BB vs BTN (3X): Constructing A Non-Linear Calling Range
Posted by AF3
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AF3
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BB vs BTN (3X): Constructing A Non-Linear Calling Range
Suppose the Button opens to 3 BB's and the blinds defend by either 3Betting or Folding. To keep the Button indifferent to opening the worst hand in his range (which we assume BTN will fold to the 3bet), we have the following for this model:
Optimal Blind Defense = 1 - (Frequency Which BTN Needs Blinds To Fold For An Immediate Profit) = 1 - (3/4.5) = 1/3
Thus, the combined 3Bet percentage of the blinds, if they chose to either 3Bet or fold, would be .33333
Suppose the SB 3Bets a range of ~14.5%. The BB would then be required to 3bet the amount which satisfies the equation:
.3333 = (.145) + (.855) * (BB 3Bet)
This implies the BB would 3Bet ~22%. Seems like a lot.
Of course, this model does not take into account things like pot odds of the Big Blind to call the BTN Open when the Small Blind folds, and I think we see that the BB should certainly have a calling range versus the BTN Open.
The first question is how wide to make the calling range versus a 3X Open. While it seems intuitive to defend any two suited and an extremely wide range versus a BTN minraise, I'm less sure how to construct the calling range versus a 3X Open but the SPR seems drastically affected on the turn and river with this extra big blind added to the preflop open. Furthermore, even after we do solve for a plausible calling frequency, I run into the following problems constructing a range:
1) If we start going super-linear then it seems most flops will give us hands we're forced to play passively since our equity on turns and rivers will often be non-robust.
2) Because of (1), we let the BTN realize tons and tons of equity with draws. He also gets to play these in position against a fairly condensed range on our part on many boards, and this doesn't bode well for us.
3) If we start going non-linear and adding more suited hands off-suit connectors, then we should gain some robust equity-share on many flops, but we end up with more dominated holdings.
Do any of the coaches have input on this? Specifically, how wide to make the BB Calling Range Versus a 3X BTN Open, and secondly how to construct it?
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Just a quickie: the minimum defense only holds true (in theory) if the blinds had no calling-range and would only defend by 4bets. Once you call, the BTN has equity with any hand, so you have to defend more than the minimum.
Right I was using that model to imply we need a calling range before asking how to go about constructing it.
I'd play with building very in-depth CREV model.
Outside of that I try and think of what type hands work well for different calling ranges:
Off suit high-cards work well from the blinds because when they make a pair they're easy to play.
Small suited connectors realize their equity from fold equity and making the nuts, so they work well in 3-bet pots where you'll have a betting range which needs bluffs and since the pot is bigger having the nuts work better.
The main two issues I'm seeing with my BB defense strategy against the button are: 1) a big/wide 3bet range consumes so many of the good value hands that the calling range can be left very weak, and 2) I don't know how big/wide an optimal BB calling range should be.
In order to strengthen a weak calling range, a select few of the strong pre-flop value hands that most players would 3bet can be treated as calling hands. A system such as 'big spade/club pairs' or 'premium suited heart hands' can be used to designate and easily remember the special hands you want to treat this way.
I like having a BB 3bet range against the button that is both polarized and balanced, i.e. a range that has reasonable potential to solidly hit almost any type of flop. To achieve this the bluff hands in the 3bet range should include a sizable number of small pairs, suited aces, and suited connectors.
Both the button's opening frequency and the raise size should be considered to determine how wide to make optimal BB 3bet and calling ranges. I suspect opening frequency is generally the more important consideration. Against a button that opens roughly half of all hands dealt to 3bb, I'm using a ~15% 3bet range and a ~30% call range but I'm not sure that what I'm doing is correct or optimal.
In order to strengthen a weak calling range, a select few of the strong pre-flop value hands that most players would 3bet can be treated as calling hands. A system such as 'big spade/club pairs' or 'premium suited heart hands' can be used to designate and easily remember the special hands you want to treat this way.
I don't think this is "correct". One of the main tenets of game theory is that you always take the line which is highest EV against your opponent. You never really take a lower EV line for the sake of balance. I know what you're talking about and I used to do this too. If you think that 3-betting Ace-King of diamonds is the highest EV versus the button, though, then 3-betting Ace-King of hearts should be as well. With that said, there are also arguments that the optimal strategy in poker is certainly going to be mixed and I agree suits are a good way to randomize it. If you're slowplaying some hands pre-flop, though, I don't see how a 15% 3-bet range would be laughably unbalanced.
I don't think this is "correct". One of the main tenets of game theory is that you always take the line which is highest EV against your opponent. You never really take a lower EV line for the sake of balance. I know what you're talking about and I used to do this too. If you think that 3-betting Ace-King of diamonds is the highest EV versus the button, though, then 3-betting Ace-King of hearts should be as well.
If what you state above is correct, then it would never be correct to just call with a strong hand or to bet/raise with a weak hand.
We should strive to achieve the highest EV possible with our overall strategy for calling and 3-betting from the big blind. It is reasonable to include some weak hands in our 3-bet range (as bluffs) and to include some strong hands in our call range (for balance). Both ranges include some hands which, individually, are not being played in a highest possible EV manner. However, doing this is not at all contrary to having an overall game theory optimal strategy.
1) We choose the decision that has maxEV.
2) When two or more decisions have the same EV against the maxEV-counterstrategy, we mix it up in a way that supports the rest of our range.
Obviously those "mixed strategies" are nothing that most of us "human brains" can proceed in any reasonable way, so I guess it will remain blank theory.
Balance play is an effect of playing hands in the most EV way. It's not a goal in and of itself. It's a human construct to understand the game. Nothing more.
BigFiszh,
Do you have any thoughts on my original question/issue? You can see the problem I run into, right?
Would you go with a fairly linear 8% calling range against the 3X Open? Maybe something like:
A9s-A7s
KJs-K7s
QJs-Q8s
ATo-A9o
QJo-Q9o
99-55
Sulksy proposed a 3bet range of AK, AQs, JJ+, 45,64 type hands at one time, call everything else that has a +ev realisation of equity. but saying that i saw him 3bet KJsuited in the big blind vs Alex millar last week who was UTG [kanu7, Ireadyrsoul]. so i guess the pro's are keeping their strategy secretively quiet.
i think the big point with poker is adjusting to stakes, so a good strategy at 1knl is not the maximally exploitative strategy as at 25nl. take some time to view zoom poker at 25nl, 50nl, 100nl, 200nl, 500nl, and 1000nl. you'll notice key differences constantly throughout. 25nl being people CALL alot more than 4bet, the 3bet sizing is horribly small and they don't bluff with correct frequency to make enemy calling breakeven. furthermore, they minimally go to showdown with bluffs in 3bet pots. it's very commonly, value vs value.
then skip yourself to 1knl, and you'll very often see value is balanced with bluffs a lot more!!!! so one guy has call call called with the nuts, and the other has a bluff.
just to provide minimal evidence to my hypothesis,this is visible off the first 2 hands i clicked:
lazio1200: folds
cipple444: raises $10 to $15
Go0se.core!: raises $30 to $45
Muladkhara: calls $45
Zero 1100101: folds
soydelmillo: folds
cipple444: calls $30
*** FLOP *** [Js 5h As]
cipple444: checks
Go0se.core!: checks
Muladkhara: bets $77.50
cipple444: calls $77.50
Go0se.core!: folds
*** TURN *** [Js 5h As] [6s]
cipple444: checks
Muladkhara: bets $212.50
cipple444: calls $212.50
*** RIVER *** [Js 5h As 6s] [3d]
cipple444: checks
Muladkhara: bets $792.15 and is all-in
cipple444: calls $792.15
*** SHOW DOWN ***
Muladkhara: shows [7h 7s] (a pair of Sevens)
cipple444: shows [4s 5s] (a flush, Ace high)
__________________________
Hevydevy27: raises $0.60 to $0.85
evofit78: folds
pokeritouko: calls $0.85
imjimmylee: calls $0.85
Darkcreo: folds
baoureri777: folds
*** FLOP *** [Ad 8d 2d]
Hevydevy27: bets $1.50
pokeritouko: calls $1.50
imjimmylee: calls $1.50
*** TURN *** [Ad 8d 2d] [8s]
Hevydevy27: bets $4
pokeritouko: calls $4
imjimmylee: raises $9.53 to $13.53
Hevydevy27: folds
pokeritouko: calls $9.53
*** RIVER *** [Ad 8d 2d 8s] [2s]
pokeritouko: checks
imjimmylee: bets $20
pokeritouko said, "lol this is sick"
pokeritouko: raises $16.33 to $36.33 and is all-in
imjimmylee: calls $16.33
*** SHOW DOWN ***
pokeritouko: shows [8c 8h] (four of a kind, Eights)
imjimmylee: shows [3d Kd] (a flush, Ace high)
Those posts have nothing to do with the original question, thanks though.
it's these. The confusion seems to be about how many mixed strategies there actually are preflop. For that we'd have to know every strategy an optimal villain takes in every line on every board.
if you refuse to take a mixed strategy where one should be taken, an optimal opponent will not be exploiting you (b/c an optimal opponent never changes his strategy). but a nemesis opponent will.
I'm making this distinction b/c the optimal strategy for BB is dependent on the optimal strategy for BTN (and vice versa). The optimal strategy for BTN has been derived from running through the motions of all possible nemesis options available to BTN if BB refused to take a mixed strategy where one should be taken. Optimal for button is unconcerned with BB taking correct mixed strategies b/c it is the future version of the events that already took place if BB didn't take correct mixed strategies.
If BB unmixes, optimal BTN goes into his time machine and becomes past nemesis BTN. I think it's a good demonstration that optimal is derived from an understanding of maximum exploitative strategies. The only way this wouldn't be the case is if the simulation started with one player using a completely GTO strategy on his first guess of his range, and that's a lottery
I think it's a good demonstration that optimal is derived from an understanding of maximum exploitative strategies.
This is how I've always understood "optimal". I've also never really understood the idea of a "optimal" strategy in isolation-- I've always understood game theory in terms of strategy pairs. MOP defines a game-theory optimal strategy pair as two strategies who are maximally exploiting each other. Because of this, we know that (by definition) we are at the equilibrium where no player has incentive to change their strategy because they would be sacrificing EV by doing so.
Thus, my understanding of an "optimal strategy" is just the single-player strategy which is played at the equilibrium but it seems a subtle abuse of language to talk about an "optimal strategy" since they always come in pairs (or more) for a multi-player game. Nick, is this how you understand it as well or do you think I am missing something?
Also, to Nick and Big Fizsh: Do you guys think a combined defense from the SB + BB or ~40% is enough against the BTN's 3X open or does it need to be like 45%?
that looks right.
i really don't know about optimal defense from the blinds. i suck at preflop. working on it. i just defend as many suited combos as i can muster the courage to.
Even to the 3X Open?
To the min-raise I can see calling any two suited no problem, but I'm less sure of the 3X. I guess you need about 30.7% equity based on pot odds alone if you get to realize 100% of your equity. Maybe we'll assume that you realize your equity 65% of the time and then you would need:
X*.65=30.7 ==> X=30.7/.65 = 47% equity
That actually seems quite reasonable, that would be hands like J7s, 69s, T6s (which actually does the best against ATC of those three).
i think all those would be calls on the bb vs a 3x
AF3: "Also, to Nick and Big Fizsh: Do you guys think a combined defense from the SB + BB or ~40% is enough against the BTN's 3X open or does it need to be like 45%?"
Seriously, I don´t know. It depends on the ratio between calling- and 3bet-hands. The more hands the blinds call (instead of 3bet), thus the more hands BTN will realize his equity with, the more hands the blinds have to defend overall.
Yet, I think you´re maybe approaching the problem from the wrong side. The amount of hands the blinds "have to defend" with optimally does not tell you anything. You should rather start with your hands and think about the EV of calling / 3-betting / folding. There´s no quick fix and no solution, but you can make some estimations and build a range that you feel comfortable with.
Yet, I think you´re maybe approaching the problem from the wrong side. The amount of hands the blinds "have to defend" with optimally does not tell you anything. You should rather start with your hands and think about the EV of calling / 3-betting / folding. There´s no quick fix and no solution, but you can make some estimations and build a range that you feel comfortable with.
The amount the blinds have to defend to prevent the BTN from opening any two cards profitably tells you exactly that. I agree there's no quick fix, but isn't the entire point of applying game theory that there is a solution, humans just won't know what it is without the aid of a computer or some such crazy augment to our brains?
Your approach of starting with hands and thinking about the EV of various options is kind of implying our intuition and experience trumps mathematical models of the game. For this to be the case, I would argue that it's more that we don't have the right models than that models don't apply to real poker. I do agree that you should end up with some pretty good ranges if you've played a lot of poker and use your approach.
By the way, the problem I have with statements like "build a range you feel comfortable with" is that it's not only ill-defined, but it's also essentially assuming that you won't propagate the errors that already exist in your thinking when building these ranges. One of the fundamental sticking points with applying game theory has always been that you end up protecting a bad strategy and making it worse if you aren't careful.
You got me wrong. :) Obviously there IS a solution, but there are two ways to come to that solution. The first is the "nemesis approach" where you calculate the defense-frequency of SB+BB combined to deny BTN autoprofit with any2. The second is the "constructive approach" where you look at your hands and decide which hands to play +EV. Both approaches will lead to the same optimal solution!!
"The amount the blinds have to defend to prevent the BTN from opening any two cards profitably tells you exactly that."
I know, but what I meant is - what does that number help you? If I told you SB + BB have to defend 40% in combination, how do you know what´s the optimal calling-range for SB? For BB? What hands to 3-bet from SB? From BB? There are gazillions of possible combinations that eventually lead to a defense-range of 40%, that was why I meant that this single (!) number is useless for range construction theory.
"Your approach of starting with hands and thinking about the EV of various options is kind of implying our intuition and experience trumps mathematical models of the game."
NO! I´m not talking about experience, I´m talking about math. You have to start with a BTN-range for opening and for defending vs. 3bets (obviously this is where experience comes into game or you take a "predefined" BTN-range from a book or a coaching-site or whatever), then you estimate the equity realization for different holdings and then you start to define a postflop-strategy. And when you´ve done that you get an EV. No experience, no intuition, just beautiful, cold, hard math. :)
I know, but what I meant is - what does that number help you? If I told you SB + BB have to defend 40% in combination, how do you know what´s the optimal calling-range for SB? For BB? What hands to 3-bet from SB? From BB? There are gazillions of possible combinations that eventually lead to a defense-range of 40%, that was why I meant that this single (!) number is useless for range construction theory.
It would help you construct multiple models under various assumptions and then fit those models based on how well those assumptions apply to each table and player combination (I know this is getting into theory to help exploit type stuff, but my point is it's very useful).
Also, it helps you build an overall strategy in the sense if you think you have some previous ideas that might be useful, you can then trace those to their logical conclusion. For example, let's say I think the Small Blind should never have a calling range versus the BTN Open. If I know how much both blinds need to be defending, I can see what no calling range from the Small Blind does to both the Big Blind flatting range and the Small Blind 3-betting range itself under various assumptions and so on. This is exceedingly useful.
NO! I´m not talking about experience, I´m talking about math. You have to start with a BTN-range for opening and for defending vs. 3bets (obviously this is where experience comes into game
... =)
I'm not saying your approach is wrong, I'm saying it seems fairly unreliable and a bit incomplete as the constructive method because you're not even presenting arguments for which hands must be opened.
I agree that the methods are equivalent, since constructing a pre-flop opening range is actually the same as defending against a bet (with the bet you are defending against being your share of the blinds).
I don't agree with the question. Linear ranges hit lots of different flop textures because we'll have pairs, offsuit cards, and suited cards and they don't completely overlap. Also, btn doesn't have 100% of hands, he typically has lots of dominated hands that have to scramble to win the pot.
I'm not sure what you mean by you don't agree with the question. Do you mean you don't think it's a problem to use a linear range?
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