Random Game Theory Stuff - Page 5

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