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forming ranges around exploitive play.
some background:
so lately i've been doing a lot of study around some (for me) very fascinating game-theory concepts like maximum exploitive strategy, unexploitable strategy etc. specifically, the (0, 1) range model has helped me a lot in my quest to get my brain around this on a conceptual/practically applicable level. and this has lead me to want to do a heap of work on forming my own ranges in spots with the goal of exploiting my opponent's strategies. so here's one exercise i did recently based on a hypothetical holdem situation, against one of the regs i have the most hands on in my database (his screen-name is fun_ex700, with no _ in the middle). this guy is a nitty, yet positionally aware, 50nl FR reg on stars. so here's my made-up situation and my attempt at exploiting his strategy (as best i can infer it from HUD stats/reads). this post also outlines the steps in/order of our thought-processes, as best i understand them, involved in forming maximum exploitive strategies.
before i start, i want it to be clear that this is not an attempt at a "strategy post", i hold no delusions about my skill level at no-limit holdem - i fucking suck at this game. but i'm trying very hard to get better.
The situation:
villain opens to 3x in CO with 100bb effectives
hero is on the BU with two cards.
both blinds fold 100% of the time (just so we don't have to factor in too many variables)
let's form an optimal exploitive strategy as best we can. how do we go about doing that?
- first, what's his strategy?
some stats:
VPIP: 10.6%
PFR: 8.28%
ATS: 28%
4b PF: 2.78%
3b PF: 3.68%
fold PF 3b: 88.6
Cbet flop : 66%
fold to flop CB: 33%
these seem to be the most relevant stats in getting a feel for his playing style/trying to determine an optimal exploitive strategy (though i'd warmly welcome suggestions of other relevant stats)
i have not got down to him yet on my list of regs to study in my database, so i have no notes on him except that he opens for 3x in all positions from UTG through to the BU.
so after a brief overview on his playing style, let's form some ranges and assess how we think he would probably play them. which is always our first consideration in forming our own ranges
so what's his preflop opening range?
with incredibly nitty blinds, probably something like:
[22+,A2s+,A8o+,K8s+,KTo+,Q8s+,Q9o+,J8s+,J9o+,T7s+,T 9o+,
97s+,86s+, 76s, 65s, 54s]
what's his preflop 4bet range?
we'll say [KK+,AKs,ATs]
(ATs is in there just to add some bluff combos because he probably does 4bet bluff some non-zero %. especially vs me - any aware 50nl reg would probably see me as being excessively aggro to the point of being spewy pre and post-flop)
what's his flatting range?
probably something like [88-QQ,AKo]
so his different ranges break down as such:
opening range: 394 combos
flatting range: 42 combos (10% of opening range)
4b range: 20 combos (5% of opening range)
4b/fold range: 4 combos (20% of 4betting range)
4b/call AI range: 16 combos (80% of 4betting range)
in total, he continues to my 3b, by either flatting or 4betting, 15% of the time. when he 4bets (5% of the time), he is willing to put the rest in 80% of the time.
now to forming our own ranges..
so what is our 3bet for value range?
while we do get value from his 3b-calling range with hands like
JJ,QQ,KK (because he is calling with 88,99) we do not want to have to 3b/fold them (as best i understand) especially if he is 4b bluffing some non-zero % of the time.
i'm unsure of the validity of the above statement. but anyway,
thus we want to value 3b a range which we are willing to felt vs a 4b. his 4b/felting range is [KK+,AKs]
thus the only hand we can 3betting for value (assuming above premise regarding "never wanting to 3b for value/fold" is correct) is AA, as KK only has 32% vs KK+,AKs. while this seems bleak (we can't even 3bet KK for value?!?!?! wtf?), there is a flipside to this coin, which is his exploitability to 3b bluffs. which i'll get to later.
what is our flatting range?
as best i understand this, this range should contain the maximum amount of hands we think we can play profitably vs his range (which don't have a higher EV as 3bets for value). to determine this we need to consider a few factors:
- card advantage
- positional advantage
- skill advantage
- initiative advantage
we also need to consider how he plays his range postflop. his opening range is currently relatively wide. and doesn't connect particularly well with flops. we can also assume that he is cbetting a relatively weak range because he has initiative in a heads up pot. and cbetting is all the rage in HU pots with initiative. thus we are looking to play hands which have decent equity against his opening range, and also hands which flop some decent equity so we can semi-bluff raise/float some flops, which exploits his weak range (the fact he is likely to play very straightforward after cbetting the flop makes fucking with him like this more enticing)
after considering all of these factors, i came up with something like:
[22-QQ,A2s+,AJo+,KJs+,KQo,QTs+,QJo,J9s+,T9s,98s,87s,76 s]
i think that determining flat-calling ranges is probably the hardest one of them all, so i'll go into more detail about why chose that range. 77-QQ is in there for obvious reasons - we have good equity against his range, we can flop sets, and also float flops which he is unlikely to have connected with. 22-66 i was kind of torn on, they only flop very well something like 1/10 of the time, and they are pretty shit candidates to use as floats vs a weak range because their equity is pretty black/white. we either flop a set or we don't. and when they don't flop a set, they rarely have much equity against any pair, or even two naked overcards. so i'm unsure if i can even profitably flat 22-66. A2s+ seems pretty standard because these can flop flush draws (which have great equity which will allow us to exploit his weak cbet range with semi-bluffs etc), plus we often get a free bet on A high flops when he cbets with a weak range. AJo+ flops pretty well against so many worse Ax hands in his range, as does KJs+,KQo,QTs+,QJo+ due to amount of dominated K/Qx hands in his opening range. the rest of the hands are basically in our preflop flop range because they have the value of suitedness/connectedness and so they can flop pretty well (that is to say they have decent and stable equity across ranges), and thus they can be candidates for flop semi-bluffs, which seems to be an important aspect of exploiting this guy's weak opening/cbetting ranges.
so now, we need to determine:
1 - whether or not we want to be 3b bluffing and then;
2 - what range we want to 3b bluff with,
we determined earlier that he is folding to our 3bet a total of 85%. which is pretty huge. a bit of quick math shows that if we 3bet to 9bb, we require him to fold 9/(9+4.5) = 66% of the time (this is our required fold frequency in a vacuum, not factoring in the fact that we have post-flop equity). so we see that he is verrrrrry exploitable to 3x 3b bluffs. so we have figured out our answer to part one of the 3b bluffing question - we most definitely do want to be 3b bluffing this guy
now, with what range? there are three factors to consider here, everyone knows them:
- hands which are NOT profitable enough to flat or 3b for value
- a range which increases our fold equity (has blockers to his continuing range)
- a range which has the most pot equity against his flatting range (because we are never going to turn any of this range into 5b bluffs, as he stacks off with 80% of his 4b range, we are looking for hands which flop well vs his flatting range)
so, let's look at some candidate hands based on the above criteria:
an ace is our most valuable blocker, but most Ax hands have already been determined to be profitable enough to flat. here is a selection of hands which are probably good candidates to 3b bluff based on above criteria:
[A2o-A8o,K6s-KTs,K9o-KJo,Q9s,Q8s,J7s,J8s]
however, if we 3b all of those hands, even this nit is going to notice we are 3betting him like a monkey on a decent dosage of PCP, and will probably adjust (i recently had a nitty reg with similar stats start playing like an utter madman against me after i pissed him off enough with my 3b/4b's)
so here we want to determine exactly what % of our 3b range we want to be bluffs. the nut/bluff ratio in our 3b range should be a direct result of his fold to 3b frequency. obviously the larger % he folds to 3bets, the more of our 3b range we want to be composed of bluffs. because his 4b range is dominated by nut hands, we found we may not even want to 3b KK, but an opponent which forces us to tighten up our 3b for value range is usually going to be highly susceptible to a wide 3bet bluff range.
i actually don't know how to determine the game-theory optimal 3b bluff frequency here. (if anyone can help me here that would be much appreciated), but i'm intuitively going to advocate a 3 or 4:1 ratio of bluffs:nut hands in our 3b range in this particular case.
so we are 3betting 6 combos for value.
thus a 3:1 bluff:nuts ratio would have 18 bluff combos
and a 4:1 bluff:nuts ratio would have 24 bluff combos
so we could use:
- KTs-K7s and two combos of A8o for a 3:1 ratio
- or A8o-A9o for a 4:1 ratio
i prefer the latter, and to be honest, i want to 3bet bluff this guy wayyyyy more, but i'm unsure how to go about figuring out what the optimal amount is.
so our preflop range here breaks down as such:
3bet: AA,A8o,A9o
-3bet/call: AA
-3bet/fold: A8o,A9o
flat: 22-QQ,A2s+,AJo+,KJs+,KQo,QTs+,QJo,J9s+,T9s,98s,87s,76 s
fold: the rest
some concluding thoughts:
- i'm not sure about the "preferring to flat KK because it is -EV to stack off with against his felting range" statement. it seems absurd that the only hand we can 3bet for value is AA.
- even with a 4:1 bluff:nut ratio, we are still only 3betting 2.3% of total hands. i think we can be 3betting this guy wayyyyyyy more. but our incredibly thin value 3b range kind of restricts our 3b bluff range (is that so, or can we just ignore it and 3b a way more unbalanced range, like 7:1 or something)
so this took me absolutely ages, and i'd love to hear some feedback on my thought process and the conclusions i came to. i also hope it helps other players better understand the process of forming their own ranges around exploiting their opponents' tendencies at least to some degree.
for those interested, here are some of the threads i have been studying which address the concepts i have been trying to get my head around and are relevant to this post:
- http://www.flopturnriver.com/pokerfo...ns-161354.html
- http://www.flopturnriver.com/pokerfo...ng-160256.html
- http://www.flopturnriver.com/pokerfo...he-163171.html
- http://www.flopturnriver.com/pokerfo...em-156835.html
- http://www.flopturnriver.com/pokerfo...er-184365.html
- Pokersback
- ISF - There's No Such Thing As a Made Hand
- ISF - There's No Such Thing As a Made Hand: Part 2
- Spoony Exercises 1-7 or however many there were (look in BC Digest for these, i'm not linking each one individually)
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