How do I construct a 3-betting range?

[MadMojoMonkey]

Lets assume Villain is to my right w/ stats something like 40/20/3 ranges like.
EDIT: Ignore the red.

Villain limps 20% of the time
{ K9s-K2s,Q9s,J9s,T8s+,97s+,86s+,75s+,64s+,53s+,A9o-A5o,J9o,T8o+,97o+,86o+,76o,65o,54o }

Villain bet/calls a 3-bet 17% of the time:
{ JJ-22,AQs-A2s,KTs+,QTs+,JTs,AQo-ATo,KTo+,QTo+,JTo }

Villain bet/4-bets 3% of the time
{ QQ+,AKs,AKo }

When Villain bet/calls, he will either donk or c/r the flop a huge percentage of the time.

I've been thinking about this for days and the best I can come up with as my calling-a-raise range is 16%
{ TT-22,ATs-A2s,KJs-KTs,QTs+,JTs,98s,87s,76s,65s,54s,AQo-ATo,KQo,QJo,JTo,98o }

So my 3-betting for value range is 4%
{ JJ+,AJs+,KQs,AKo }

And my stack-it-off pre range is 2%
{ KK+,AKs,AKo }

But this just seems way too thin, even for a nit like me.

What am I missing here when I try to work this out?

[Pascal]

40/20/3 means he'll limp 20%, raise 20%, and 3bet 3% of the time. The 3rd number isn't bet/4bet, so both the 2nd and the 3rd lines of stats are both wrong.

To take an example:

This is a 40% range:
44+,A2s+,K2s+,Q4s+,J7s+,T7s+,97s+,87s,A3o+,K7o+,Q8 o+,J8o+,T9o

And this is 20% for raising:

66+,A4s+,K8s+,Q9s+,J9s+,T9s,A9o+,KTo+,QTo+,JTo

So the limping range theoretically would be hands in the first set but not in the 2nd set:

44-66, A2s, A3s, K2s-K7s, Q4s-Q8s, J7s, J8s, T7s, T8s, 97s+, 87s+, A3o-A9o, Q8o, Q9o, J8o, J9o, T9o

However, he's more likely to limp hands like 34s than Q4s, and more likely to raise A9o than Q9s etc

[d0zer]

Calling pfrs contributes to that 20% diff pascal, it isn't all limps.

[MadMojoMonkey]

Ugh. I dont use a HUD, so ignore the stats part and just go with the ranges I posted.

[DoubleJ]

What am I missing here when I try to work this out?

What are you trying to do here, Moj'?

you'll need stats for (or some idea of) Villain's fold-to-3Bet tendency, and then apply this:-

http://www.flopturnriver.com/pokerfo...ng-162986.html

unless i've totally misunderstood OP due to sleep deprivation.

[The Bean Counter]

To confirm, are we saying villain raises 20% pre? And the same range from every position?

[MadMojoMonkey]

you'll need stats for (or some idea of) Villain's fold-to-3Bet tendency, and then apply this

If Villain raise/calls 17% and raise/4-bets 3%, then isn't Villain's FT3

(17 - 3)/17 = 82%

?

I'll read that article.

To confirm, are we saying villain raises 20% pre? And the same range from every position?

Let's put Villain on CO, and Hero on BTN. Ignore the stats. I don't use them, and I don't fully understand the nuances of them. Just go with the ranges I've posted.

[bikes]

villains fold to 3b, call 3b and 4b is the most important part in determining 3betting ranges.

[DoubleJ]

If Villain raise/calls 17% and raise/4-bets 3%, then isn't Villain's FT3

(17 - 3)/17 = 82%

100-(17+3) = 80%

[The Bean Counter]

Doesn't really answer your question (and I don't really like the idea of constructing a static, non-polarized 3betting range where we assume villain doesn't adjust), but in position I tend to 3bet and 4bet for value on the basis of 50% i.e. if villain opens 20% CO then I'll 3bet 10%, if villain 3bets 5% then I'll 4bet 2.5%.

Obviously I'll open this up for bluffs depending on villain and adjust for positions and stack sizes. The 50% rule is also too nitty as ranges get tighter i.e. if villain 4bets a non-polarized 3% then jamming 2.6% is profitable (QQ+,AK) if we assume villain never 4b/f.

Happy for those better at algebra to rip this post apart if required..

[bikes]

Doesn't really answer your question (and I don't really like the idea of constructing a static, non-polarized 3betting range where we assume villain doesn't adjust), but in position I tend to 3bet and 4bet for value on the basis of 50% i.e. if villain opens 20% CO then I'll 3bet 10%, if villain 3bets 5% then I'll 4bet 2.5%.

Obviously I'll open this up for bluffs depending on villain and adjust for positions and stack sizes. The 50% rule is also too nitty as ranges get tighter i.e. if villain 4bets a non-polarized 3% then jamming 2.6% is profitable (QQ+,AK) if we assume villain never 4b/f.

Happy for those better at algebra to rip this post apart if required..

-.- i'll tear apart this logic when i get home from work.

[The Bean Counter]

Please do - I'll learn a fuck-load from it when I'm at work in the morning.

Cheers in advance.

[MadMojoMonkey]

Apparently in the ranges I constructed, Villain's FT3 is 0%... since he either bet/calls or bet/raises.

This gets at the heart of my problem: getting past VPIP/PFR when it comes to ranges and adjustments.

I'll rework the ranges tomorrow.

[Stacks]

Apparently in the ranges I constructed, Villain's FT3 is 0%... since he either bet/calls or bet/raises.

This gets at the heart of my problem: getting past VPIP/PFR when it comes to ranges and adjustments.

I'll rework the ranges tomorrow.

To figure out villain's fold to 3bet %, you need to consider villain's opening range compared to the range he continues to 3bets with, regardless of if it's by calling or 4betting.

So if he is 4betting the top 3% of hands, then calling another 17% of hands that he opened with, he's continue to a 3bet with the top 20% of hands. His fold to 3bet is still dependent on what his opening range is to begin with, as if he is only opening 20% of hands (and thus continuing with all) he would have a FT3 of 0%. But if he's opening with say 50% of hands, and continuing with 20%, he's folding 30/50 or 60% of the time.

Considering a 3x open, and 9xbb 3bet, you need him to fold 9 / (9 + 3 + 1.5) or 67% of the time to have a breakeven 3bet based on fold equity alone. That is, you could 3bet, then not put another bb into the pot regardless of what you hit, and still be breakeven (which is of course not going to happen).

So if you know he's continuing with 20% of hands (calling with 17%, 4betting with 3%), it would be breakeven to 3bet bluff with ATC if his opening range is roughly 61% or more. His opening range would need to increase a bit, or his continuing range decrease a bit, in practice if there are other players left to act, as there is still a 3% chance or more for each remaining player to have a premium hand they want to continue with.

Now if you know how he reacts to 3bets, you can begin constructing your 3betting range. In spots where you expect villain to 4bet/fold primarily, such as a good player getting 3bet and being OOP, I'd typically say you want to form a polarized 3betting range. That is, depending on how often he continues, form a range of hands you want to 3bet for value and profitably shove over his 4bets. Then form a 3bet bluff range of the best hands you would typically fold (frequency dependent on how often he folds). Typical ABCD theorem.

Reasoning behind this is you don't want to 3bet hands that could profitably call the open and play postflop, but can't continue to a 4bet, since the only time he is continuing is by 4betting. Since those hands would show the same profit by 3betting (based on him folding) as weaker hands, yet you would lose the value of calling those hands. So you are best off just calling the hands you can profitably do so, then 3betting the hands you can't, thereby increasing the range of hands you play profitably versus villain.

Now in cases where you expect calls/folds more frequently (usually always against fish, or when regs are IP), then it seems to make sense to 3bet a more merged/depolarized range. Now, there is merit in expanding your "value" range, and reducing your "bluff" range. The weaker part of your value range (think AJ/KQ/KJ/etc) now has more value than in the 4bet/fold scenario, since it still gets to see a flop and realize a portion of it's equity the majority of the time. But the bluff hands you had in your range from before don't really do as well, since now you are having to take those weak hands to postflop, rather than profiting due to villain folding preflop.

So in this scenario, you would have a value range of hands you can 3bet/shove with profitably. Then a range of hands that you can 3bet/decide with (deciding being either folding or possibly shoving as a bluff). Hands that play well against villain's calling range (broadways, suited Aces, mid-high pairs, good suited connectors).

So in the situation you described with villain calling 17%, and only 4betting with 3% of hands, it's pretty reasonable for you to be 3betting a moderately wide range of hands, but only shoving against his 4bets with a strong range. You 3bet a wide range of hands that do well against his calling range, then fold all but the best against his tight 4betting range.

*Disclaimer: Above is just like my opinion man. And I'm pretty much a fish nowadays who can't win to save my life, so yeah*

[JKDS]

In spots where you expect villain to 4bet/fold primarily, such as a good player getting 3bet and being OOP, I'd typically say you want to form a polarized 3betting range. ...

Reasoning behind this is you don't want to 3bet hands that could profitably call the open and play postflop, but can't continue to a 4bet, since the only time he is continuing is by 4betting. ...

Now in cases where you expect calls/folds more frequently (usually always against fish, or when regs are IP), then it seems to make sense to 3bet a more merged/depolarized range. Now, there is merit in expanding your "value" range, and reducing your "bluff" range.

*Disclaimer: Above is just like my opinion man. And I'm pretty much a fish nowadays who can't win to save my life, so yeah*

And thats why i suck at 3betting and why it never made sense to me...because i was only polarizing it. wow. mind blown, thanks stacks!

[Stacks]

And thats why i suck at 3betting and why it never made sense to me...because i was only polarizing it. wow. mind blown, thanks stacks!

Yeah, this raise/fold, or call/fold response logic kinda clicked with me somewhat recently, and at least in my understanding it seems to make sense. But I could be entirely off, so my initial response is just as much for critiques of my logic as it is for anyone else that might benefit from it.

The logic used for determining 3betting range, also seems to apply postflop in spots where you are considering whether you should bet a polarized or merged range as well.

For instance, say you are IP postflop considering what range to cbet. Obviously you want to be cbetting your value hands most of the time, but what about the weaker "marginal" (B range) hands? Well in spots where you expect calls or folds from villain, I'd say it's typically going to be correct to cbet rather than not. As you can get value (albeit maybe thin), you collect dead money from all the hands that villain folds, you have more profitable aggression spots on the turn/river (where you can put in more money if you are ahead, or decide to bluff), and you don't turn you hand face-up to good hand readers. You would also bet bluffs if you felt it was correct/profitable. So again call/fold response, you are betting a merged range.

But what about if it's say a villain that is check/raising often (or a board texture where you get check/raised often)? Then, again there is less merit in betting hands that have value in checking behind, if you don't intend to continue to the check/raise. Basically, if you thought villain was only folding, or check/raising, you wouldn't really want to bet/fold a marginal hand that has value in checking behind and bluff catching (or valuebetting on later streets). As bet/folding would just be wasting your hands pot equity, as you never get to realize it at showdown. Obviously not a problem if you are bet/folding a hand with little pot equity because you think villain folds often enough for it to be profitable.

[DoubleJ]

To figure out villain's fold to 3bet %, you need to consider villain's opening range compared to the range he continues to 3bets with, regardless of if it's by calling or 4betting.

So if he is 4betting the top 3% of hands, then calling another 17% of hands that he opened with, he's continue to a 3bet with the top 20% of hands. His fold to 3bet is still dependent on what his opening range is to begin with, as if he is only opening 20% of hands (and thus continuing with all) he would have a FT3 of 0%. But if he's opening with say 50% of hands, and continuing with 20%, he's folding 30/50 or 60% of the time.

Sorry if i'm being dense here, Stacks, but the maths here doesn't make sense to me.

If we are talking about fold-to-3Bet frequency, then if Villain is continuing in 20% of spots that his raise is 3Bet, by definition, he's not continuing (i.e. folding) the other 80%.

Regardless of his opening range.

I agree that we need to take opening range into consideration when thinking about his 4Betting and Continuing ranges, and that the strength of Villain's opening range is going to have a direct correlation to his continuing frequency, but i don't get your calculation at all.

Can you go over it again, plizz?

[MadMojoMonkey]

if Villain is continuing in 20% of spots that his raise is 3Bet, by definition, he's not continuing (i.e. folding) the other 80%.

Stacks has it here.

In the ranges I posted, Villain folds 60%, limps 20%, and raises 20%.

Of the 20% Villain raises, 17% of it is b/c and 3% of it is b/r. 0% of the raising range is b/f.

I am going to create new ranges right now.... post to come.

[MadMojoMonkey]

OK, so here I've got 3 ranges for Villain's response to 3-bet.

b/b 2.56% { QQ+,AKs,AKo }

b/c 17.8% { JJ-22,AQs-A2s,KTs+,QTs+,JTs,AQo-ATo,KTo+,QTo+,JTo }

b/f 5.73% { K9s-K8s,Q9s,J9s,A9o-A8o,T9o,98o,87o }

total betting range is 26.09%

FT3 = 5.73% / 26.09% = 22%
Call3 = 17.8% / 26.09% = 68%
4-bet = 2.56% / 26.09% = 10%

[DoubleJ]

OK, i c wot ur doing now....

[Stacks]

Sorry if i'm being dense here, Stacks, but the maths here doesn't make sense to me.

If we are talking about fold-to-3Bet frequency, then if Villain is continuing in 20% of spots that his raise is 3Bet, by definition, he's not continuing (i.e. folding) the other 80%.

Well yeah, if he continues 20% of the time, then by default he is not continuing 80%. But that wasn't the question 3M posed. He gave him a continuing range of 20% (17% call, 3% 4bet). So to determine how often he folds to a 3bet, you must consider how often he is opening. And since 3M made a mistake and had him only raising 20% of hands, and thus continuing with all of them, he was folding 0% of the time.

In your example of him folding 80% of the time, he would have to be opening 100% of hands.

[Stacks]

OK, so here I've got 3 ranges for Villain's response to 3-bet.

b/b 2.56% { QQ+,AKs,AKo }

b/c 17.8% { JJ-22,AQs-A2s,KTs+,QTs+,JTs,AQo-ATo,KTo+,QTo+,JTo }

b/f 5.73% { K9s-K8s,Q9s,J9s,A9o-A8o,T9o,98o,87o }

total betting range is 26.09%

FT3 = 5.73% / 26.09% = 22%
Call3 = 17.8% / 26.09% = 68%
4-bet = 2.56% / 26.09% = 10%

From here, I'm not really sure how to best go about determining exactly what hands to place in our ranges, and with what frequency we should be taking each action.

Given he 4bets such a tight range, and isn't bluffing, we need ~45% equity to shove over a 4bet, which only KK/AA has against his stackoff range. Shown by this math:

Ev[shove] = (equity)(total pot) - (amount shoved)
0 = X(201.5) - 91
91 = 201.5X
X = 0.45

So while 3betting hands like QQ/AK will be incredibly profitable given how often villain calls with worse, shoving those against villain's narrow 4betting range would be incorrect.

Since we know our 5b shoving range {KK+}, we should try to find out what hands we can profitably 3bet. Now this is where I have no real clue on how to do the math. My best guess is something like:

Villain folds 22% of the time, we win the 4.5bb pot = 0.22 * 4.5 = 0.99

Villain 4bets 10% of the time, we lose our 3bet = 0.10 * -9 = -0.9

Villain calls 68% of the time (anyway to actually calculate this?)

So:

Ev[3bet] = (%fold)(Evfold) + (%4bet)(Ev4bet) + (%call)(Evcall)

0 = (0.22)(4.5) + (0.10)(-9) + (0.68)([X](19.5) - 9)
0 = 0.99 - 0.9 + 13.26X - 6.12
6.03 = 13.26X
X = 45.5% equity

But see, this is where the above feels irrelevant. That 45.5% equity number would be the needed pot equity if we were to 3bet, and then it gets checked down everytime. And doesn't take into profitable bluffs we can make postflop, valuebets we can make, etc. So the overall hand could be +EV even if we had less than 45.5% equity, if we made up for that slightly -EV decision on a later street. For instance, we could 3bet with 0% equity if villain was check/folding 100% of the time postflop, and the hand still be profitable. Just like we can cbet the flop knowing villain never folds, knowing that the fold equity we have on the turn to a double barrel makes up for the flop "mistake".

But, looking at his calling range of 17.8%, and looking at the hands that have at minimum 45.5% equity, it does include most of the hands I would choose to 3bet with.

Putting it into Equilab, we can see that against his 17.8% call range, the range {44+, A3s+, KTs+, QJs, A8o+, KJo+} has 45.5% equity or better. I would definitely be 3betting hands like AT/KQ/KJ/KTs/99/TT/etc for value against this villain. I would probably opt to call hands that play well postflop like 44/55/QJs.

How he plays postflop could help you determine what other hands you can profitably 3bet. If say he's really fit/fold postflop, you could 3bet hands with less pot equity, as your flop cbet fold equity would make up for the lack of pot equity. And so on.

So yeah, the above could also be wrong. Anyone know how to do it correctly?