• Bronze
Joined: 01.03.2008
Hello all.

After reading some range-construction GTO approximation stuff around the place I thought I would have a go. I made up the action in this hand and used a board run-out from a randomly selected other hand.

So, from someone who actually knows what they are talking about, is this the sort of analysis you might think about using if you were playing some sort of GTO game to decide on your ranges? Apologies if this is difficult to read.

So am going to attempt a sort of GTO range analysis.

Note: I copied this out from a sheet of paper and have already corrected several mistakes. Sorry If there are too many more that I missed.

[SIZE=16]Preflop[/SIZE]

6max with 100bb stacks. Hero is on BU.

Dealt to Hero: [A range] (We open 60% range when its folded to us)

3 folds, Hero bets 2BB, SB 3bets to 7BB, 1 folds, Hero????

Analysis: We want to defend enough so that SB cannot 3bet ATC with a profit.
If we fold more than [6.5/(7+1+200]x100 % i.e 65% he would profit. So we defend a minimum of 35%.

4bet hands: If we are taking a somewhat old-school 4bet/Jam range of JJ+ AK we need to add some 4bet bluff hands. (I'm going to simplify here and just go for a 50/50 range assuming our villain is the type who just jams rather than 5betting small)

So JJ+AK is 40 combos and A6s-A9s, A9o-A8o is 40 combos of 4bet/folds.

Calling hands: Adding 5% to required calling range because villain realises some equity when we just call. We are looking for 210 combos to make 280 defence combos alltogether.

Sample defense: ATo-AQo, KQo, 33-TT, A5s-A2s, AQs-ATs, K8s+ QTs+ suited gappers 75s or better, SCs 54s or better.

Imagine We call.

Flop

K 9 5 [15BB]

SB Bets 8BB, Hero????

This dry flop is one where I believe raising as part of our defence will be exploitative and would make our continuation range by calling vulnerable so I choose to call or fold. We need to call [1- 8/(8+15)]*100 = 65.2% to stop him bluffing ATC profitably.

If we call any pair and gut-shot or better that is 113/177 hands or 63.84% So if we add a couple of Ahi hands we should make the 65.2%.

Turn

5 [31BB]

SB bets 18BB, Hero????

[1- 18/(18+31)] * 100 = 63.26% defence required.

According to Equilab we have now have 107 combos taking into account blocking by the board so need to defend about 68. We can now fold 33-44 and gut-shots to leave us with 71 combos so a couple more than needed.

On this street I tried to think about whether we should have a raising range or not but found things getting to complicated so am sticking with just calling.

River

6 [67BB]

SB goes ALL-IN 67BB, We continue 50% by calling.

This is where it gets tricky with Equilab not distinguishing various hands from each other, but I digress.

We have 62 combos so need to call 31. We have 15 trips+ 2 combos of K9, and get 15 combos of KQ, KJs (folding 1 KJs)

We fold K8 9x, 77, 88 and TT for our final solution. We call K9 KQ 3 KJs and trips or better.

Looking forwards to some feedback, not sure how many mistakes I made but sure it was a lot.
• 19 replies
• Black
Joined: 27.11.2008
1. PF defence should be way more than 35%, I think 45%-50% in this position should be good

2. You need to see who connects better with this flop. The person who has a significant equity edge should be able to play a wider range of hands.
• Bronze
Joined: 01.03.2008

Quick questions:

Originally posted by mbml
1. PF defence should be way more than 35%, I think 45%-50% in this position should be good
So am I to understand the calculation I used to see what % of folds villain can 3bet ATC with are somewhat irrelevant or is there something I am missing?

Wondering if your response is based on feel and experience or a calculation/tool/model or some such that could be applied to think about other situations.

2. You need to see who connects better with this flop. The person who has a significant equity edge should be able to play a wider range of hands.
This sounds quite complicated. I don't think I know what model/calculation/tool one might use if they were trying to approximate a GTO solution from this. Can you point me in the right direction?
• Bronze
Joined: 10.06.2012
If BTN opens 2bb and SB 3b's to 7bb, SB is risking 6.5bb to win 3.5 bb.

So, % needed to defend to deny autoprofit =

6.5/(6.5+3.5) = 65%

So, you need to defend 35%. But thats if you only defend by 4 betting. If you defend by calling, you need to consider the ev of BB's bluff 3bets when they see a flop. It gets a little complicated here and if you are interested, grab Jand's book and he walks through it.

It works out to be about another 10% if one is calling with 2/3 of their defending range.
• Bronze
Joined: 08.08.2010
You are all missing an important point!

The sb does not need to defend 35% to deny autoprofit. The SB and BB as a combination need to defend 35% to deny autoprofit.
• Bronze
Joined: 10.06.2012
OP is talking about BTN defending the SB 3bet, not the others defending the BTN's open.
• Bronze
Joined: 13.05.2009
Isnt the bluff-value ratio of a 4b 2.5:1?
• Coach
Coach
Joined: 21.07.2011
[quote]Originally posted by mbml
1. PF defence should be way more than 35%, I think 45%-50% in this position should be good

That depends on the sb 's 3bet tendencies and how wide we open.. isn't it?

For example vs 99+,AJs+,KQs,98s,87s,AJo+,KQo 3bet range if we open around 40% from button we should defend sth like 20% (according to 45-50% rule) which has 40% equity vs that 3bet range.

The problem is that if we then 4bet the best part of that 20%, i.e JJ+,AK (+some 4bet bluffs) and call the rest then the calling range has equity sth like 35-37%. So I can't see how this is profitable in vacuum.

According to GTO 35% is what you should defend
• Bronze
Joined: 08.08.2010
2. You need to see who connects better with this flop. The person who has a significant equity edge should be able to play a wider range of hands.

@ mblm: I wish you would expand on that? Do you mean there will be some flops where the BTN will fold such that BB can bet ATC profitably. 222 for example, because its essentially a blank flop and BB's preflop range was stronger.

@DaPhunk: Why do you start with 60% range. Janda says 45% BTN range is optimal, and it does kinda make sense. I think 60% might be too hard to defend...

The SB and BB as a combination need to defend 35% to deny autoprofit. tongue out

I hope some good comes on this thread and tells me i'm right... because I am

That depends on the sb 's 3bet tendencies and how wide we open.. isn't it?

@asimos: GTO does not depend on tendencies imo.
• Coach
Coach
Joined: 21.07.2011
That depends on the sb 's 3bet tendencies and how wide we open.. isn't it?

@asimos: GTO does not depend on tendencies imo.[/quote]Yeah.. I know.. That was going to 50% btn defense.

According to GTO you should defend 35% of your opening range vs both big blind and small blind as combination.
• Bronze
Joined: 08.08.2010
hmmm it appears that there is a paradox...

Lets take an extreme example. We are UTG in 6-max and get 3bet to 9bbs after opening to 3bbs . Lets say we are 3bet from the BTN and have to defend x% range to stay unexploitative.

Now lets say we are 3bet from MP instead. I don't think it makes sense to defend with the same range! MP's 3betting range is much much stronger since there are 4 players behind! Also his bluffs are much stronger - he might be bluffing with AJs,KJs,KQo,AQo etc... So we have to defend x-y% vs MP.

However if we fold x-y% vs MP, then aren't we folding too much? Lets say the whole table is colluding against us...

So my question is do we defend x or x-y% when facing a 3bet from MP.

I am not going of topic, OP. This is basically the same as asking - do we defend the same range vs a SB 3bet and a BB 3bet.
• Bronze
Joined: 08.08.2010
According to GTO you should defend 35% of your opening range vs both big blind and small blind as combination.

hmmm it appears that there is a paradox...

Lets take an extreme example. We are UTG in 6-max and get 3bet to 9bbs after opening to 3bbs . Lets say we are 3bet from the BTN and have to defend x% range to stay unexploitative.

Now lets say we are 3bet from MP instead. I don't think it makes sense to defend with the same range! MP's 3betting range is much much stronger since there are 4 players behind! Also his bluffs are much stronger - he might be bluffing with AJs,KJs,KQo,AQo etc... So we have to defend x-y% vs MP.

However if we fold x-y% vs MP, then aren't we folding too much? Lets say the whole table is colluding against us...

So my question is do we defend x or x-y% when facing a 3bet from MP.

I am not going of topic, OP. This is basically the same as asking - do we defend the same range vs a SB 3bet and a BB 3bet.
• Coach
Coach
Joined: 21.07.2011
Originally posted by Itsnevereasy
According to GTO you should defend 35% of your opening range vs both big blind and small blind as combination.

hmmm it appears that there is a paradox...

Lets take an extreme example. We are UTG in 6-max and get 3bet to 9bbs after opening to 3bbs . Lets say we are 3bet from the BTN and have to defend x% range to stay unexploitative.

Now lets say we are 3bet from MP instead. I don't think it makes sense to defend with the same range! MP's 3betting range is much much stronger since there are 4 players behind! Also his bluffs are much stronger - he might be bluffing with AJs,KJs,KQo,AQo etc... So we have to defend x-y% vs MP.

However if we fold x-y% vs MP, then aren't we folding too much? Lets say the whole table is colluding against us...

So my question is do we defend x or x-y% when facing a 3bet from MP.

I am not going of topic, OP. This is basically the same as asking - do we defend the same range vs a SB 3bet and a BB 3bet.

1) From early position we open a tighter range first place, so our 35% is a very strong range, i.e. in comparison to that 35% of button.

2) If both sb and bb would 3bet the same frequency we should defend the same range. Obviously if sb 3bets tighter = we defend less.

But all these have nothing to do with GTO. According to GTO we should defend 35% no matter how our opponents play.
• Basic
Joined: 05.08.2013
@ Itsnevereasy

I think I can explain what you are asking...

When we open UTG there is a GT justification for defending a lower percentage of our range vs a MP 3bet and a higher percentage vs a BTN 3bet. When MP 3bets the 'responsibility' for defending is shared between us and the CO, BTN, SB and BB. When the BTN 3bets we only have the SB and BB to help us defend. Thus we have to defend a slightly higher % of our range vs a BTN 3bet compared with vs a MP 3bet.
• Bronze
Joined: 01.03.2008
Originally posted by Itsnevereasy
@DaPhunk: Why do you start with 60% range. Janda says 45% BTN range is optimal, and it does kinda make sense. I think 60% might be too hard to defend...
I was definitely unaware of this statement. I shall try to sum up what my understanding of opening ranges from a GTO standpoint was:

"Estimating an optimal opening range with anything resembling decent accuracy is not going to be possible with the vast number of potential decision trees that can be possible for each and every hand"

That said I am able imagine how one might be able to work backwards using a model where calling is not possible, like an open/3bet/4bet/5bet game. You could start with the ORs calling range for an all-in and work backwards calculating the strategy pair. Is this similar to what Matt Janda used or was his reasoning different?

To try and answer your Question: I may be blindly copying fashion or have somehow misused recent knowledge but I thought 45% was kind of tight nowadays especially for a min-open size which I don't believe Janda uses. We want to maximise our positional advantage by opening as many hands as possible whilst not opening so many that we cannot defend. 60% seemed an appropriate number given my recent impression of the game and it didn't even seem that loose to me. (maybe I played too much HU recently)

Originally posted by Itsnevereasy
I am not going of topic, OP. This is basically the same as asking - do we defend the same range vs a SB 3bet and a BB 3bet.
I'd just like to highlight some differences between these two examples:
A) Comparing an MP vs EP 3bet and a BU vs EP 3bet
B) Comparing an SB vs BU 3bet and a BB vs BU 3bet.

1) Both of the ranges in A are going to be a lot narrower than in B
2) Our defence option OOP might well be different to IP
3) SB will make much of his defence in the form of 3bets so % could be more similar to BBs even if hand-ranges are completely different.
4) The BB gets a better price to 3bet than the SB so we should defend more against him for that reason alone.
5) Cold 4-betting in Example B is going to be much more likely.

I can't say how important these things are going to be from a GTO point of view, but just being aware that there are several differences makes me think the two situations separately despite the obvious similarities.

As far as answering your question from a GTO standpoint goes, the only answer I can think of is that BB pays a different price to 3bet bluff than the SB so it won't be exactly the same defending range

• Bronze
Joined: 16.09.2009
Originally posted by StuHunger
@ Itsnevereasy

I think I can explain what you are asking...

When we open UTG there is a GT justification for defending a lower percentage of our range vs a MP 3bet and a higher percentage vs a BTN 3bet. When MP 3bets the 'responsibility' for defending is shared between us and the CO, BTN, SB and BB. When the BTN 3bets we only have the SB and BB to help us defend. Thus we have to defend a slightly higher % of our range vs a BTN 3bet compared with vs a MP 3bet.
This correctly explains some of the main misconceptions about optimal defending ranges. It doesn't make theoretical sense to defend the exact same range against different positions, so our intutition to defend less often isn't just a feeling, it is mathematically correct.
If our RFI/f frequency is still too high, or if our bottom RFI range doesn't show a higher EV in SR pots than openfolding, then our adaptation will be to use a tighter RFI range. From then on we can defend with the optimal frequency against 3-bets and we can play profitably in SR pots.

Another point is that the current understanding of GTO does not always suffice when we try to estimate the EV of one play over another. The reason is that our goal is to play the line with the highest EV, or in other words the most optimal line.
First and foremost GTO shows the least exploitable lines. It doesn't always tell us whether there's more EV in a different line. This means that GTO can help us seperate all lines containing negative EV from all lines containing positive EV. After that we still have to find out which line contains the highest EV.
At this point GTO becomes less useful because there are many unknown factors to consider. Poker is a game of incomplete information and GTO can't work with the unknown. We can only take sensible guesses, put the values in and slowly improve our evaluations over time.
• Bronze
Joined: 23.09.2013
1.) All assumptions about SB 3-Bet Range automatically fall under the category exploitive play. If we want to play GTO style, we only have to focus on our range and not about Villains Range. We assume that Villain is playing GTO( how ever GTO looks like) and just focussing on denying profitable play by Villain.

2.) In this spot i would assume that BB is never cold-4-betting to simplify things

3.) To the concret example: I defenitely would consider reconstructing your preflop ranges:

If you assume that villain never call your 3-bet why 4-betting with hands like A9s which has defenitly +EV calling.

So put your Axs and A9o in your flatting Range and 4-Bet/fold with garbage hands like A6o or K8o. The blocker effects are the same and you have way better hands in your calling range.

Than you can exclude hands like 66-33 because they have a poor postflop playability. You don't hit often enough your set against a wide SB 3-Betting Range to justify the call.

Also i would flat some AA combos, some KK combos and AK combos. If the board is dry like K52r or A22r etc. your Range never has nut hands in it and it is hard defendable.
If you don't do that you have to give up more hands on dry boards and probably have to give villain autoprofit on those boards because Villain and your Range are asymmetric (Lnternet has made a nice video about this).
That's the problem on this hand in particular.

4.) On the flop i would fold pocket pairs 88 or lower because of the poor playability on turn and river and add some backdoor FD and Straightdraw hand which can turn 2nd or TP. Axs beats 2 barrel bluffs as good as 88 when villain barrels very polarized which he probably should and Axs can make nutdraws on the turn and it is easy to play on the river and blocks AK and AA combos in villains range,

5.) On the river i would consider to Bluffcatch with blocker hands instead of hand strength. So Kx8s is a way better Bluffcatcher than KhJh. Kx8s blocks 87 and Xs8s.

Overall my ranges would be:
4-Bet call (32 combos): 3 combos AA, 5 combos KK, 6 combos QQ, 6 Kombos JJ, 12 combos AKo
4-Bet Bluff (32 combos): 4 combos K7s, 12 combos A8o, 12 combos A7o, 4 combos K6s,

3-Bet Call (286 combos): AA (3 combos), KK (5 combos), 77-TT, 76s+, 86s+, K8s+, A2s-A5s, A8s+ A9o+, Alle Broadways, J9s+, Q9s+

So it's a total defend Range of ~43% and we have roughly the 10% more call hands jules97 mentioned and with position we should have a good defense here.

Flop call-range: 176/255 combos ~ 69%
5x,9x,Kx,AQ,TT, all Gutshots, Axs + Backdoor FD down to A8s and T8s + Backdoor straight and FD

Turn call-range: 113/176 combos ~ 64,6%
Any Pair+, AQ and all FD

River call-cange: 55/113 combos ~ 47%

AA,KK,99,AK,KQ,K9,A5s, All Flushs, KxTs(3 combos) ,KxJs (3 combos),A9, AQ with Qs or As (4 combos)

We need 50% and as i said i would call hands which block nut hands.

My range suffers a lot that i cut my range at 76s and 86s instead of 75s and 65s, so i have to give autoprofit on these spots. But you always have to cut the range anywehre.

Hope my analysis makes any sense to someone.
• Black
Joined: 05.08.2007
Hi, nice topic.

Regarding defending less than 35% when MP 3bets vs
ep:

If we assume that players behind will defend QQ+, AK 2,5% range then the probability that
CO, BU, SB, BB all fold is:
P = 0.975 * 0.975* 0.975 * 0.975 = 0.9. (90% all fold)

How much hero needs to defend so that MP has total FE of 65%

hero_fold * P = 0.65
hero_fold = 0.65/0.9 = 0.72

So we can fold 72% instead of default 65%
• Bronze
Joined: 01.03.2008
Originally posted by Free89
Hope my analysis makes any sense to someone.
It seems like it makes a lot of sense and it was pretty awesome to read too

You did make a typo in your final preflop ranges though. You had 5 combos KK in both 4bet/call and in call vs 3bet ranges and you didn't have AKs in either range but I can guess what you really meant there so its not much of a problem.

Originally posted by GingerKid
If we assume that players behind will defend QQ+, AK 2,5% range then the probability that
CO, BU, SB, BB all fold is:
P = 0.975 * 0.975* 0.975 * 0.975 = 0.9. (90% all fold)
Nice of you to do the sums for us!

Thanks for contributions to the thread everyone! Perhaps someday I should make a new one
• Post removed