Let's say that we are playing 6-max or 9-max and stealing from the BTN and we notice that a player in the blinds is likely to 3bet us a lot from our HUD data, perhaps as crazily high as 25% of the time over a medium sample size so far.

Now according to exploitative theory, part of our adjustment will be for us to tighten up our stealing range and perhaps fold Q9o, 96s etc. from the BTN for example, and also at the same time we hope that he doesn't notice this so that he still proceeds to resteal with a 25% range.

Now we can essentially call his 3bet and 4bet him at a much higher frequency as we are only stealing with say a 30% range and not a 45% range to start with.

So I can see how once we steal with a 30% range, we can gain EV against his unchanged 25% 3betting range, however, doesn't our opponent also gain EV from us because he have now folded a large chunk of slightly +EV steals so his blinds get stolen less often than they theoretically should?

How do we know that the EV our opponent gains from our 'incorrect' folds, is less than the EV we gain later on? Maybe it all just kind of evens out and it doesn't matter what we do?

This principle also applies to all manner of other spots too, where our adjustment doesn't come for 'free' so to speak, as we can be losing EV down other branches of the game tree in order to manufacture what we think is an EV exploit down a different branch of the game tree.

What gives?

Everytime a player deviates, they're making someone else who correctly exploits them win money. But that doesn't mean they get to win money with every single hand. Sometimes, the leaky player will make more money with some hands.
For example, if someone only bluffs the river 5% of the time, the exploit player will fold every single hand to a bet. And that will make the leaky player make BUTTLOADS of money with those 5% bluffs.

You could easily grab pen and paper and calculate that this extra money he makes with those 5% bluffs doesn't make up for all the EV he is losing from never getting called when he has value.

Basically, you can calculate this by hand, but you don't need to. It's intuitively a foundamental truth of poker that whenever someone deviates from GTO and another player correctly adjusts, the former will be losing money.

In your example, you make all of the exploitative money with the top of your range, your premiums and very strong hands that end up on a bigger pot more often, while you are "losing" EV from your bottom of range hands, the ones that used to be profitable opens but now are 0 EV folds. If you didn't adjust, you would lose all of the exploitative money you win with premiums whenever you open your weaker parts of the range. By exploiting, you are removing your downside and taking on all of the upside.

I’ve been thinking about the basic concepts of adjusting as a beginner myself and although there are probably correct answers that pros would agree on (roughly) I doubt it’s computable in any sort of reasonable sense.

I thought about trying to write a computer simulation for, say, having a super drunk loose player on your right and a super tight one on your left.

But even if I spent the hundreds or thousands of hours programming this, it’s still almost certain it wouldn’t help my game that much because who knows how the tight player will change their strategy to the drunk one?

Multi-way dynamics can be very complicated.

I don't think our opponent would gain any EV in this situation.

Let's take Q9o and let's say our EV of opening this on the BTN is 0.05 on average over a large sample.
But that's against blinds with an average 3bet of let's say 7%

If we put someone in the blinds who 3bets 25%, the EV of Q9o goes down, since we cannot call the 3 bet.
So by folding 15% extra of our range, we don't "gain" any EV, we just stop opening hands that have now become negative EV instead of slightly positive EV.
We gain EV by dropping negative EV hands in this situation, not by increasing the EV of our other hands.

I'm actually not sure if the EV of the top of our range goes up?

The only way our opponent could gain EV from this is by counter-exploiting us, I think this would mean significantly tightening up against our tighter range?

The EV of some part of your range has to go up if part of it went down. You lost .05 EV from folding Q9o compared to equilibrium, some part of your range needs to get that back.

Yep, exactly this.

Now hopefully, the rest of our range more than makes this back so that we are actually making more EV from this spot than we 'should', and our opponent is losing more EV from this spot than he 'should'.

However, how can we be sure that this is happening? I mean we are probably having to fold 15% of combos that could have been earning us anywhere from 0.01bb/hand to 0.2bb/hand say, so we are down a lot of big blinds to start with from our over-folding of the weak combos.

you are never making -EV plays (you're folding what would be -EV) whereas your opponent is (he is bluffing into a strong range), that's the only proof you need.
You don't need to know or care about what your opponents EV is with different holdings, as long as you never make a -EV play you are correctly exploiting your opponent and making money by definition.

What is your alternative, to not exploit him? To keep opening the threshold hands? You're just losing money with those, how is that better than exploiting?

It's not irrefutable proof, as we are stealing with a 30% range instead of a 45% range for example, so we aren't just stealing with strong hands, there is still an awful lot of 'air' in it. Essentially we still have 2bet/folds even in our new tighter range, and these combos still cost us EV against someone who 3bets a lot too.

Don't get me wrong, I do think that we very likely gain from our opponent 3betting too much, but I am only 95% sure that we win lots of EV back, not 100% sure.

What can be better than taking the highest EV line with each hand individually? Are you not 100% sure that this is the most money you can make?

You think there's a 5% chance that making -EV or suboptimal plays is equal or better than not making them?

True, but isn't our opponent not happy with us 'over stealing' from his point of view in the first place, (hence his aggressive 3betting), so we could be playing into his hands by not stealing as much now. Maybe he is exploiting us because we are just giving up and auto-folding Q9o on the button for instance, which is exactly what he wants so that he gets more walks in the blinds and more SB stealing opportunities for himself as we over fold the button.

What makes your opponent happy or what he thinks is irrelevant if he doesn't understand the spot. He is over 3betting because he thinks we are stealing too often, he is wrong, he loses money.

That 5% of doubt comes from I guess the idea that we can't be fully sure that we make the EV back, as for example we could end up spewing in 3bet pots vs him and it is complicated to know that we are up overall, but that is the beautiful enigma of poker.

Sure, you could be leaking that EV in a different node of the tree, but that would be because you play bad or make mistakes, not because of your exploit

Yes, I think we are in agreement on this.

We still have to play well down the other nodes of the tree to lock in the solid EV gain overall, and that is where that 5% of doubt comes from, as our opponent could be a beast in 3bet pots and outplay us and earn EV back that he shouldn't if we were a better player.

Why?
He's already 3betting too much, so the EV of our strongest hands will already be higher, regardless of whether or not we open or fold Q9o, as long as villain doesn't adjust.

The EV of some other hands in our range doesn't go up because we choose to fold Q9o.
The total EV of the range we do play does go up, since we're now folding the -EV Q9o.

Why would the EV of say AA suddenly go up when we start folding Q9o?
It goes up when villain starts 3betting more, but he does that regardless of us folding Q9o or not, as long a he doesn't adjust to our new strategy.

I guess the easy thing to do would be to declare Q9o as -EV in this scenario. But if you’re going to make the effort to make such an adjustment, why not put a little more effort into it? You may find that you shouldn’t tighten up at all and instead open even more, and not fold a hand like Q9o in this spot.

It's an interesting question. How does our EV shift when the BB deviates and we exploit that behaviour? I might be able to offer some insight.

Humans have this internal unconscious bias that getting to play more hands or open wider is somehow better. But that's not how you maximize value.


So I solved two BTN vs BB preflop situations. On the left side we have the GTO-ish situation, on the right side we have a super aggro BB and BTN tightening up to exploit that. The expected value of the BTN open is shown for both cases. (Hands with a border are opens.) This sim was solved with 5% rake with a 2bb cap.





So obviously BB's 3bet strategy is horrendous. We can see that hands like Q9o which fold to a raise lose 6bb/100, so they become pure folds. On the other hand, AKs gains 90 bb/100. K9s gains 15 bb/100. Etc.


What ends up happening is that you fold many ~0EV hands, and gain a ton with the top of your range.

It's also worth noting that a good portion of BB's extra losses will go to rake and SB. SB gains because BTN folds more often. The house gains because BB inflates the pot a lot. So BB's loss isn't completely your gain - you pay a lot of tax on their mistakes.

Tombos21 - I’m not certain whether the above post is in reference to my post or not, but if so, this is exactly the type of analysis I’m questioning. I realize that this can be difficult when using a preflop solver (since post flop mistakes can’t really be accounted for), but why not also input some assumptions for the BB’s response to a 4b too? I just don’t understand the reasoning to investigate this situation only to stop so short.

Regarding the Maniac BB defense range - why did you use such a small flatting frequency for this player? When I think of a maniac, I don’t picture them folding A8o, Q7s, 95s, etc BB vs a BTN open.

The example in this thread is referring to a villain from whom our only read is he has too high of a 3bet.
Everyone here is aware that if that villain had other leaks, our strategy would be different than if his only leak is 3betting too much, but that's besides the point.

Great question bigburge. The primary answer to your question is because I'm lazy. The BB maniac range was just some BS I came up with in 5 seconds. The main takeaway is that you shouldn't open many hands that fold to a raise, if your opponent is raising way too often.

The other reason is that it's very difficult to isolate underlying mechanics when you change multiple variables. I've tried that before many times. You can end up with misconceptions about the underlying correlations. So now I prefer to change one variable at a time. Step 1 would be this, step 2 would be plug in the 4bet and so on.

If you wanted to go all out with this kind of analysis it doesn't make sense to guess at the ranges. Why not just use hand-history generated data from actual maniacs and really try to zone in on the exploits? Why stop at 4bets when you can include 5bets and squeezes? Hell, you could even apply a "postflop edge" by adding a flat value to every hand to represent your implied odds. Maybe weight those values by the EQR. But all of this is way too much effort for a simple 2+2 post.

I tell you what. If you describe BB's strategy, I'll nodelock and solve it.

Fair enough Anero.

I realize that if you don’t have a read on future actions, perhaps it’s the safest to not make any further assumptions. However, maniacs are going to maniac. I would feel more comfortable assuming they will continue to be overly aggressive given their range (ie they may 5b/call at a proper frequency, but their initial range is too big) rather than falling back into line. I realize others may have a different opinion.

Up to some amount of postflop over-aggression, we would want to be even tighter preflop, since even versus an over bluffing opponent, our medium strength hands tend to not make enough money on a river call to win back our investment (half of the pot or >50% equity versus his river betting range). We would only want to play hands that flop strong hands since anything else won't quite cut it.
Past a certain amount of over-aggression, our bluff catchers would start having a lot of equity on river, enough to win back our investment, and at that point we would be happy flopping a pair and therefor we wouldn't necessarily tighten up preflop, but of course it would depend on the degree of the leaks.

There could also be competing leaks like villain being a station, or having very face up lines... Anything you can imagine, and it's your job to udnerstand how each variable individually affects your decision to then put everything together into one strategy.