Random Game Theory Stuff - Page 3

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