Help me plan my range vs range strategy here in a common spot
Posted by Zizek
Posted by
Zizek
posted in
Mid Stakes
Help me plan my range vs range strategy here in a common spot
We open the following 13.7% range UTG
http://gyazo.com/a2441f59af2c1a77f722f1f4294d5255
and it folds to a competent villain in the BB who flats the following 8.75% range
http://gyazo.com/9e4b9d310255641f5429f39398f47c51
(Ranges seems pretty typical so far, right?)
The flop comes Jh 7c 4d.
Help me compose my ranges in this spot in as balanced a way as possible. (I'm looking for go-to, GTO-ish ranges rather than exploitative ones).
I believe we have just barely enough fold equity on the flop w/ a .75 psb to be able to bet 100% of our range irrespective of hand value, but we have a decent number of pairs lower than Jx that likely play better as flop checks (Slightly too weak to vbet) As a result we probably need to develop a semi-wide flop check back range, as well as a bet bet bet range, bet bet check range, etc.
Assuming we can valuebet QQ+ on the river w/ my most board runouts, what combos do you think are optimal to barrel turn/river with? How are you balancing your Bluff : Vbet ratio combinatorically here? With hands like AJ, KJ, etc where only 2 streets of value are likely are you preferring a b/c/b line, or b/b/c?
I have a general idea of how I'm composing these ranges myself but I'd really appreciate hearing from others more experienced than I in this kind of macrocosmic analysis. (That means you Mr. Sulsky!)
Thanks!
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I think your ranges are quite simplistic, for instance I would not raise A9s, less {22,33,44,A2s,A3s,A4s,A5s} and more 54s+,75s+. And in the big blind I would not 3-bet all my AKo and snapfold AJo against a 13.7% range.
Also if you want to have real GTO ranges then the big blind should flat his QQ-AA here preflop with a decent frequency in order to have an uncapped range on a high quantity of flops.
But simplicity makes for simple calculations, I'll assume these ranges from now on:
UTG:
BB:
This is a quite worthless statement if you want to calculate GTO ranges, just that betting 0.75 times pot is better than open folding does not imply that betting 0.75 times pot is better than checking behind. If you balance your ranges you will have enough fold equity on later streets aswell.
But you seem to imply that at least 1/1.75th (57%) of his range calls the flop.
The BB range is 101 combos on the flop, 44,77-JJ,AJ, (AQ,KQ-98):xx is 61 combos. So that would be a minimum defending range.
You say you can valuebet QQ+ on the river but that is quite stange since the BB has no QQ+ itself and there are no hands between AJ and QQ on a blank runout. And AJ blocks a decent part of the sets and two pairs (on a numerous runouts) of the BB. That seems to imply that AJ gets either valuebet by UTG or bluffcatched by the BB, or that QQ checks back on one of more streets, or a combination.
Doing a full street analysis is rather difficult, since we need to calculate optimal betsizes, turn check raises, overbets etc etc.
But what we can do is doing static analysis, no check raising or leading and UTG either valuebets or gives up, assume the board does not change, and the UTG valuebets 0.75 times pot 3 streets QQ+, ignoring card removal.
QQ+ value betting 3 streets:
UTG has 165 combos on the flop. 44,77,JJ-AA is 27 combos.
Betting 0.75 times pot on 3 streets means there should be 1 value combo to every 0.75/(0.75+1) = 0.43 bluff combos on each street. That means the value part of his flopbet range is (1/1.43)^3=(0.7)^3=0.343.
Or 1.92 bluff combos to every value combo on the flop.
Meaning he can bet 51 bluff combos and 27 value combos on the flop, totalling 78 out of 165.
Hence UTG can cbet 47% under the assumption of a static game where he either valuebets QQ+ or bluffs with air. This means that the board doesn't change, there is no card removal, the BB is forced to check on all three streets, and UTG can only check or bet 0.75, the BB cannot raise or bet, only call or fold.
Assume the BB want to make UTG different between bluffing 1, 2 or 3 streets with A2s. This implies he has to call at least 57% of his range on each street: (all combos are given dead cards As2s)
Preflop: (AT,98-KQ):xx,AJ-AQ,22-JJ = 90 combos
Flop: 44,77-JJ,AJ, (AQ,KQ-98):xx = 57 combos (63%)
Turn: 44,77,TT-JJ,AJ,QJ-TJ:xx = 30 combos (53%)
River: 44,77,JJ,AJ = 18 combos (60%)
Given that in this example the BB has fewer QQ+ combos he should protect his marginal showdown value hands by slowplaying his sets with a high frequency. Otherwise his calling range would become so weak that he opens himself to getting overbet for value very wide. Also ignoring sets valueraising on the river since this effect gets (partly) calcelled when UTG makes a higher set, or straight or flush.
Potsizes and betsizes:
Flop = 6.5, betsize = 4.9;
Turn = 16.3, betsize =12.2,
River = 40.7, betsize = 30.5.
Now lets look at the value of betting QQ 3 streets. Given runout 2h3c, counting combos from he river:
First cbet works 28/84 times: 28/84*6.5
Turn bet works 24/84 times: 24/84*16.3
Rive bet works 11/84 times: 11/84*40.7
River bet loses 9/84 times: 9/84*(-4.9-12.2-30.5)
River bet wins 12/84 times: 12/84*(40.7+30.5)
Total = 8.7bb which is 134% out of the 6.5bb on the flop while it has 78% equity on the flop vs the BB range.
And note that this runout was one of the most favorable runouts for QQ.
AJ cannot bet the river since it doesn't fold out better and has only 23% against 44,77,JJ,AJ.
On the flop, JTs had 57% against the flop calling range and TT 47%, so JTs is the worst hand that UTG can bet for value here. Also TT has very smooth equity against the BB range on any turn, so it would be a waste to turn that hand into a bluff. Mid pairs should be checked back here with a high frequency.
On the turn, if it is a blank, KJs is behind (40%) the calling range and AJ is slightly ahead (54%. AJ is he worst hand that can be bet for value. This implies that KJs should be bet with a low frequency since it still can force out equity from hands like AQ. Note that this low frequency can also be 0%.
On the river, QQ is a clear value bet (57% when called). Since AA blocks half the AJ combos it is no longer a value bet (40% when called). This likely implies that both UTG modifies his barreling frequencies with QQ-AA, and that the BB calls some KJ-QJ because they block the KK-QQ value combos and not the AA.
In order to balance all ranges it is also very important to balance your check back ranges, so you have to check back strong hands on the flop and turn in order to defend against both floats and the BB turning the bottom of his bluffcatching range into a bluff with impunity.
But I wanted to leave some material for the talented Mr. Sulsky!
I'm not going to argue for a precise near-optimal strat for this board, but I do want to suggest that the analysis so far shows some lines are likely to be dominated. For example, betting 2 streets with JTs unimproved, or betting 3 streets KJs unimproved, or even betting 3 streets with AA unimproved (at least given these preflop assumptions and the assumption of no flop x/r- in practice it's almost certainly optimal to go three streets with any overpair). A hand like JTs is a "one street" hand, so it's reasonable to bet one street with it- you pick which street (or mix up which street).
Try to design your ranges so that you get the right amount of bets in with your range and have good board coverage. For example, on the flop, you want to be able to call one or two large bets on almost any runout after checking- and to do so you'll need to check back a flushdraw or straight draw occasionally against a tough opponent or else he'll overbet on those cards. You'll also want to check back some made hands which can call a bet, for example, AJ-JT. And of course you want to hit some overcards and some blankish cards which you'll do by checking back middle pairs and overs. Similar considerations apply for your cbets.
Be careful not to add too high a bluff multiplier in this spot, since if you bet too many underpairs or overcards OOP can punish you on a board like this by semibluffing frequently.
As GT noted, to get a reasonably precise analysis here (without spending a ton of time working) we need to make some very large assumptions- namely that OOP never raises and defends ~1 minus alpha on every street, that we bet .75 pot on every street, and that our flop xback ranges are balanced enough we can get away with our cbetting strat. None of these things are likely to be true in practice, and so you'll have to just think hard about each decision- I can't give you a formal methodology which will easily tell you what to bet in spots like this. To be honest, I don't think anyone is playing particularly near GTO in spots like this, myself very much included.
I'll refrain from asking all the questions I have and just touch on a few...
Game Theory, when you said the following: “Betting 0.75 times pot on 3 streets means there should be 1 value combo to every 0.75 bluff combos on each street. That means the value part of his flopbet range is (0.57)^3=0.187.
Or 4.36 bluff combos to every value combo on the flop.” I became very confused. Can you try explaining the logic behind this math to me again somehow? I'm having trouble understanding how you reached the 4.36:1 ratio.
Ben, can you elaborate on “I do want to suggest that the analysis so far shows some lines are likely to be dominated. For example, betting 2 streets with JTs unimproved, or betting 3 streets KJs unimproved, or even betting 3 streets with AA unimproved (at least given these preflop assumptions and the assumption of no flop x/r- in practice it's almost certainly optimal to go three streets with any overpair)”? I don't understand precisely what you mean when you describe a line/strategy as “dominated”. I'm confused because the JTs / KJs examples seem to be examples of poor line choices while the AA line is described as optimal - yet all are examples of dominated strategies?
Also, here's my first attempt at developing a flop betting range:
http://gyazo.com/fe365bb5ec0294e58d1f4c606398d7e5
and a flop checking range:
http://gyazo.com/d3b6009206f35f2f7c5337356feb676f
My checking range includes those mid pairs 88-TT that are almost certainly best included in a flop checking range and is “balanced” with some combos of Jx, AK, AQ, KQ overcard type hands, and a few A3s/22 type hands which I've removed from my betting range in order to keep my bluff to vbet ratio a bit lower.
Do you think these ranges are reasonable?
+1000
After correcting the numbers in my first post, a 2:1 bluff:value ratio seems closer than the 4:1 I came up with earlier. But be aware that this is only a very rough estimate under a couple of strong unrealistic restructions: UTG can and will bet all his value combos on all three streets, he can only bet 0.75 times pot on every street, the BB cannot bet or raise on any street.I don't think that it will often be GTO to valuebet QQ/KK but not AA. Not only because a GTO calling range preflop would include QQ/KK, but also because that would imply that calling KQs-QJs is better than AJ:
Betting 0.75% times pot the BB needs to call 0.75 to win 2.5, or 30% equity:
But then KJs-QJs have almost 40% equity, so there is no need to call AJ when we have a much better bluffcatcher.
The only downside to this is that we leave ourselves open to let AJ make two sides bets: fold out split pots and get called by worse.
Lets figure that out first:
On the river, the BB has: 44,77,TT-JJ,AJ,KJ-QJ:xx,TJ:xx = 36 combos unremoved. And 25 when UTG has AJ.
The pot is 40bb and the bet is 30bb.
Assume the BB defends KJs-QJs,50% of AJ, JJ,77,44.
That yields to
7 combos of better hands (44,77,JJ)
3 combos of AJ that fold
3 combos of AJ that call
4 combos of KJs-QJs that call
8 combos TJs,TT that fold.
EV of checking behind: 40*(12 + 1/2*6) /25= 24.
EV of betting 30: (-30*7 +40*(3+8) + 1/2*40*(3) + (100-30)*(4))/25 = 22.8 so he cannot profitable bet AJ.
Is it possible for the BB to make it worse for UTG? Yes it is!
Lets now look at the value of checking behind with QQ/KK on the river for UTG.
We need to actually split QQ/KK into two subranges, one with the Qh/Kh and one without, since the Jh is on the flop so QhJh/KhJh are not longer in the BB range. Since so far the BB has played KJ and QJ identical, we can take QQ without loss of generality, since the case for KK will have the exact same odds.
So QhQ is a better hand to valuebet, it will get called by one combo of QJs more.
Checking back yields: 40*26/35 = 29.7
The range of BB is
9 combos of better hands (44,77,JJ)
6 combos of AJ that fold
6 combos of AJ that call
5 combos of KJs-QJs that call.
9 combos JTs,TT that fold.
Betting 30 yields: (-30*9 + 40*(6+9) + (100-30)*(6+5))/35 = 31.4.
This is only slightly better than checking behind. This got me thinking that the BB can defend even better to make it unprofitable for UTG to bet QQ-AA on the river. The way to do this is to check raise bluff rivers.
This is my conjectured strategy. When UTG bets 30, raise all-in with JJ, 77 and 2 combos of JTs. (Choose the combos of JTs random or uniformly over all suits otherwise you can get exploited by an opponent who calls with AdJd if you only do it with {JsTs, JcTc}.)
The pot is 40, our opponent bets 30, and needs to call 50 more for a pot of 200. Hence his required equity is 25%.
Here are the equities of QQ, AA, AJ and 44 against the check raise all-in range:
Bingo!
Now we can do the calculation of valuebetting QhQ/KhK again:
Checking back yields: 40*26/35 = 29.7
The range of BB is
9 combos of better hands (44,77,JJ)
3 combos of JTs that will shove
6 combos of AJ that fold
6 combos of AJ that call
5 combos of KJs-QJs that call
6 combos TT that fold.
Since UTG is indifferent between calling and folding to the all-in we can assume without loss of generality that he folds. This makes the calculation of the value easier. (Note that this does not imply that always folding is optimal itself.)
Betting 30 yields: (-30*(9+3) + 40*(6+6) + (100-30)*(6+5))/35 = 25.4, less than 29.7!
UTG can no longer bet 3 streets with QQ, KK or AA without getting exploited, even on the best possible runouts!
The implications of this are gigantic, UTG can no longer bet 3 streets for value with 27 combos, hence his bluffing ability on earlier streets greatly dimishes, he is forced to check behind much more often. However, in non static games, the value of betting overcards on the flop for instance increases since his hands can improve or bluff more effectively when overcards fall on later streets, of course for draws the same applies.
First off, if UTG cbets 18% value and 82% bluff on the flop, he comes extremely vulnerable to getting checkraised, which he then has to counter by floating air and/or 3-betting the flop when he holds a lot of non nutted strong hands, called overpairs. After correcting the numbers this becomes a 34% value and 66% bluff on the flop, which is far less vulnerable.
I'm not going to argue for a precise near-optimal strat for this board, but I do want to suggest that the analysis so far shows some lines are likely to be dominated. For example, betting 2 streets with JTs unimproved, or betting 3 streets KJs unimproved, or even betting 3 streets with AA unimproved
It is optimal to bet most of your JTs combo on the flop and check back with AJ. Since a lot of hands from the BB contain an A, letting the BB see a turn for free is much worse with JTs than with AJ.
(at least given these preflop assumptions and the assumption of no flop x/r- in practice it's almost certainly optimal to go three streets with any overpair). A hand like JTs is a "one street" hand, so it's reasonable to bet one street with it- you pick which street (or mix up which street).
As I've shown in my previous post, going three streets of value with overpairs is exploitable by a decent margin. This leaves room for some set combos to x/r flops and turns. But I think they key part about this subgame is that UTG has 18 overpair combos and 9 set combos, while the BB only has 9 set combos. These overpairs beat 90% of the BB range on this flop, so they definitely have strong value. This allows the BB to barrel wide for value and as a bluff on early streets.
The main objective of the BB must therefore be to make his defense ranges very strong, discouraging the BB from betting overpairs 3 streets for value, and hence shutting down his ability to bet flops and turns with a wide range. For this reason it is very important that the BB keeps his calling range very strong and nutted. Check raising the top of his range on the flop will allow UTG to effective bet up to AJ for value, which is terrible for the BB.
I imagine that the GTO strategy for UTG will go for 2 streets of value with overpairs most often, balancing with checking back flops and turns with a decent frequency in order to protect himself against getting check raised. Certainly he has to bet his overpairs with a nonzero frequency on the flop to have an uncapped range on Q,K,A turns/rivers.
Or 4.36 bluff combos to every value combo on the flop.” I became very confused. Can you try explaining the logic behind this math to me again somehow? I'm having trouble understanding how you reached the 4.36:1 ratio.
If you bet 0.75 times pot on the river you need 57% valuebets. Hence if you have 57 value combos and 43 bluff combos you can bet all 100 on the river.
Now on the turn, if you bet 100 combos on the river and your opponent cannot raise you you can now bet 175 combos.
Lets see the EV of a bluffcatcher (pot is 1000 on the flop, flop bet 750, pot is 2500 on turn, river bet 1875):
Fold the turn, EV = 0
Call the turn, fold the river: EV = (75*1000 +100*(-750))/175 = 0
Call the turn, call the river: EV = (75*1000 + 43*(+1750)+57*(-750-1875))/175 = 0
So if you continue to bet 57% of your range on each street with air you make your opponent indifferent between bluffing 0, 1, 2 or 3 streets with air like A2s. If you start doing this on the flop you only have 18% value and 82% bluff. But this is not realistic.
Since poker is not static, A2s can beat KJs. The value of betting say QQ or even JJ isn't so high that you win 100% when called. And if you bet so much air on the flop you open yourself up against a profitable check/raise by the entire BB range, which in turn would imply that you need to defend with bluffs.
As for your betting range, I think you bet too much given that betting 3 streets with QQ can be exploited easily. Also in general you should rather bet your lowest pairs than your medium pairs, since you rarely fold out better and medium pairs are less vulnerable, thus giving free cards hurts less with them.
If they cbet very wide and give up all their air then you can check raise any hand profitably. But you still need to be looking at all your ranges, for instance they might barrel you much more if they think that you checkraise all your sets and overpairs.
It is very clear to me that BB needs to continue with at least 57% of his range when UTG bets 75% of the pot. But when you say that "If you bet 0,75 times pot on the river you need 57% valuebets. Hence if you have 57 combos and bluff 43 combos you can bet all 100 in the river."
I thought that if you come to the river with 57 value combos and intended to bet 0,75 of the pott you could only bluff with 17 combos( 75/75+100+75=0.3x57=17,1). In which way am I misunderstanding what you are saying?
You are correct, I made a mistake.
Accidentally I confused the ratio of hands that the BB must defend in order to make UTG indifferent to bluff with air on the one hand with the value to bluff ratio on the other hand.
You are the first to notice my mistake, I have corrected those posts and put it in the first line.
I also made a small mistake. If we are offering 30% pot odds(75/75+100+75=0,3) and have 57 value combos the correct number of bluff combos should be 24 (57/0,7=81,4-57=24,4)
First cbet works 28/84 times: 28/84*6.5
Turn bet works 24/84 times: 24/84*16.3
Rive bet works 11/84 times: 11/84*40.7
River bet loses 9/84 times: 9/84*(-4.9-12.2-30.5)
River bet wins 12/84 times: 12/84*(40.7+30.5)
where all these 24/84 11/84 times etc. come?
I made these ranges for calling multiple streets:
These numbers are the number of combos that are left, from the perspective of the UTG player holding QQ. I did this in order to calculate if going for 3 streets with QQ was most profitable and to look for how the BB could improve his strategy.
I got .77142 for flop bluffing frequency. Not sure if im doing this right. Betting .75P implies we need to check back .75/1.75 of the time OTT and OTR?
-OTR we have 3 bluffs for every 7 value hands.
-Amount of betting combos OTT relative to OTR=10*7/4=17.5. Betting 10 hands OTR and checking back 7.5 bluffs =3+7.5=10.5 bluffs OTT
-Amount of betting combos OTF relative to OTT=17.5*7/4=30.625. Betting 17.5 hands OTT and checking back 30.625-17.5= 13.125 bluff combos. Total bluffing combos OTF=30.625-7=23.625
-Flop bluffing frequency =23.625/(7+23.625)= .77142
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