could play GTO, I just doubt it would ever open anything greater than min OTB as it would be able to use every possible bet sizing postflop and better utilize it's position. Humans aren't able to perceive the slight differences in range interactions on flops that computers can. If we raise the button larger, it slightly diminishes our positional advantage. This is all assuming 100bb tho. If we assume fewer bb's then minraising obviously becomes better.

I dont think we know enough about the game to make such statements its very likely we would lose a lot by rising small with strong hands pf

On February 13 2015 03:57 AndrewSong wrote: before discussing all this stuff, how about we first figure out what the GTO preflop is for 100bb?

lol, GTO preflop is the hardest part to figure out.

GTO pre is simple, many programs to help with that.

GTO on the turn and river were my biggest leaks I had to plug

On April 22 2015 19:54 Ryan Neilly wrote: GTO pre is simple, many programs to help with that.

dont comment on topics you have no business discussing, like this thread or any cash hands above nl2

On April 22 2015 19:58 dogmeat wrote: Show nested quote + On April 22 2015 19:54 Ryan Neilly wrote: GTO pre is simple, many programs to help with that. dont comment on topics you have no business discussing, like this thread or any cash hands above nl2

lol boom.


They are right, GTO get considerably more complex the earlier the street, river GTO being the simplest

This does not mean river is the easiest street to play though, our brains are not computers trying to solve GTO, they work very differently

There are several GTO programs on the market now that can solve postflop situations to reasonable accuracy for all streets, usually within 1% distance from nash for flop and much closer on turn and river. As far as I'm aware there's no software that solves for preflop. It's obviously by far the most complex because for there to be a solution the computer would have to compute all of the preflop options, that is Call, 3bet, 4bet yada yada, and compute how those ranges fit into all flop, turn and river run outs. Far more complex than postflop and we're definitely some way away from that.

There are programs that can figure out nash ranges if you exclude the option of postflop play, i.e. you're all in or folding preflop. HoldEm Resources Calculator can give you Nash push/fold ranges, but it's not very useful in a cash game scenario to know you can jam K2o SB v BB with 10bb stacks without being exploited

anybody using piosolver or simplepostflop here? i've read thread on 2p2 but not sure which one to get yet

i ve been using both but i only use pio now, its not very user friendly but lastest build is really fast and browsing thru various turn and river runouts is incredibly easy in pio, the main reason for ditching sp

I started using PioSolver, but some of his strategy seem to be retarded, maybe im doing something wrong lol

I have SimplePostflop. I think it's a good program, but haven't used any of the others so can't compare. One plus point is that you can import the hands into GTORB if you prefer viewing the hands that way, which I don't think (perhaps someone can correct me) you can do using PioSolver

On August 10 2015 09:26 drone666 wrote: I started using PioSolver, but some of his strategy seem to be retarded, maybe im doing something wrong lol

hey i read it before your edit consider these: stack depth (lower spr = more agressive oop play, your range composition might be off or you somehow limit flop options when facing a raise. also smaller betsizing could result in higher c/r % with spr 5 or less. 35% is way too high thou

haha, well my original post was that PIO was saying that SB should raise 35% vs cbet 3bp on A84hh board
my mistake was that I had no 3bet range on the flop for the BB, so the SB could raise a lot vs small cbets, once I changed his conclusions make a bit more sense, interesting tho, most players dont have a 3bet range on this flop texture

when stacks get shallow you are trying to realise your equity, even ip

On August 10 2015 10:19 ToT)MidiaN( wrote: I have SimplePostflop. I think it's a good program, but haven't used any of the others so can't compare. One plus point is that you can import the hands into GTORB if you prefer viewing the hands that way, which I don't think (perhaps someone can correct me) you can do using PioSolver

SP is somewhat retarded, it gives out slightly(0,01%) different strategy for the same flop situation and sizings than pio, i also don't get how to input weight and suits for starting ranges lol.
However, in general, both algorythms come up with almost identical flop solutions, i wonder how one can do poker related programs not even knowing is called clubs

SimplePostflop has proved to be faster on 2+2 benchmarks which is actually the most important thing about a GTO software, also the ability to export to GTORB online to share with people is fantastic.

Both interfaces need a lot of work though but that isnt that important you get used to it very fast

Im surprised so many of you have 700+ USD softwares tbh

In my opinion, the best approach to any kind of statistical question is a Gordian knot system.

You might take a sequence of propositions and request yes or no answers a la the Poker "box" system.

[ ] NAME: X (dies) - eventually you will find a "yes" answer to this question.
[ ] NAME: Y (dies) - eventually you will find a "yes" answer to this question.
[ ] NAME: Z (dies) - eventually you will find a "yes" answer to this question.

Most successful bureaucracies, namely the Mafia, use this system.

Usually the first question is simple, like "X clearly does not deserve to die by any avoidable means -- no rational entity would will the death of X."

If the reply is confusing, an answer like, "In my narrative, X was dead 1 year ago and was deserving of death" then the author's narrative is replaced by a narrative the Mafia deems suitable.

It's impractical to write personally-tailored narratives for each individual who replies with a wrong answer to the first question.



The wisest course of action, and the course favored by the Mafia, is to write personal narrative for those who answer the first question and subsequent questions correctly.

Correct answers are surprisingly easy to identify. To my knowledge it is impossible to answer each and every question perfectly.

By way of example, consider the first three questions the character of which is similar, "It is true of Names X, Y, and Z that each of X, Y, and Z does not deserve to die by any avoidable means -- no rational entity would will the death of X, Y, or Z."

Again, I emphasize that correct answers are surprisingly easy to identify.

Statistical techniques are applied with painstaking precision. These statistical techniques obtain accurate forecasts about the life expectancy of a given Name, e.g. X. Truth-preserving propositions are necessarily entailed in each forecast.

Acceptable answers to the first question and subsequent questions qualify one to be a member of the Mafia.



Members of the Mafia write personal narrative for those who answer the first question and subsequent questions correctly. Typically there is not only one winner.

Encompassing narratives are written with respect to results of longevity forecast.

Not everyone has a Name for whom he or she writes personal narrative. It is not uncommon for personal narrative to describe an entity who is not a member of the Mafia.

Dignity and well-being have seldom characterized a good narrative.