I’ve been thinking about multiplayer games, as heizenburg mentioned, with one player using GTO and the other not...

I read that an algorithm for the GTO strategy in multiplayer games hasn’t yet been found, but, I can’t help thinking everyone is just confused??? In RPS, if you add an extra player, the GTO strategy is obviously going to be exactly the same as with one opponent. The number of opponents doesn’t matter to GTO. GTO is a Level One strategy, the opponents are irrelevant... Right???

What I’m guessing has confused the mathematicians is that in games with multiple players, or in games with multiple decisions, a GTO player is beatable... Provided some decision by some player is none GTO.

In a tourney this is easy to see. An exploitative player can always make money faster than a GTO player provided there are imperfect players in the tourney. This means he’ll consistently have a bigger stack than the GTO player. It’s only when they face each other heads up in the final that the exploitative player will lose his strategic advantage. By then though, he will have strengthened his position by earning more chips, and so he does still have a clear advantage over his GTO counterpart.

If you’re trying to find an unbeatable strategy for a multiplayer game against imperfect opponents, said strategy must be exploitative... Well... it must be exploitative to some degree...

I do think there is an unbeatable strategy in multiplayer games, but I think it is part GTO and part exploitative. Using this strategy enables you to exploit some players whilst remaining unexploitable to others.

Let’s say that the perfect amount to tighten up against the imperfect opponent to exploit him is x. This strategy sacrifices all the profit we would have made from the imperfect players “mistake”, and instead we counter-balance to take our advantage from the GTO opponent or any players future moves.

Now, let’s say we face this same imperfect player, but this time we also face one player using x. We could widen our bluffing range to take back the profit the opponent has gained from us by using x, but this leaves us exploitable. Instead, I think we can tighten up slightly more than x to further strengthen our position. Let’s call this strategy y.

If we faced one weak player, and one player using y, I think we could widen our bluffing range more than before, or, we can tighten up more than before but by a smaller margin than before. I think you can tighten up more and more by smaller and smaller margins each time you exploit. Eventually the margin you tighten up by would be irrelevantly small and thus you find the unbeatable strategy against a GTO player when there is this imperfect player in the game.

I think, that if the original mistake made was to tighten up by z, then, x will be between z and GTO. Y will be between z and x. In the end, my instincts are telling me, that you’d have a strategy that’s 2/3 of the way towards z from GTO.

... I think all that is right, but this is getting extremely complicated now!! If some genius mathematician either now or in the future wants to try proving or disproving this, that’d be awesome! But to stand a chance of doing that, you’d first have to get over this whole “GTO can’t be beaten” nonsense.

If you talk about exploiting GTO you need to assume it's perfect GTO, not just some bad player trying to apply GTO.

You say a perfect exploitative player will have higher EV in tourneys (with good and bad players in the pool) than a GTO-bot. Yep that's correct because a perfect exploitative player will exploit every villains deviations from GTO (and play GTO vs the GTO-bot, because of no deviation from GTO by the bot), which the GTO-bot won't do.

Your arguments are confusing because you are talking about players that make big mistakes that you can exploit, and you call these players "GTO players". They're not GTO players period.

Perfect exploitative players will always make more money than GTO-bots in a field with people deviating from GTO. But the exploitative player can't get an edge vs the GTO-bot.

Should change the thread title to "how to exploit players deviating from GTO".

This sentence was wrong... it should have read:
“we could widen our bluffing range to take back the profit the opponent has gained from us by using x, but this strategy will lose money against GTO on future plays.

Atleast you agree that exploitation makes more money than GTO. You don’t seem to realise that making more money than the GTO bot is literally you taking an edge over him. You think I wouldn’t beat your GTO bot if I had a stack twice the size of his?

What I’m saying in this thread is that there are many ways you can bounce off a weaker villains mistake to take your profit from GTO plays or players.

Of course someone can use a partial GTO strategy.

And mate, this thread isn’t about “exploiting players who deviate from GTO”. It’s about exploiting the players when they make their GTO plays. I really can’t make that any clearer. In the RPS example I showed undeniably that it is possible.

If you are left heads up with a GTO bot in a tournament and you have a 10x bigger stack, sure you will win most of the time. But that's not the point of all this. Already told you if you can exploit weak villains you will have higher EV than the GTO-bot vs the weaker players. Same thing in cash-games. Someone finding right exploits will make more money, but just not vs someone playing a full GTO strategy (say the tournament pool was only GTO-bots).

But I agree that if someone only plays GTO in one node but plays suboptimally/shitty in the rest of the game-tree, i.e. the strategy overall becomes non-GTO, you can exploit that. That's why we take notes at the table and adjust.

I'm pretty sure there are some fish following a solved pre-flop chart (in this case someone playing a partial GTO-strat). Would never talk about exploiting a GTO play though, you are exploiting the overall bad strategy and not the GTO play alone.

Yeah yeah, almost all of that is right. And so you must agree that a player using GTO in a mixed field can regularly be beaten by an exploitative player? If so, you are saying that GTO can be regularly beaten. And every reply that has called for my ban claiming that “GTO is unbeatable” is wrong.

You are mistaken in thinking that only fish will use a partial GTO strategy. The truth is that nobody applies GTO perfectly. All villains use a partial GTO strategies, and all of said villains can be exploited by widening your range or by strengthening your range.

I’m just pointing out that if you exploit by strengthening your range, you increase your profit against all future plays. If you exploit by expanding your range, you decrease your profit share against all future plays. I’m not completely certain of how it works in multiplayer games, but it is clear that in multiplayer games you can gain an advantage over a GTO opponent by using the weaker opponents mistakes to strengthen your position.

If you play LLinusLLove at a heads-up table. How are you going to exploit him? He plays very close to GTO and has probably studied limping strategies etc. He makes no deviations based on your strategy. Where do you see your edge?

I didn’t ask for the counter strategy to a partial RPS GTO strategy. You started off with assuming playing against a GTO 3-bet.While no one yet knows what a complete GTO poker strategy is, it is naturally assumed in theory discussions that the “GTO player” is playing full, not partial, GTO.

Since we do know the complete RPS GTO strategy, you then answered my RPS challenge as if you always were thinking of a player who sometimes plays GTO. In your RPS answer, the “sometimes “was playing Paper twice as often as GTO says. That’s a pretty big deviation. Why not make it paper “all the time?”

Instead of continuing this sham for so long you should apologize for bad thinking, or at minimum, bad posting, and end the thread.

This guy has studied the game in a completely different way to me. I’m a purely exploitative player whilst he is a purely GTO player.

We are polar opposites in lots of ways:

- He has spent his career studying one strategy, whilst I have spent my career learning how to be as flexible as I can possibly be.

- When he sits at the table he knows the strategy he is going to try and use. I go to the table with an open mind, and work out each decision as I come to it.

- He studies by memorising hands and numbers, but having a good memory isn’t very important for me. It’s not as important as being able to make rapid heavily in-depth calculations.

- This guy doesn’t care for his opponent nor his opponent’s strategy, but all my decisions are based upon my opponent and his strategy.

- I have spent my career delving into the mind of my opponents, but he knows nothing of the mind.
The only advantage he has over me is that he knows the GTO strategy more accurately than I do. I don’t really know it at all, but I can roughly guestimate it for each decision in real-time, which makes his advantage over me minimal at best.

My advantages over him are many, as he has massive holes in his understanding of exploitative theory. These holes could lead to a massive advantage for me:

My Advantages

I know the decision-making process he’s been using since he was first conceived by God. I know why he cried when he saw Iron Man die. I know why his sweet little puppy sometimes makes him angry. He doesn’t know his own mind, he doesn’t know my mind, and this does leave a massive hole in his understanding of key factors involved in this game. I know his thoughts better than he knows them himself. I can see all his inner-demons. I know what riles them up. If he’s facing me, I’ll be bringing those demons out to play and there is nothing he can do to stop me.

His cognitive dissonance will be terrible as he has trust for so many plays, and so I would definitely try to use this against him to obliterate his mind.

You say that he won’t adjust in relation to my strategy, and I’m sure he’ll try not to, but, if he doesn’t realise that he’s using this same exploitative thought-process when deciding how to react to a puppy that chewed up his dildo, he won’t notice when he uses it after I lure him away from GTO either.

I am confident I can lure any human from any pre-planned strategy, but if not, if he somehow maintains his GTO strategy and doesn’t go in some way mental, I’d still hold a massive advantage over him because he doesn’t use the perfect GTO strategy and he doesn’t know how I’d exploit that. He’d literally be aiming to achieve a strategy that makes less money than the strategy I’m aiming for. I’m sure he’s spent a lot of time learning his strategy, but my strategy makes more money so I wouldn’t need as much time studying in order to beat him.

How I’d Exploit Him

The way I’d exploit him is clearly very difficult for people to understand, but in essence it is relatively easy to apply:

The exact mistakes he’s making will be very small and hard to spot, but I don’t need to know the exact mistakes that he’s making. All I need to guess is how much of a mistake he will make, and whether he will make more mistakes when I check or when I bet, when I limp or when I open.

Wherever more of his mistakes lie is where I lean towards with my weaker hands. For example, if I think he will make more chips worth of mistakes in limp pots rather than in open pots, I will take some of the weaker hands from my opening range so that I can strengthen my opening range. The GTO opening range is around 70%, so: I’ll open maybe as little as 50% against him, and would add the weaker hands to my limping range. When I open, I am now going to be stronger than a GTO play giving me vastly improved profit margins. He might not make the perfect GTO play when I open, but that only means that I take more profit from tightening up my opening range (This means you want to “lean” more in earlier streets). It’s only when I limp that he has a chance to win back the profit I made from my first exploitation.

After I’ve limped I’ll do the same again. On the flop, if I think he’ll make more chips worth of mistakes when I bet than when I check, this time I will bet the flop with a slightly weaker range than GTO would dictate. I’d still fold with GTO numbers against this guy, but I’d check with a slightly stronger range than GTO dictates.

I’d keep shifting my strength toward his GTO-like plays. This would give me more and more of an advantage over him during those plays. Then I’d use my fluidity to beat him in the spots that he is less familiar with, whilst using a weaker range than GTO dictates. I’d control the game by constantly strengthening one portion of my range so that it beats GTO, whilst playing my weaker hands in the more obscure situations that I think the opponent will struggle in.

This is a valid strategy to exploit this guy, and so when he see’s me using this strategy, his cognitive dissonance will rage!! I could make it worse by winding him up, but I wouldn’t need to. When he plays GTO vs my open he’ll see that he is losing way more than usual, he might put down to luck, he might think its fine because he’ll make up for it when I don’t open. He will justify it in all kinds of ways, but he wont be able to see the real reason I’m doing it. His subconscious mind will hide the truth behind a wall of rage. He’d just start to hate me.

Against some micro stakes version of this player we could be extreme in our exploitation of them, we could probably limp some 60% of hands because they only know tiny fraction of the GTO strategy. It won’t be hard to find plays that are obscure to them and in those spots they will make many expensive mistakes. This means that we can massively strengthen our range in our chosen spots against them. Against this guy though, who studies GTO in immense detail, I’d only be able to adjust slightly. If you go to far you’ll start losing your advantage.

If I played this guy, HU, right now, I would actually expect to get beat for a little while but only because I always play 6 max cash. If we played 6 max cash, with a load of other players in the game, I’d expect to destroy him straight away using this strategy. HU is different, I’m not so familiar with it. I’d want to spend at least a little time studying GTO for HU before I’d be confident that I’d beat this guy. Do be aware though, I’d only learn the GTO strategy more accurately so that I could avoid it more accurately. I wouldn’t ever actually use it. I’d rather not play.

I would hold many advantages over this player at the tables, but that’s not why I’d advise that you learn using exploitative means. The real reason exploitative training is better is because; the better this guy gets at poker the worse he will be at making decisions in life. His cognitive dissonance will effect him through all his life decisions, not just at the poker tables. This guy will have hidden his natural thought process so deep in the back of his mind that he will never be able see it. His poor puppy will suffer the consequences as he's subjected to a life of sadistic rage. If you or anyone tried to teach this guy how he naturally strategizes, he’d just lose his mind and somehow get rid of you. In contrast, the exploitative learning method teaches you how to make better decisions in general. As I learn poker, I delve into the mind like the monks of old. When this guy learns Poker, he’s slowly climbing down into the Devils net.

See what you did Snipnickle... To satisfy his cognitive dissonance, for 4 weeks this guy has been trying to find a reason my RPS example was wrong, and you gave him an answer! Now he's gone and jumped straight on the bandwagon.

I did explain this clearly in the SECOND LINE OF THE FIRST POST:

READ THE ORIGINAL POST CAREFULLY and you'll see that it is extremely obvious that I have always been talking about a villlain who uses a partial GTO strategy. AND IT IS POSSIBLE TO USE A PARTIAL GTO STRATEGY!!! If someone knows the GTO strategy for 3bets, he can make a bloody GTO 3bet!!

I was also perfectly accurate in my wording of the title. If this thread was about exploiting someone using the entire GTO strategy I would have called it "How to exploit someone using the GTO strategy" As it happens, I was only explaining how to beat someone who uses part of the GTO strategy. The example I used, was the GTO 3bet.

Am I repeating myself here?? I feel like I'm repeating myself over and over again...

Look, if what you're spouting is true, what you are saying is that nobody in the history of poker has ever made a GTO play, nobody has ever balanced their range. I mean, you could define GTO in this way, but that is a crazy ass way to define it and so banning me for not using your personal crazy weird semantics is absolutely ridiculous. It just highlights the effects of your condition.

How has this strategy worked out for you so far at the higher stakes? You've started a thread as a microstakes player in 2018, and another one as a microstakes player in 2019. (Based on 2+2 usernames people have mentioned on here)

You come across as a very unique player that can accomplish stuff no one else can. Do you have any kind of proof of this working because it seems like plain words so far and a lot of assumptions about how well you play spots vs villains who are crushing the toughest games.

I started a challenge last year, but it was closed on this site for obvious reasons... I started it to show I was clearly better than people like you, who post in forums like this. I started in the 1c cash games at stars with $50, and after 120k hands I turned it into $2000. All fully recorded etc. You can see me limping loads.

Right now, I'm mostly playing £200 online cash games ($300 or so). I do also play the £400 but that's as high as this site goes. The strategy is doing very well in all games, even the high stakes regs dont have a clue whats going on. The site i'm on is a bit dodgy so the standards are quite low, but I would expect it to work just as well in other games.

I dont play very much atm, regardless of the fact that I make about $100 an hour. Poker led me to becoming buddhist and so I dont care for material possessions like you do. The only reason I play at all is because I'm trying to build a website and it needs funding. However, instead of working towards that goal, I keep wasting my life trying to teach people like you.

Hows your game? Can you beat the micros yet?

Good if you're making some $. And I believe you. No WR or sample size by stake provided though.

My goal is to get better at poker, both theoretically and exploitatively. Those things are related. I've never claimed to be superior to high level crushers or any crusher. If I would It's quite obvious I have to prove it at that level in some way with a big enough sample.

You said you'd expect to destroy Linus in a 6-max game with your strategy. That's a bold statement for someone playing low/mid stakes for a couple months.

I would crush LLinusLLove heads up because he is a GTO player, unwilling to deviate, and I am an exploitative player, who goes off of my reads. I would "obliterate his mind."

-said no reasonable person ever

LLinus plays very far from GTO btw and exploits a lot.

I’ve made something like $250,000 gross profit throughout my short playing career, that’d be around $6 million net profit in your Hemdon database. I’ve also written a book on poker theory, which I spent more time on than I did playing. It took 5 years to write. I started my career by moving to Bulgaria and living in a poker training school. The second best exploitative theorist on the planet is now my brother, who advises a casino network and currently stakes and teaches approximately 50 players.

I am a rare master. A street rat, whos not even very good at maths, but climbed through the stakes and can now beat anyone. I’m a legendary game theorist the likes of which the world has never seen before. I’ll be remembered for ten thousand years for the developments that I’ve given to the field of game theory.

And you guys are all micro-stakes losers who want me banned because you cant understand what I’m saying. Malmouth and Sklansky hide away to avoid embarrassment. Nobody else will waste their time even talking to you. Is this the best 2+2 has to offer nowadays? Sklansky should be happy that I’ve furthered his theorem, Malmouth should be happy that there are books to release after his GTO series has ended.

What you saying Rusty, does 2+2 still just think I’m chatting nonsense? All your best theorists have run out of arguments against my theories and are trying to attack my sexy career. Does 2+2 not have anything else to say???

Haha no way, you actually copied the beginning of MPT in your first paragraph.

What's the title of your book? Where can we get it?

This also cracked me up a lot. Gotta admit you make people laugh.

Bloody trolls, isn’t there a rule against this Rusty? We’re supposed to be talking about exploiting parts of a GTO strategy.

I'm genuinely interested in this book. You're talking about the possibility of capturing an additional payoff or EV, by deviating from a payoff maximizing strategy, against a player that employs a payoff maximizing strategy.

I mean if you're right that would actually be mindblowing for the field of game theory.
All of John Nash's findings and all findings based on his findings could then just be thrown right into the trash. You could probably throw every solver and every poker book already written (except for your book) into the trash.

If you're right that we can exploit a GTO-strategy, then you will probably be remembered for thousands, if not millions of years. If you're right, everyone in this thread owes you an apology, every author that has written a poker book owes you an apology, even every professor teaching game theory owes you an apology. If you're right, you can become the great founder of the academic field of actual game theory.

Now why would I not want to get to know about a book that can bring these things in motion?

Seems to me like you've got nothing to lose. So why don't go ahead and tell us the title of this book, so everyone can get up to speed to discuss this with you?

------------------------------------------

Now I did see something that might be worth discussing skimming through your discussion with Shipnickle. It was about exploiting a partial GTO-strategy. Though there is no such thing as a partial GTO strategy, as this would just not be a GTO-strategy, it gave me an interesting thought.

It would be interesting to see how much EV is lost if a player currently employing a GTO-strategy, would be restricted to pure strategies. i.e. there can be no mixes in this players strategy. So if the GTO strategy is to 30% bet, 50% check and 20% fold with a certain hand the strategy would change to checking 100% of the time.

Where would this player lose his EV? And how can a MES-player take advantage of this player?

At no point did I say I could exploit someone using the full GTO strategy... I’m not allowed to promote my book, you trying to get me banned!?

If there is NO such thing as a partial GTO strategy, to learn how to do a GTO 3bet you’d need to learn how often to bet the river in a limp pot that ran AAA23. “Hey Snipnickle, how do you make a GTO bet?”. “Well, on the river...”. That is a ridiculous way to define a GTO play!! It also makes absolutely no difference to the content of this thread anyway!

I’ve explained the difference between tightening up and loosening up to exploit. You don’t need to throw anything “in the trash”. This is new exploitative theory, because nobody ever explained it before. Until now, nobody realised that when you tighten up to exploit you are taking your profit from the rest of the villains hands rather than the one where the mistake was made.

This is useful to game theory as a whole, there are massively holes in everyone’s understanding of exploitative theory.

I’m really tired of repeating myself. It’s obvious you’re all just trolling over my thread now. It’s obvious the mods are with you. I’m getting really bored so I presume all the level headed people here will be bored of this too...

You are all over the place with your posts Y.J, but if I understood correctly you are basically talking about "taking GTO players into nodes in the game-tree they haven't studied or seen before". This is nothing new and people talk about it all the time. Min 3beting pre, limping OTB or cbeting 5x pot are probably lines a solver would never take, and most players trying to play GTO won't include or node-lock for these types of plays in their solves. Most people who know GTO well often know quite a lot of poker theory concepts and can navigate rare nodes based on them vs fishy lines. Also if you decide to take a line outside GTO, you must be sure you know how to play that spot better.

But again. It's not a new concept. Those who try this stuff usually overestimate their ability to gain back the EV that they lose in theory from deviating. Usually they have to assume the "GTO player" is gonna play much worse in that node, which I doubt is the case very often.

I'm thinking you are in that exact position. You overestimate your ability to play better in the nodes you want to take the partial GTO-players.

This is an outstanding post.

Lol, taking the players to “nodes they haven’t studied” is a tiny part of what I’m saying. What I’m saying is that when you tighten up to exploit you take your profit from the opponent when he makes his GTO plays. I’m not all over the place. I’ve said that many times, but you’re still all being batshit crazy!

6-max table. 5 GTO players and yourself. Do you gain EV by only opening AA preflop vs if you tried to play the GTO strategy? Let's assume they will never adjust to this (and are unaware of your new strategy).