I know you have been talking about opening from the button but did want to ask another question.

Is it true if UTG opens at a 6 max table then each player should be defending 6.5% to make it so that his bluffs are 0ev?

Basically we take the 33% and divide by the number of players left to act.

I don't think it's that simple. First, there is play after the flop, and sometimes his "bluffs" hit the flop. But let's neglect this. Second it depends on the raise size. Assume that he raises to 3x then in order for his bluffs to be profitable they have to work 2/3 of the time. So the 5 players left should defend 1/3 of the time. However, if everyone defends 1/15 of his bluffs are still profitable since - assuming independent ranges - they are challenged only 1- (14/15)^5 =29% of the time. The reason is that sometimes two players have a defending hand at the same time.

So if everyone defends with the same range then they should defend with 1-(2/3)^(1/5)=7.8%. But of course usually that range will vary with position.

on average, yes, but you don't split the responsibility evenly. The button should theoretically be defending the most and the SB the least.

I agree that the Button should be defending more than the CO because he has positional advantage (although I'm not sure what this equates to in terms of EV), but the SB has already put money into the pot, so he will be getting better odds on a call and there will only be one player left to act. So my guess is that the SB will have quite a bit more responsibility than UTG+1 and even possibly more than Bu.

Theoretically, each player should defend enough so that UTG+1 could not open any wider than he should theoretically be able. But the EV of all hands for every player vs UTGs opening range will be different, so each player will need to vary they play slightly.

Another Question about Exploitative strategie.

Going back to the button example.

Lets say a balanced range for opening on the BTN is 40%

If the small blind and big blind are folding more then 33% of the time then we should use an Exploitative strategie and raise more.

But what should we do if they defend more than 33% of the time. Should we use a Exploitative strategie and raise less/more or should we just use our balanced 40% range.

If it is true that we should be using our balanced range then is it also true that tightness should be exploited and looseness should be balanced.

This is correct, but I want to clarify that we should be raising 100% of our hands even hands like 72o.


The blinds should be defending enough, so we are indifferent between raising or folding a hand which be 0 EV to open raise, and let's assume that the blinds need to defend 33% a piece for this. And we're going to continue with your assumption that against this range, that we should open 40% of hands and the worse hand will therefore be 0 EV to open raise.... let's say this is hand 32s. Also let's say that the Buttons EV is 1 bb for his entire opening range.

So what happens when the BBs defend wider, it's easier to think through this type of stuff if you use extremes. So let's say that they never fold, they're defending 100% of the time. If we don't change our GTO opening range, then hands like 32s will likely become -EV to open, since a lot of their EV came from it's preflop fold equity. However, just because it's -EV now to open 32s does NOT mean that we're being exploited by the blinds because the EV of our good hands like AA is going to go up MORE than the EV of 32s is going to go down. So our total EV for opening 40% of hands will go up from 1 bb to 1.5 bb, or something like that.

However, just because the blinds cannot exploit us does not mean that we should not MAXIMIZE our EV by exploiting them (which is the whole point of the article!). So the correct way to exploit them defending 100% of the time is to use the same criteria that we used for maximizing our EV agains their game theory optimal defending strategy which is to only open hands which are +EV to play. So while it was correct for us to open 40% of hands and the worse one being 32s against the blinds original defensive range of 33%, the correct adjustment to them defending 100% of the time would be to FOLD 32s because it is now -EV to open this hand. And we should fold all hands which are now -EV to open against their 100% defending range.

I hope this makes sense. If theirs enough interest I can post a completely game theory optimized preflop range and show the specific mechanics.

And in case I wasn't clear. If opening up 40% of hands was optimal against a gto defending rage from the blinds, then if the blinds start defenind more than that, we should open tighter in order to exploit them. However, just because we're not opening as much, doesn't mean that the blinds have increased their EV. Contrarly, they're EV has lowered because the correct adjustment against a GTO opener it to play GTO yourself.

Great great thread and the ensuing discussion is as great!!

Thanks to OP and the contributors, specifically DDAWD, NJD77 and Cangurino.

P.S. I love Roshambo!

Thanks think I have got that but will read it a few more times.

Another question

Moving from Exploitative Strategy back to a balanced Strategy

I will try and use extremes as an example.

bb and sb are both nits so we decide to raise 100% on the btn.
When we get raised by the bb we cant balance our range at this point because our range would be too wide. But once we do our initial response then then for the rest of the hand we can play a balanced Strategy.

Another example.
bb and sb are both nits so we decide to raise 100% on the btn.
We get called by the BB. We see a flop and get checked to at this point we can balance our betting range but our checking range will still be unbalanced.

So when we are trying to use an exploitative strategy we have to think which part of our range is unbalanced.

Also when I try to balance my range on the flop with a bet we only bet our bluffs that are 0ev.

basically
Value range
Checking Range
Bluff Range
unbalanced range

Another Question.
Because using a balanced Strategy is a defensive Strategy we cant know if someone is balanced when they bet. Eg when someone c-bets we cant know if they are balanced. We can make a guess eg if they are betting 100% all the time but there is no way of knowing.

Can answer these questions but I think you can also. Take a stab. Then I'll weigh in.

I was a little drunk last night. I'll just answer these questions now.

So we get 3-bet by the BB, who's a nit, what should I best response be? Well we shouldn't try and play balanced, since the BB is a nit, I'm assuming that he's not 3-betting a balanced range, so our best response if probably too fold too much, since he's never bluffing. But if you want to assume that the nit has a balanced 3-betting range, then our best response is to just call or 4-bet with as many hands which would be +EV to do so. But there's nothing we could do to stop the BB from being able to 3-bet us to death, but he's a nit, so we don't need to worry about it.

And when you design your 4-bet range, you could easily make it balanced just like you would as if you were opening a normal % of hands.


I'm not exactly sure what you mean by "we can balance our betting range but our checking range is unbalanced". This would not be a balanced strategy. You need to balance all your ranges simultaneously. Your betting range needs to be balanced with your checking range... they're not independent of each other.

At each decision point, you need to think about how all your ranges will be tied together which also requires you to think about how all those ranges will play on all future cards on future streets.


I'm not sure what you mean when you say since a balanced strategy is a defensive strategy we can't know if someone is balanced when they bet. I don't think we could know even if we used an exploitative strategy. None-the-less, I don't think it matters either way.

A balanced strategy does NOT care if your opponent is balanced or not because your opponent cannot exploit you. So as long as you have a balanced calling range, then your opponent could c-bet 100% or 0% and it wouldn't change what we do, since our balanced strategy does NOT ADJUST to how our opponent plays.

Maybe he meant that hero couldn't be sure if villain was using a balanced strategy or not and therefore couldn't know how/if he could exploit him.

There are definite ways of telling. If the Villain is c-betting 100% of his range, then it's almost certain that he's unbalanced. If the villain is betting at a high frequency but not value betting thin enough means that he's bluffing too much. If he showsdown a hand which he bet on the flop which is too thin means his non-betting range is unbalanced. etc.

Agree. Was just stating what MARK R could have been thinking.

Still working through a lot of this thread. Fantastic stuff!

Coincidentally, I've been working on this problem, via a slightly unorthodox route. I built my role playing STTs and once I got to the $55s there were so few fish to go around I started focusing more on how to stack them before anyone else did. I'm now trying it out at NL25 - basically trying to do what you are suggesting here: play a balanced strategy against multiple opponents whilst exploiting their leaks.

My approach is to have a bunch of villain-dependent balanced lines, with different ratios of nuts or air depending on how they play and how they're adjusting. I don't do formal maths on these situations for frequencies, I spot the situation and consider what villain has seen me do with this line recently, what the FE/value potential is, etc. I guess I'm dynamically altering the ratios, but that would be to dress it up in fancy language. I single table, so I rely on the table dynamic a lot.

This way, you are effectively playing a HU balanced strategy in HU pots, and villains will find it tough to work out what your ratios are because they'd need hundreds of thousands of hands and my reads to work out what I was doing. By which time, it's changed, because they're countering.

It's obviously still not amenable to a simple mathematical analysis when broken down like this, but I think it partially solves the problem of exploiting villain's leaks whilst remaining balanced against all villains. You design some balanced strategies which exploit their leaks, and use them selectively. You make sure a lot of your lines look similar despite having radically different purposes and weightings (nuts/air/showdown value) when used against different villains. The line that makes a rock fold might get a LAG to rebluff which allows a re-rebluff and gets that LAG dying to engage you again if he has to fold, setting up a profitable situation for later, ideally when he is deep. You can even pound on the rocks with an aggro line in order to set up the LAG to rebluff you. That kinda stuff.

Exploiting somebody means taking advantage of leaks they have. This usually implies a loss of balance. I don't know if your posts makes sense to anybody else; to me it doesn't.

You have a different balanced strategy for each villain. They see the same lines, but they don't know what parts of your range you're doing it with, and with what frequency, against different types because they only see what you're doing it with overall.

Dance with a LAG a few orbits to create a bluffy image, then stack a rock with your nut hand. The rock will take a while to call enough times to work out that you have the nuts a lot more against him. The stations who see your bluffs will get more call happy.

Just that. Not rocket science.

Following you from another thread, ymu.

Balanced strategy isn't villain dependent. I don't know how many times you need to be told this.

So can somebody please define "balanced" to end this confusion?

Try reading the OP?

Try reading the whole thread?

Great read

Thanks for this man!

What happened to Lunatic Fringe? Is he Empty Promises now? I can never keep up.

Pretty sure he is.