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6-Max Concepts (Part 1: BTN Stealing)

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6-Max Concepts (Part 1: BTN Stealing)

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Sean Lefort

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6-Max Concepts (Part 1: BTN Stealing)

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Sean Lefort

POSTED Feb 08, 2013

Sean begins a 7-part series involving some mathematical theory tools and their application to generic 6-max pre-flop scenarios.  The goal of the series is to help provide some strong mathematical justification for pre-flop frequencies and minimize qualitative speculation when deciding opening and defending ranges.  This first video focuses on playing the BTN and helps provide a template for deciphering just how wide one should be looking to steal from this position.

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tehduper 12 years, 1 month ago
Great video as always, Sean. It's nice to see some 6max. I was wondering if you could clarify some concepts for me since I haven't really studied GTO in depth ever and only recently started thinking about it more. A lot of the times in your vids you talk about minimum defense frequencies and the situations where you can auto profit with any 2 cards. Don't we also have to consider reciprocity? For example, in heads up, we minraise any 2 because we notice the opponent folding too much. But if we then fold too much to his minraise we haven't really autoprofitted. Now let's say we do defend against his minraise preflop enough, but our range is so wide that we can no longer prevent him from having even more profitable postflop spots, then even though we have "autoprofitted" preflop, we are giving up more EV in the reciprocal situation and therefore still -EV overall. So is it possible to have situations where it's actually GTO to be below the minimum defense frequency?
Sean Lefort 12 years, 1 month ago
Yes, when saying "auto-profit" I'm using it in the context of isolation for that specific junction of the hand. In your HU reciprocity example, we simply look at the two situations separately: Pre-flop we look to (1) immediately exploit from the BTN (if possible), and (2) look to not be immediately exploited from the BB (by folding too much).

When we're calculating MDFs, we're doing it with a focus on the worst part our our opponent's betting range. Ie. if he's opening 100%, 72o is his worst hand. So by defending greater than the MDF, we force 72o (the bottom of his range) to have to see some post-flop equity to be profitable as a pre-flop steal. If we're playing a villain who's only opening the top 6% of hands and thus his worst hand is AQo, it becomes obvious that we no longer care to defend MDF+ against his opening range as we are totally fine with AQo auto-profiting pre-flop. So of course, that leaves us with some sort of threshold steal% at which his worst hand is strong enough that we no longer care to defend enough to stop him from auto-profiting preflop with it. We could try to speculate what that might be, but in practice it's a pretty rare scenario to encounter. However, we certainly do appreciate the idea that our defense % should generally decrease as our opponent's steal % decreases.

mike 12 years, 1 month ago
it might just be semantics but when thinking about R - how can we every realize more than 100% equity? it seems like we are trying to estimate our fold equity when we say we are going to realize more than 100% EQ?

last year i was MRing very wide on the BUT but recently i did some analysis of my database and found i wasn't making money with the weakest parts of my range. i also think regs are better these days about not folding too much to MR. with this in mind i have switch back to 2.5bb on the BUT with 40-50% of hands. it seems like regs will fold too much seeing the bigger raise and noticing that i am am not opening the BUT super wide? itsn't there an argument to open 2.5bb in terms of getting to play bigger pots IP? so we win a little more when they fold to our CB and of course we get to make slightly bigger turn and river bets? what are you thoughts on these arguments?
Sean Lefort 12 years, 1 month ago
There's a lot of factors that go into R including both GTO as well as additional exploitative factors. GTO stuff is things like, there are certain boards where we're so dominant range vs. range that the defender's bluff-catchers become incredibly futile. Additionally, if we play perfectly and our opponent doesn't, our R% goes up. And furthermore, if we're aware of HOW our opponent isn't playing perfectly, and we adjust to exploit that, R% goes up again. So R really can fluctuate a ton.

If we both checked down, we'd both receive R = 100%. So remember that any decrease in R% for our opponent means an equal increase in R% for us, and vice versa.

As for your BTN questions regarding bet-size and such, it really just comes down to what you think your opponents will play worse against. I think in general, the better your opponents are, the better it is to try forcing them into making their mistakes pre-flop by MRing. It forces them to either let you profit too much immediately with steal from the BTN, or to adjust and defend wider with a weaker range that's difficult to defend appropriately OOP. If your opponents are weaker and more inclined to make large post-flop mistakes, it makes sense to grow the pot and care less about marginal pre-flop earnings and/or forcing them to defend wider. Essentially, I think opening to 2.5/3x against good players from the BTN simply makes it too easy on them.
tehduper 12 years, 1 month ago
Would you say that R is also affected by the actual hand itself? It seems to me that R for a hand like 23s is much higher than R for a hand like 72o even though they have similar equity.
Raphael Cerpedes 12 years, 1 month ago
I am not sure I agree with you here, I actually believe against good players opening 2x from the BTN makes it too easy for them, they just call a lot! 2x opens are a lot more effective against masstablers and weaker regs who will not call from the BB nearly enough.
The day when NLHE will be solved I will be very very surprised if 2x open from BTN 6-max is the GTO size, I think you allow way too many hands to profitably call from the BB getting 3.5 to 1.
Sean Lefort 12 years, 1 month ago
tehduper: I do think R is affected by the hand itself but I don't think it's all that drastic. As you pointed out, 32s is going to have slightly better playability than a hand like 72o and thus might find it a touch easier to find ways to get to showdown and such. I haven't put enough thought into questions like this yet as "R" is a fairly newly introduced concept and because its always an approximation, research into it's factors may not prove to be all that helpful anyways.
Sean Lefort 12 years, 1 month ago
Boa: You're right in that it's likely easier for them to play "well" pre-flop vs. a 2x because they just have to call a lot. But what you're neglecting is the fact that they now have to play all those additional hands in their range (which are all very weak and often with not great playability) well on later streets. In addition, their range as an entire whole has now become weaker. (Ie. If they want to CR% the same %, the complexion of their CR-range v. the 2x will likely have to be different/weaker in some respects than against the 3x.)

If 6m 100bb play were to ever be solved one day, I'd be very shocked if the BTN ever raised more than the minimum.
mike 12 years, 1 month ago
just watched the live play portion of video - i would like to hear a more detailed explanation about these spots as they are both not the standard advice

:43 calling 4B OOP with 65s ?

:47 so you are flatting 100% of your continuing range in SBvUTG? why? are you also taking this no 3B in BBvUTG? or other spots on the table vs UTG?

i was also wondering it you there is a reason you have no postflop stats on your HUD?


Sean Lefort 12 years, 1 month ago
It wasn't exactly a standard 4B, he pretty much clicked it back and I only needed to win 22%+ of the pot to call profitably. I think a hand like 65s flops well enough to get it in enough of the time to surpass that 22%. Against strictly {TT+/AQ+} we have 32%. So add some bluffs etc gets us over 35% and I think we should be able to achieve R = 63%+ (~22/35) in the scenario. ProPokerTools has a cool tool that lets you see what % of the time you will flop at least X% in the form of a graph. Would be fun to play with for this spot if I get some time.

And yeah I generally don't like to 3b OOP against ranges that are so tight such that I can't feel comfortable getting JJ (or even AK/QQ) all-in pre-flop. Our value range just becomes too thin/narrow/defined and so we can't add that large of a bluffing range and thus our range overall isn't great for playability nor for overall value extraction. I prefer to flat them my entire proceeding range in those spots unless I have good reason to 3bet (either for value or as a bluff).
thedoors 12 years, 1 month ago
dont want to troll but i work my game on this point, would be glad if you could have a look to this thread
http://www.runitonce.com/nlhe/math-for-stealing-compared-to-hm1-succee/
have a nice day
ps if that disturb remove my post
Sergey Nikiforov 12 years, 1 month ago
Hi Sean. Thx for the video.
When you were playing you said you'd 3bet less frequently vs BTN minraises than vs BTN 3x (the hand you 3bet/called 4bet w 65s). Can you explain this plz?
Sean Lefort 12 years, 1 month ago
Reason is that hands are much more attractive as flat calls when getting 3.5:1 (v MR) than when getting 2.25:1 (v 3x). There is a very large grouping of hands that feel very confident about profiting by calling pf getting 3.5:1 that start becoming unprofitable (or at the very least, speculative) calls at 2.25:1. So these hands start becoming candidates for 3betting. In addition, you're getting a better price in some respects on a 3bet against 3x as their is more money to be won when they fold, and they should likely fold slightly more often given the shallower SPR.
Sergey Nikiforov 12 years, 1 month ago
I'd guess that optimal frequency for opening the button with minraising strategy (S1) is higher than that of 2.5x/3x strategy (S2). So a player S1 should defend wider range vs 3bet than S2, which means BB/SB can 3bet 'wider for value'. (mb hands like AT/KJ which were flats vs S2 opponent are now 3bets vs S1). So the 'value' portion of our 3bet range has increased.

I totally agree some hands that were 3bets vs S2 can be more profitable flats vs S1, but doesnt it mean that we should add more weaker 3bets (like mb 73s) instead of 54s (that we were 3betting vs S2, but now flatting vs S1)? If we add those weaker 3bet bluffs along with 'wider for value' 3bets, wont our overall 3betting range vs S1 become wider than vs S2?

Am I missing something?

Looking forward to your response.
Sean Lefort 12 years, 1 month ago
" So a player S1 should defend wider range vs 3bet than S2, which means BB/SB can 3bet 'wider for value'."

Just because the *range* is wider doesn't mean that the *frequency* is higher. Yes, they call wider.. but because they opened wider, their fold-to-3bet% could still be higher OR lower depending on just how wide they're opening etc.. This isn't the crux of the problem, I just wanted to point it out.

@100bb, MR->3bet is far less favorable for the 3bettor because, (1) SPR is significantly deeper and (2) more "room" for MRer to have an effective 4betting range. (1) is particularly important because it means that (a) all of our value hands become less valuable and (b) all of his speculative weak hands become more valuable.

Same idea as if you're facing a 3x raise when 100bb deep vs. 200bb deep. In theory, you should be 3betting less when deeper for the reasons (a and b) listed above.

I'm not entirely certain about this topic but its the way I like to analyze it. The nice thing is that I can be very sure about my flatting range being profitable getting such great odds so I'm pretty happy about the situation in general.
mike 12 years, 1 month ago
i think this is what you were talking about

ProPokerTools Odds Oracle Results (2.22 Professional)

Holdem, Generic syntax


PLAYER_1 65s


PLAYER_2 AA-JJ,AxKx,AxQx,AxKy,AxQy



3221 trials (randomized)





PLAYER_1 HAND_VS_RANGE Next Street Equity













Sean Lefort 12 years, 1 month ago
Yep, good stuff. If we assume that villain is going to CB (obviously it won't be quite 100% but it's definitely going to be high on most board textures) and we estimate the size, we can see how often we're going to flop a hand with enough equity to proceed against the CB. It's a more useful tool with equities that run closer and shallower SPRs (ie. in PLO) but it still gives some interesting insight for NL situations like this.
dat_ass 12 years, 1 month ago
Also, the AJo I think some people cib because they think you'll flat all your Axs. Seems pretty dumb in these positions though because I don't even see why people would 3bet Axs from the bb there.
dat_ass 12 years, 1 month ago
When you flat with AK from the sb did you say you would never 3bet anything? I can understand your justification from doing this from the bb, but in the sb don't you risk giving the bb really good odds to overcall?
Sean Lefort 12 years, 1 month ago
Here's what I wrote regarding this topic from an earlier question:

"And yeah I generally don't like to 3b OOP against ranges that are so tight such that I can't feel comfortable getting JJ (or even AK/QQ) all-in pre-flop. Our value range just becomes too thin/narrow/defined and so we can't add that large of a bluffing range and thus our range overall isn't great for playability nor for overall value extraction. I prefer to flat them my entire proceeding range in those spots unless I have good reason to 3bet (either for value or as a bluff)."

You're point is valid in that it's a bit annoying that we give the BB such a nice price and we won't have great position, but I don't think that's a strong enough factor to make me want to split my ranges here. I don't think the BB has a very good squeezing opportunity at all (being up against two pretty strong ranges) so I'm not concerned about not seeing flops. The biggest concern is the terrible relative position, but I would definitely introduce a healthy donking range to try to neutralize that a bit and give us a little more control over flop pot-sizes.
mike 12 years, 1 month ago
thedoors i just DL free trial and started clicking buttons :)

@Sean how do you think GTO would split the responsibility for defending vs BUT in the SB and BB. ie if the BUT MR and the blinds have to defend ~50% combined how much should be from SB and how much from BB? thanks for your detailed replies:)
Ace 12 years, 1 month ago
Sean, I have a question about GTO and a situation that seems paradoxical to me.
GTO is defined as the optimal strategy, or an overall gameplan that cannot be exploited, and can at worst breakeven. I understand we are nowhere close to perfect GTO in NLHE at the moment, but imagine a situation in the future where we are.

We play perfect GTO, and face an opponent who plays completely GTO bar the fact that he never 3bet bluffs the CO.

Thus, everytime we 4bet bluff him with our GTO frequencies after he 3bets the CO, he wins money off us. At all other times, we play the optimal strategy pairs and breakeven. So he profits overall. But that's impossible if we are playing perfect GTO.

Sean Lefort 12 years, 1 month ago
Well firstly, we get 3bet far less often when we open UTG/MP and he's in the CO, thus we have to raise/fold pf far less often, thus we receive more equity with our opens.

Secondly, our 4bet-bluffs don't fare well but now our 4bet-value hands do quite well. Imagine how much money we're going to make with AA given that we're going to get it in pf every time he 3bets us!

These factors tend to neutralize him making any extra profits with this strategy. And then of course, we have the option of recognizing the situation and adjusting to hyper-exploit him for a ton of money (in pretty obvious ways).
frenchfish 12 years, 1 month ago
Hi Sean, only half way trough but great vid soo far, just one question: "what do you mean when you say that we might realise even more than 100% of our equity in the 7-2o example (The R include also time we make our oponent fold better equity?)"
Sean Lefort 12 years, 1 month ago
Yes, I mean that there are times when we receive > 100% of the equity we should with hand vs. range because of either (1) relative position, (ie. if we're in position we get to control pot-size and have better clairvoyance) and (2) potential range vs. range advantage (ie. some flops are going to be more favorable for us and this means our range will fare better than just its raw equity).
frenchfish 12 years, 1 month ago
Tx for the prompt answer and sorry to have asked a question that i noticed too late was allready asked...Just want to add that this format was really great and look forward to the rest of the series .
DirtyD 12 years ago
Hey Sean, here's a hypothetical for you: if the rules of poker didn't establish 2x as a min-raise, how big would you raise from the button? You don't think it's a good idea to raise MORE than 2x, but how far under 2x would you go? 1.5x? It seems at some point we start giving BB too good of a price.
Guy Thomas 12 years ago
like that question dirty D. I think this is a cool question for ante tournaments as you can raise to any size you want.

excellent video, you are really giving it all away. love the fact your HUD is similar to mine. people underestimate how important it is to organize the information correctly to make consistently good preflop decisions.
R0b5ter 12 years ago
Sean your videos are amazing. In this video I really liked the theory part followed by some live play. I'm hoping for more 6 max content.
Gameking51 11 years, 11 months ago
I will be a nit and point out a small mistake: you estimate our postflop equity with 72o vs a top 50% minus polarised 3bet range. They may be defending 50%, but since this is collectively, they do not have the top 50% of hands. The BB defends 38% and SB defends 17%, so as an approximation we should evaluate our equity against maybe a top 30% range minus polarised 3bet range. So our actual equity will be slightly worse than 30% with 72o. I know you made the point that this particular hand's equity doesn't change much when you alter the opponent's ranges, but it might make a difference in other calculations.

I really like your R concept, and it was cool that R = 72% was the break even value for 72o (did you rig it slightly :p).
tompoker 11 years, 7 months ago

In the first Zoom hand you hold 95s on the right table in the BB against a 2.5x open from the CO. You say it's an easy fold, but I had my doubts, so I ran the numbers: Even with a tight CO-range of 25% and a low R of 0.75, it is very close to a call. 96s is a call even with R = 0.72. Since it is so close to a call and it retains its equity well in a 3bet pot, I actually think it is an easy 3bet.

What do you think?


tompoker 11 years, 7 months ago

Another hand I want to comment on is the 84s on the left table at ~34:00. You bet about 90 in 140 on the river, and here is why I think this is not a good betsize:

We have a valuebetting range of weak to medium Ax and maybe KQ, which we need to bet smaller than 90 (can PM you the formula I use to find river-valuebet-sizes if you like), let's say 60-70, and a valuebetting range consisting of AJ+, with which we should bet close to pot, maybe even a small overbet. Of course we need some strong hands in our small-valuebetting-range as well to protect us from bluff-cr, for example Ax 2Pair (since it makes it less likely for him to have a strong bluffcatcher with the A and more likely he has a hand he wants to turn into a bluff). The stronger range should be balanced with bluffs which have more SDV, since there are more hands we have to get folds with (i.e. rivered lowpair). The weaker range with the smaller bet can contain bluffs with less SDV like our 84s, where basically any fold is a fold from a better hand, therefore giving our opponent good odds is not a problem.

Summary: I think betting ~60 with 84s here is superior to the 87 bet made in play.

I would appreciate feedback on this betsizing-concept.


slack 10 years, 5 months ago

Hi , so you say that if combined sb and bb don`t defend 50% i should open 100%. But i`m afraid that the number of defend showed by the hud is versus all bu opens(2x ,3x ) and i will get in trouble.So if lets say the hud tells me that they defend the bb 40% when i do the math i most asign  a bigger value vs my 2x open ?

slack 10 years, 5 months ago

i will give you an example .So i have a guy in bb (10k hands sample)and i open for the first time the bu (i have 60% open ) His hud shows vs bu open fold 71% call 20% and 3bets 9%. He calls we go to showdown , he has J8o ..  J8o is in a 20% calling range ?

egolibero 8 years, 4 months ago

I play at lower levels, the beginner kind of levels :)), so my question might sound stupid but please bear with me.

I will take your example where SB 3B 17% and BB 3B 30%, which means both will defend by 3Betting 42% because of the overlapping. And everything looks fine, but I'm trying to design my pre flop BTN opening range and based on my player pool analysis it looks like SB 3B 10% BB 3B 9%, combined should be 18% (used the same math as in your example) - SB Calls 14% and BB Calls 24%, combined 35%; but when I get to the SB and BB Fold I have SB Fold to OR 76% and BB Fold to OR 68%, combined should be 92%??? I'm lost here on the folding part; the numbers don't come together! Combined should be close to 47% if I make 100%-18%-35%.

Can you please help me out figuring out the real number or should I stick to 100%-18%-35%?!

Thanks!

kingkong 7 years, 4 months ago

Hi, could it be ok to let BTN auto profit steal very slightly since anyways when defending the BB, you are just trying to get a share of your BB back. So I mean, even if you defend enough to prevent him from auto profit, BTN is 'supposed' to make a profit in the situation where you are going to defend with a weaker range OOP. Then it would be transferring some of the EV you are supposed to lose from post flop to pre flop, and then on the flop you have better range.

I guess it's all related to the previous concepts. Like if BTN open too much you defend more and if he opens less you defend less.

Also I was surprised that you don't open A8o on CO at 32:20 but am not very good at designing pre flop ranges. I saw on a video somewhere here a recommendation to open 42% on the CO and find my A8o borderline there.

I consider Q9o in my top 33% and you also did not open it at 38:20.

TaoCore 6 years, 3 months ago

Cool Mind Process.You gave me a lots of subtleties i did not think about , adjustments , HUD biases and so on .
Merci Mr Muscle.

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