And take lines that are highest EV in a vacuum. Specifically with regards to unbalanced bet sizings and overbluffing (as most bets/bluffs are +EV in a vacuum)

We don't sacrifice ev by balancing our lines. You can disregard balance in anonymous zoom but you need to understand it anyways in your study. We only take lines that are highest ev, vacuum or not, balanced or not. We don't balance to prevent villain from doing something we don't want him to do, we do it to capitalize from the times that he does it.

And how would you know what is highest EV in a vacuum? Do you have a crystal ball that knows anonymous villain X is 3betting 10% and anonymous villain Y is 3betting 20%? Or what makes you think overbluffing is automatically highest EV because it's anonymous? How would you know if your particular anonymous opponent is an overfolder or a calling station?

Anonymous tables means less information. Less information means you should play a more theoretically sound game.

But there are pool tendencies which you can exploit and there is no way people will be able to profitably play a counterstrategy against you. Example: pool underbluffs in a given spot and overfolds to bets. You start overbluffing and there is simply nothing they can do to exploit you without getting exploited themselves, whereas on normal tables they would see hud stats and play back at you.

So let's say one knows pool average 3bet frequency in a given spot is very low. Is it more +EV to play as if unknown villain had that average low frequency (and overfold for example) or to play gto-ranges? Somewhere in between? I suspect the answer is 'somewhere in between' with the exact answer depending on the statistical distribution of 3bet frequencies. So in this case unknown villains range will be wide but strongly weighted towards strongs hands, and playing accordingly will be the most +EV.

I suppose anonymous zoom tables are kind to the nits and that's why on Bovada for example there was typically better action on regular tables vs. Zone.

i.e. even on an anonymous regular tables, after seeing some guys play 60-70 hands, I would know enough to put in a temporary note (this guy always has it, do not pay him off). On Zoom however they can do their thing all day...

That has nothing to do with the question of anonymous games. You don't need a game to be anonymous in order to exploit population tendencies (by the very definition they exist because the population is not aware it is being exploited). The game being anonymous has no bearing on whether you should or shouldn't use them. It is simply a logical fallacy to say that one should adjust his game more in an environment with less information.

Seems like two things are true:

1. Yes anonymous tables make it more likely you can exploit a population tendency if you're sure it exists.
2. You still can't disregard balance, because a lot of the point of balance isn't so much to avoid them from adjusting to you but to avoid the issue where you could be wrong about the tendency.

Like as an example let's say you're playing at a non-anonymous table, you've been playing as close to optimal as possible, and a nit shoves in a spot where the correct play is call, you have the second nuts, but you're sure they're too nitty and never shoving worse than the nuts here. Why not fold and just play gto again after that hand, so they can't exploit your fold later? Usually the answer is you could be wrong, and they could be value shoving wider, or on tilt and actually bluffing too much at this moment, or your read was wrong, etc. I'm not saying to never deviate from optimal play, just that the reason isn't necessarily to prevent future exploitation.

This is not true in a lot of cases and you can do a little experiment after coronavirus restrictions are lifted. Show up to a mostly locals Vegas Casino, where players fold to 3 bets almost every time unless they literally got JJ+/AK. It is therefore mathematically correct to 3 bet those players, particularly in good squeeze spots with almost any two. Now, try 3 betting those same players every time they open. After a half an hour, many of the same OMC players will think 'this guy is a maniac' and will start playing back at you with hands like 88 or AJ, that they would previously fold vs. a 3bet without hesitation.

Tommy Angelo wrote something that I think has some applicability to this. This portion basically sums it up. The link is at the bottom if you want to read it in full.

“ Here’s a curious thing: The cards you play do not determine your range. Thoughts do. During a hand, your range is merely a perception. If your opponent thinks your range is balanced, then your range is balanced. If your range is perceived as unbalanced, then your range is unbalanced. Your strategies should not be based on what your range actually is. Your strategies should be based only on what you think your opponent thinks your range is.

The ideal condition is when your actual range is different than your perceived range, and you know what that difference is. That’s a fun place to be. When you successfully ambush a foe, or sell a convincing lie, the joy of deception is your reward for doing the work of maintaining balance in your ranges.

Somehow my game evolved to where I get to enjoy the fun part without having to do the work. I don’t have to balance my early-seat ranges because you do it for me. I am untrusted, because you are. Thanks again.”

I ran across this when I was early on in collecting data on population tendencies at Bovada for Zone. The basis for balancing your range is that you remain unexploitable to players who understand balance. If I bet a certain amount and compose my range with strong hands that beat bluff catchers and bluffs with the right ratio given my bet size then my opponent can’t can’t win and always loses if he deviates from the optimal calling range.

Of course this doesn’t matter if your opponents don’t understand optimal play, or if they do or have an idea of it but incorrectly construct your raise. To take an extreme example if you were playing a player who thought you bluffed a certain amount in certain spot but in actuality you never bluff there then you always win when he bluff catches.

This is what Bovadas anonymous fast fold gives you. The population bluffs on the river with a certain frequency. They cbet with certain frequencies. Players know this and expect players to bluff. Theoretically you could never bluff and opponents would still think you bluff because all they know is you are player 5 on this hand at this exact moment. They have no way of knowing when they play you again and you have no way of knowing the same. There are players exploiting this by playing super nitty and others playing hyper aggressive.

https://www.tommyangelo.com/thank-yo...-dont-have-to/

This piece alone entirely discredits the author as having no clue as to what the goal of balancing is. What he says is factually true, but what he's implying is not. He wins the individual hands when he's not bluffing, but he also loses all the hands he could profitably bluff and allows his opponent to win when his opponent has a worse hand than would bluff-catch.

To put a simpler way, the author sounds like this: "I just wait for AA and shove all-in every time I get it. The reason this works so well is other people balance for me, and aren't able to fold KK or even QQ/AK sometimes because they think I'm balanced, even though they lose every time they call." Sure in that scenario you win their stack every time you get AA and someone else has KK, but you're losing a ton of money in all the other scenarios when you could have won smaller pots.

I understand he said it was an extreme example, but it was an extreme example meant to prove his point, when in reality it completely discredits it.

You are probably right and I probably have no clue what I am talking about; however, I am trying to learn. I assumed balancing was taking a line that properly constructs your range to have the correct number of bluffs to value ratio when compared to the odds you’re giving your opponent. In other words if I am playing a player who makes a pot size bet on the river he is laying me 1:2 odds on a call. That means his range should consist of 1 bluff for every 2 value bets to remain perfectly balanced and make me indifferent on a call. When I call with 66% of my range I will win 33% of the time and will lose 66% of the time and when I fold the other 33% of my range I lose 100% of the time. That is to say I breakeven on my call and lose no money the times I am folding. My EV on this call is $0 because my opponent is 100% balanced.

Your argument is that I lose the times that my opponent would fold a hand he can’t bluff catch with. I was under the understanding that bluff catching from a MDF perspective is taking the range you can’t profitably raise with and calling with X% of that and folding the other percent. That means that you might be calling with high card hands and not made hands depending on yours range you reach this spot with. A T high can be a bluff catcher even though many would say it is not. Stu Ungar called with T high in a WSOP event. I have seen similar calls of Q and K highs by pros. I can think of many times that I bluffed Flop and Turn and gave up on river to win with a high card. A couple of days ago I won with 7 high when my opponent was drawing to the bottom end of a wheel. The hands that opponent is most likely to fold are the hands that he is drawing with and hands that some of our bluffs beat. Isn’t it impossible to construct a perfect range OTR since our bluffs will sometimes win at showdown and our value hands will sometimes lose? All we can do is make assumptions and calculate from there right?

Let’s say I am playing in a player pool against three different types of opponents that probably reasonably exist. Opponent A constructs his range perfectly. Opponent B constructs his range with too many bluffs. And Opponent C constructs his range with no bluffs.

Opponent A makes a pot size bet with perfectly balanced range. My EV on this could be shown as 0=(0.666*($200*0.333-$100*0.666))-(0.333($0)).

Opponent B: He constructs his range with 1:1 ratio of bluffs to value. That means When I call with 66% of my range I will win 50% of the time and will lose 50% of the time and when I fold the other 33% of my range I lose nothing. My EV when opponent is bluffing too much is $50=(0.666*($200*0.50-$100*0.50))-(0.333($0)).

Opponent C: He constructs his range with all value and no bluffs. That means when I call with 66% of my range I will lose 100% of the time and when I fold I lose nothing. My EV against this opponent is -$100=(0.666*($200*0.00-$100*1.00))-(0.333($0)).

I have no way of knowing who I am playing; however, against these three opponents I lose more to opponent C. The more one opponent moves closer to optimal either way, the more he gains or loses depending on the direction he goes.

What am I missing here?

No where in my response do I remember saying that I play this way, that I never bluff, or that I do anything one way or the other. I said Bovada gives you the opportunity to play against an opponent with him having no clue how you are playing. I have read players responses on different forums who claim high winrates by playing super nitty and those that play extremely aggressive due to players not knowing what they are doing. I think it is an interesting dynamic that you don't find anywhere else and is worth discussing.

You should always take the highest EV line. Always. The only time we see an equilibrium is when multiple strategic options are exactly the same EV, which means the opponent is playing in a way that makes you indifferent between your options. In most spots, real players aren't doing this, so just take the line that is more EV.

Thanks everyone. I think this thread helped me clear up a misunderstanding I had about short and long term EV. Correct me if there is a mistake in my updated understanding:

The balanced/GTO line is unexploitable, and is also the highest possible EV line when playing against a balanced/GTO opponent. Against non-GTO opponents who have leaks, there exists higher EV lines that exploit the Villain's deviations. This exploitation, however, is also a deviation from balance and opens one up to reverse-exploitation if Villain catches on and adjusts. In an anonymous zoom pool, you never have to worry about Villain playing back at you. However, because it is anonymous zoom, you never have specific reads on a player to allow exploitation in the first place besides general population tendencies. Therefore, one should still strive to play a balanced strategy in anonymous fast-fold games.

I think playing balanced is definitely not a a bad way to go; however you can most likely uncover population tendencies that are so far from correct that you can deviate and show a profit long term.

I have a database with 326k hands that I analyze pretty often looking for different population tendencies that deviate pretty far from optimal. For instance do the cbet way too much but fold to bets vs their missed cbets either by check folding flops or checking back flop and folding to turn probes. Are they not X/R flops enough or 3betting in the blinds enough? Does the population only 4bet a certain range. These are just a few tendencies that could cause you to deviate from optimal.

What the absolute **** is he talking about.
Well ok, read the whole thing, it must be a level.

Old style play.

This is actually a very accurate and concise summary.

If the pool bluffs too little, you lose a stack after a stack by trying to catch virtually non-existent bluffs; GTO is for idiots. If they like never bluff-catch and you don't balance your bets with bluffs, you don't get enough value. So, no, you can't ignore balance. One needs to learn the pool before one can turn a profit. Some think GTO is winning play; I happily leave them with their opinion.

One adjusts to the pool and many others also do; that's the only GTO there is when you look deeper into it, and the thing is that all better players in the above game will be bluffing too much and calling too little, according to GTO. They know you will be mucking too much and bluffing too much but won't know who you are (w/o looking deeper into it) and can't adjust; nor can you, so that makes is GO.