Some people post advice about GTO and it's applications in LLSNL

Other people respond with misconceptions and misunderstandings of what GTO is and how it relates to poker.

If you meant the HH, I called the river and villain had Ac5c for the better 2 pair.

Yes, this makes sense. Sorry the confusion.

This hand officially jumped the shark on 4/21/17. RIP thread.

Op, LLSNL advice is bad enough as it is. What the hell did you expect to happen when you started discussing GTO strategies relating to a fictional hand that is nearly identical to the hand in the OP except for the fact that V2 no longer exists in your fictional hand (while ignoring the fact that your BTN raising range is going to be different with V2 limping vs. V2 folding, as is V1's calling range from the BB ... but I digress).

Honestly what you are looking to discuss really doesn't fit into LLSNL and the ensuing discussion shows why. If you really want what you are looking for then ask this in the Theory sub.

I agree that this is a huge derail of the thread, but I disagree that these concepts don't fit in with LLSNL. GTO play, nash equilibriums, balance etc. are fundamental poker concepts and hardly anybody has any idea what they mean or why they matter as you can see in this thread. They are really not that hard to understand at a basic level.

@ Johnny

You're right that this discussion derailed a long time ago and doesn't belong in LLSNL. My bad

Dude you have not the first clue what you're talking about, this is embarrassing. GTO strategies exist at an equilibrium, which requires that neither player can unilaterally improve their outcomes. Hero can do so by not folding every hand preflop.

First sentence here is correct, but the rest is not. Never calling or raising is an example of a strategy playing "same actions as a GTO strategy, but at the incorrect frequencies" and will lose.

A GTO solution always exists for any zero-sum game with a finite set of actions, that's a mathematical fact. "But there are blinds" does not matter. From the Wiki article on Nash equilibrium:

Man, you need to be a certain level of educated before you can believe things this stupid. Take poker without blinds. Folding every hand except AA and wagering all your money with AA is a GTO strategy, right? Cannot be exploited. Well, this strategy wins against any strategy that ever wagers money with a non-AA hand. How many examples do I have to construct before you realize that what you believe about GTO is not true?

Yep.

I stand by what I said... See this post (#98) for clarification: http://forumserver.twoplustwo.com/sh...6&postcount=98

This. Also, apparently a bunch of people here got their ideas from the same misleading LLSNL post:

Terminology is being used a bit fast and loose here. Strategies including Pebble are not strictly dominated (for instance, they can win against opponents who always throw Scissors). But what this is basically saying is "GTO will always break even unless there's a way for the opponent to unilaterally choose a bad strategy".

But RPS is unusual in being a game in which it is not possible to choose a bad option. The vast majority of games have a way for the opponent to unilaterally make bad decisions. Tic Tac Toe for example, or chess.

"Choose an amount of money to give your opponent" is a very simple zero sum game with an obvious GTO solution (give $0 every time). Giving your opponent a penny is a directly worse strategy, but it's not strictly dominated (it wins against any strategy where the opponent gives more money). Most games are like this, where the GTO strategy breaks even at worst and the opponent can unilaterally opt to play a losing strategy. Poker is like that.

Your example is right in that the gto opponent has made you indifferent to calling when he bets his polarized range. You will break even regardless of your fold and call freqs if that player doesn't deviate from gto strat.

But what if your own betting frequencies are out of balance?

It's the same idea... Pretend that a GTO strategy includes raising AA preflop to 3BB 30% of the time, and 4BB 70% of the time. Then for that GTO strategy against a GTO opponent, EV(raise 3BB) = EV(raise 4BB). It has to, or else a GTO player would never choose the lower EV action.

The GTO opponent will not adjust to your frequencies, as its strategy is fixed. So you can do whichever 100% of the time, and still have the same EV as a GTO strategy IF you're playing a GTO opponent. Only an exploitative non-GTO opponent will adjust to your frequencies.

Similar ideas with bluffing or checking behind, etc -- any mixed set of actions for a given spot.

But as I mentioned in my post, for poker, since you have 1326 possible hands in your range, a true GTO strategy would divide most of your frequencies across hands. I.e., value bet your best hands, bluff your worst hands. Also, blockers will always affect EV. E.g., having 7c7d in your hand on an Ac3h2s board is going to be (very slightly) different than it is on an Ah3c2s board. You can't swap actions around through different hands as each hand creates different states in the game space, with different EVs. So there may very well be a limit to how many spots have a mixed/randomized GTO strategy where this idea actually applies.

I loved this thread so much, Ima resurrect it.

I suggest you folks go here for more information:

http://forumserver.twoplustwo.com/17...heory-1679187/

That GTO thread is so terrible.

I dont know why you would call the river. He is calling out of the sb and our range is face up and he is donking 3 streets oop. Im folding river. Only calling flop because bdnfd. We just have middle pair otf so i would pitch it with only 5 outs but good implied odds on the spades so call is ok. Turn call is good.

This thread probably has the most misinformation per post of any 2017 2+2 poker thread.

May as well correct this one while I'm here.

As I tried to explain upthread, it is clearly not true that simply varying your frequencies against a GTO player cannot lose, because folding every hand preflop at heads up is a massively losing strategy. Counterexamples didn't seem to count for much ITT though, so I'll explain further...

A strategy can only be balanced such that we're indifferent what the opponent does if the opponent only holds a single possible hand. It is not possible to balance a strategy such that you both don't care what the opponent does with AA and don't care what they do with 72o.

As a simple example, if a GTO player raises preflop at HUNL, that raise is going to have a negative expectation when it runs into the opponent having been dealt JJ. Because their preflop play is calibrated to be balanced against the opponent's entire range, it's losing when it runs into a much better hand than average. Therefore, we're not indifferent to what the opponent does with JJ. We vastly prefer they fold it. If all the opponent ever held was JJ, we would change strategy to eliminate this preference, and it then wouldn't matter what the opponent did. But we can't, because we have to play against an entire range.

As a result of this inability to balance against individual hands, players are able to unilaterally lose against GTO players by doing whatever it is we prefer with individual hands.

I've defended what I said here on several occasions in multiple different places on twoplustwo... What I said is correct.

To be clear, of course it's possible to lose against GTO. Of course we can't fold 100% of our hands. We obviously should never fold AA preflop... However, suppose that we're facing action preflop with like T8o or something, and also suppose that there is a GTO strategy where it is correct to fold this hand 30% of the time, and call 70% of the time. If that is true, then *if* we are playing against a GTO bot, we can simply fold this hand 100% of the time because the GTO bot will not adjust to our frequencies (it won't figure out that we're never calling with T8o and adjust against us).

If there's a mixed GTO strategy where we raise AA to 3BB 30% of the time and to 4BB 70% of the time, then yeah we can never fold AA. But we *can* raise to 3BB 100% of the time and do no worse than the mixed strategy *if* we are playing a GTO opponent. Again the GTO opponent won't adjust to the fact that our frequencies are 100%, 0% instead of 30%, 70%.

So yeah, if there's something that every GTO strategy does 0% of the time, we can never do that thing. However, if any GTO strategy does something ever, even 0.001% of the time, we can do that thing 100% of the time against a GTO bot and do no worse than a GTO strategy, even though we're not playing a GTO strategy ourselves.

In summary, there is always a pure strategy that has the same EV as a GTO strategy when that pure strategy is playing against a GTO opponent - even if all GTO strategies are mixed strategies.

Even this more limited argument is still not correct, you haven't taken on board what I'm saying about being unable to reach equilibrium against single hands in ranges. Your argument that the GTO bot is indifferent to our frequencies with a given hand relies on the idea that the GTO bot's play has been calibrated to reach an equilibrium against that hand, which is never the case. (Edit: "never" is too strong here, I should have said that this is only ever the case in very limited, toy situations, or by coincidence).

Take the best hand that a GTO bot would ever not threebet preflop at HUNL (say JJ for the sake of argument, it doesn't matter to the argument what it is). Take the worst hand it would ever threebet, let's say 45s or something. Your argument is that it doesn't matter if we invert those percentages completely, start almost always threebetting 45s and almost never threebetting JJ. Furthermore, that we can do that for all our hands - just almost always threebet the ones at the bottom of our range and almost never threebet the ones at the top. Think about it, you cannot do this, these hands have different equities against GTObot's range. We're threebetting the same frequency but doing it with a range with vastly worse equity, that has consequences when we have to show our hand down. It runs counter to everything you know about poker to say that you can substitute JJ with 45s and everything will turn out the same.

The only reason you're resistant to this otherwise obviously true argument is that there's something you think you know about GTO which is incompatible with this. The problem is that you've taken something which is true in a toy situation (playing against a bot which knows what hand you have) and overgeneralized. If the bot's strategy is not in equilibrium against our actual hand - which it never is, because it wasn't designed to be - then there are better and worse ways to play that hand.

Dude, you're just wrong by disagreeing with me, and you're missing something very fundamental about GTO by what you're saying.

Yes, if we play at the non-GTO frequencies, then we are exploitable and we will lose against an opponent maximally exploiting us.

But against a GTO opponent, we can change frequencies as we please - as long as we always play GTO "permissible" actions (i.e. actions that some GTO strategy would play) - and end up no worse than GTO.

Look, if a GTO strategy says to 3bet JJ 90% of the time and flat 10% of the time then against a GTO bot, EV(3bet JJ)=EV(call JJ). Therefore, if we're playing against a GTO opponent, it doesn't matter how often we 3bet or call JJ, as long as we're doing one or the other (and not folding). It would matter if we were playing an exploitative opponent though.

Suppose there's a game called rock-paper-scissor-suicide. Same as RPS, but there's an extra action called suicide that always loses.

The GTO strategy is to play at frequencies of 1/3, 1/3, 1/3, 0.

If we are playing against this GTO bot then we may play 100% rock or 100% paper or 100% scissor and break even, but if we ever play suicide we will have -EV. This is the same exact concept.

This is absolutely not true. You're accusing me of not knowing how equilibria work, but I do. I understand that in a situation on the river where we have TPTK, say, and the bot has some combination of value bets and bluffs, it will set its betting frequency and sizing such that EV call = EV fold and it doesn't care what we do. I understand that.

That's absolutely not what's going on with JJ preflop, though. The reason we're threebetting most of the time is that the hand is a good hand, with high equity. We throw in some flats in order to add uncertainty to our range on later streets, but this does NOT mean we can just not threebet at all. What blows my mind is that I know you get this. You understand poker. JJ is absolutely smashing the bot's raising range, how can you think that a sprinkling of magic GTO dust somehow makes this no longer true? It's like arguing with a religious person, you're taking obvious truths and just overruling them with this belief about GTO you've convinced yourself is some axiom of truth.

Your mistake is to imagine that the bot is in an equilibrium strategy against JJ, but it isn't. It's obvious that the bot's play is not optimized against JJ specifically, if it were then the bot would have folded. What makes the bot unable to optimize against JJ is that it has to play a strategy that is balanced against our whole range. We have an information advantage against the bot in that we know what actual hand we have. It absolutely matters that we press our equity advantage when it turns out we're near the top of our range. Like I said this is poker 101. Stop and think: what's more likely, that fundamental poker concepts suddenly no longer apply, or that you're wrong in this generalization about GTO?

Rock paper scissors is not an appropriate analogy. Chess has a GTO strategy, but that does not mean that it doesn't matter what moves you play against an engine. Again, you're overgeneralizing from toy situations.

I think the thing that's tripping you up here is that you think that if GTO bots are playing a mixed strategy against each other, that has to be for the same reason as in toy situations, i.e. that the EVs are equal. The main reason GTO bots play mixed strategies on earlier streets is to keep ranges open on later streets. When a GTO bot flats JJ preflop, it does not mean that EV(flat) = EV(3bet) on that street. Rather, the GTO bot is sacrificing immediate equity in order to keep its range wider on later streets, enabling it to regain the lost equity later. But beyond what is necessary to keep your range unpredictable, you're just burning equity not threebetting JJ.

Gonna try one more tack. If the bot knew before it acted that we had JJ, would it alter its strategy? Yes, right? It'd just fold most of its range preflop. You agree with that, right?

But your contention is that it doesn't matter whether WE put in more money or not. How can both things simultaneously be true? How can the bot react to the news that we have JJ by wanting to wager less money, yet when we find out we have JJ, it doesn't matter at all whether we wager more money or not?

This is getting ridiculous.

Suppose A and B are NLHE players that are in equilibrium, I.e., they are both playing GTO strategies.

Suppose A's strategy includes 3betting JJ 90% of the time and flatting 10% of the time.

By definition, this means that for player A, when playing against player B, that EV(3Betting JJ)=EV(flatting JJ). Suppose this isn't true. Let's say EV(3betting JJ)>EV(flatting JJ). Then A would choose to 3bet JJ more often, and therefore it would not be in equilibrium at the 90, 10 frequencies.

The EVs are the same because in order to get to equilibrium, B has adjusted its strategy to make A indifferent between the two. A, however, must choose the exact frequencies to minimize B's EV. In this case, A found that 90,10 minimize B's EV.

However, now that it's in equilibrium, if we fix B's strategy, then A can choose any frequencies it wants to. It's only if B is allowed to exploit A that A would have to retain the 90,10 frequencies.

I don't know how else to make this any clearer. Maybe post a link to this in the poker theory forum or something; perhaps somebody there can explain better.

But the EV of 3betting JJ does not vary linearly by frequency because there are two EV considerations. There's immediate equity on the threebet, and then there's the consequence to our equity on later streets when we can never have JJ because we always threebet it preflop. I mean it's not in dispute that JJ has an equity advantage over the opponent's range, so if our 3bet closed the action for the hand, we would always threebet. The fact that we sometimes don't logically has to relate to what happens later in the hand. So threebetting at a given frequency has pros and cons and at a given point they balance out, like solving simultaneous equations.

I'll get someone in here from Poker Theory.

Arbitration request

I agree with this.

http://forumserver.twoplustwo.com/15...whosnext+mixed

whosnext puts it quite eloquently here:

Vs non equilibrium strategies, mixing is both non maximally exploitive and unnecessary to maintain a minimum ev.

Vs equilibrium strategies, mixing is both maximally exploitive and necessary to maintain a minimum ev.