static flop

A flop texture that improves the preflop raiser's pot share such that an immediate profit is earned with the bottom of the preflop raiser's range in asymmetrical range situations.

dynamic flop

A flop texture that improves the preflop caller's pot share such that an immediate profit is not earned on the flop with the bottom of the preflop raiser's range in asymmetrical range situations.

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static flop

In asymmetrical range situations on static flops, the preflop raiser will have such a significant pot share that the only hands to be checked will be bluffcatchers that will earn more by checking than betting.

In asymmetrical range situations on static flops, the preflop caller will have such an insignificant pot share that it will be correct to offer a profit to the bottom of the preflop raiser's range.

The more static the board and the greater the pot share for the preflop raiser, the greater this effect will be.

dynamic flop

In asymmetrical range situations on dynamic flops, the preflop caller will not allow an immediate profit to the bottom of the preflop raiser's range due to the abundance of profitable draws. The preflop raiser will build a bluffing range with draws in order to maximize the profitability of the bluffing range, while giving up on the weaker, unprofitable bluffs.

The more dynamic the flop, and the greater the pot share for the preflop caller, the greater this effect will be.

extreme cases of asymmetrical ranges

On extremely static flops with extremely asymmetrical ranges, the preflop raiser's pot share may become so great that it will be correct to bet 100%.

On extremely dynamic flops with extremely asymmetrical ranges, the preflop caller's pot share may become so great that it will be correct for the preflop raiser to bet 0%.

I believe the former case to be likely to happen in practice, while the latter will be extremely rare.

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While the threshold flop between static and dynamic is not known, I believe that these definitions hold true in asymmetrical range situations. The threshold between static and dynamic flops in asymmetrical range situations will be dependent on the exact ranges in question.

I've been thinking about the spectrum of flops lately and thought this was the right place to put this.

Each situation has it's own flop spectrum ranging from the most static flop to the most dynamic flop. The threshold between static and dynamic will be different flop types depending on the preflop action. For example: button raises, only the big blind calls. Flop falls XXX. The flop benefits the big blind in such a way that, should both players maximally exploit each other, neither opponent will have an advantage. This is the threshold flop,* the probability of which occurring is very close to zero. The threshold flop will be a different combination of cards depending on the starting ranges. So button vs big blind will have a different threshold flop than cutoff vs big blind.

By looking at the extreme situations, we can see a pattern in the spectrum of threshold flops:

6 handed limit holdem

utg raises, only the big blind calls.

flop: XXX

Think about what kind of board will benefit the big blind just enough to negate utg's advantage. Since utg is quite strong here, I'm guessing it has to be a board that both uncaps the big blind's range and caps utg's range. My guess is a flop like 987r, T87r, or T98r, but my guess isn't important. The point is that it takes a very draw friendly board to negate utg's huge advantage preflop.

Compare that situation to this:

button raises, only the big blind calls.

flop: XXX

Here, the threshold flop will be very different than in the previous example because the ranges are much wider and both players can have uncapped ranges on many board types. My guess here is a board like T94r, T83r, or 983r, but again my guess isn't important. The important thing here to notice is that the board is much less draw friendly than in the previous example.

Add it all up and imagine the spectrum of threshold flops.

Why is this important? Because in the former example, static flops make up the vast majority of flop textures, while in the latter example there are many more dynamic flops, which by definition benefit the player with the weaker preflop range. If the player with the weaker preflop range can hit more dynamic flops, then this will bring down that player's folding frequency relative to a less advantageous preflop position.

Yeah but why is this important? I don't know, maybe I just like the word "spectrum" and will use it whenever possible.

* "The flop benefits the big blind in such a way that, should both players maximally exploit each other, neither opponent will have an advantage. This is the threshold flop..."

I'm not sure about this part. Perhaps I'm wrong and the threshold flop is one that doesn't improve either players ev relative to preflop. If the definition of static flop holds, then the stronger range will have a profitable bluff with the bottom of his range on static flops. If the big blind has gained ev due to the nature of the flop, then the flop is by definition dynamic. Because of this, I think that the threshold flop is the only decision point that will result in both players bluffing and folding according to the indifference principle, if both players are maximally exploiting each other.

On the more dynamic flops, the weaker preflop range will call more frequently, while the stronger preflop range will bluff less frequently.

On the more static flops, the weaker preflop range will fold more frequently, while the stronger preflop range will bluff more frequently.

What about the fact that strong ranges have less bluffs to bet? This is the extreme case of asymmetrical ranges, where the strong range bets 100% and the weak range folds 100%. This is a rarity that I don't think will occur on the flop in neither a no limit nor a limit holdem game, unless you're playing against a really tight player.

/ramble

Just looking at the first post, I have no idea if those are widely accepted definitions in the first two paragraphs, but I personally don't like them, partly because "static" and "dynamic" have fairly clear definitions in the English language.

For me, a "static board" is one where equities will not change much on the next street. A "dynamic flop" is one on which a great deal of turn cards will radically alter the equities of many combos in both player's ranges.

When players have optimal ranges for opening and calling pre-flop, it's actually quite rare for either player to have a large "range advantage" in equity terms. Although we often speak of "a good flop for the big blind's range" or "a good flop for the pre-flop raiser", I'm not convinced that it's because the board is static or dynamic. On most boards, optimal pre-flop ranges will both have close to 50% equity*, whether the board is wet, dry, high, low, static, or dynamic. If someone's range has less than 40% equity on many common boards, his pre-flop range is likely too loose/weak/unbalanced.

In addition, just because someone has a range advantage, it does not follow that they should bet more often. Their bluffs will likely have a higher EV than on other boards because of the higher amount of fold equity, but maximising EV of the "value hands" might involve more checking to induce, or slowplaying.

I enjoyed the post nonetheless, and would like to see some example boards for further discussion of the definitions. I'll have a look at the "ramble" more closely tomorrow.

* The BB will typically have less than 50% equity, but he doesn't need that much to break even, since he saw the flop for a discount price.

I think that both of these conditions are correct and are perhaps worthy of inclusion in the definitions somehow.

It's true that in no limit, the advantage isn't as obvious. Defending ranges are tighter and have to be able to withstand more future action than in a limit game due to the geometrically growing potsize and the resulting betsizes. The result is that the preflop raiser has a much smaller postflop equity advantage in no limit compared with limit, but it's still there. I would even argue that a 5% equity advantage in a no limit game is worth more to the preflop raiser than a 15% equity advantage is worth to a preflop raiser in a limit game, specifically because of the large bets.

Because of this effect, the threshold flop in a no limit game will be more draw heavy that that of a limit game with the same positions and preflop action. It takes a more draw heavy board to benefit the preflop caller's range in such a way that his strategy gains ev relative to preflop. Static boards are more plentiful in a no limit game because of this. The result is that in no limit, we should more frequently build our bluffing range from the bottom of our range because of the frequency of static flops. This doesn't mean that I don't semibluff on static flops. I do. I bluff a ton on static flops specifically because by definition the opponent should offer an immediate profit on the flop equal to my ev of checking back the flop with those bluffs. On the other hand, on dynamic flops, because by definition these flops don't offer an immediate profit for me with the bottom of my range, I give up on more pure bluffing opportunities, while semibluffing a lot with my stronger draws.

It's also true that in no limit, on earlier streets, slowplaying is a part of any good strategy, particularly on the more static boards with hands that block your opponent's range. In a limit game, it's tougher to make up those missed bets, which makes slowplaying more rarely correct.

no limit 100 big blind stacks:

button raises 3x, only the big blind calls.

2KAr

Here, I have lots of junky hands like 76s, 87s, 97s, etc, that will immediately profit by betting the flop. The flop is static by default because of this.

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button raises 3x, only the big blind calls.

QJTr

Here, I have lots of junky hands like 76s, 87s, 97s, etc, that will not immediately profit by betting the flop, so I give up on these bluffs. The flop is dynamic by default because of this. This example may be a bad one as I have not done any no limit range vs range analysis for this specific board, but I think it's far enough on the dynamic side that it's safe to say that we shouldn't bluff from the bottom of our range on this board. Semibluffs rule this type of board, while junk is not a profitable bet. Thus, the board is dynamic.

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So what is a static board in a no limit game could in fact be a dynamic board in a limit game. Thus the dynamic static threshold is dependent on game type, preflop position and preflop action.

Agreed. After posting, I couldn't immediately think of any flop textures that would fit my definition of "static" that didn't also fit yours, although I probably could find some if I thought about it a lot.
I also realised that you're a fixed limit guy. I think that probably changes a few things strategically, for the reasons you mentioned. I won't pretend to know what "good" pre-flop ranges look like in limit, let alone the optimal way to play them post-flop. (I'm not exactly an expert NLH player either, but the theory fascinates me.)
I agree it's a fairly static board. There are no flush draws, but jacks, queens, tens, threes, fours and fives on the turn will all complete gutshot straight draws.
I would initially have thought that the button has a clear range advantage and "fold equity advantage" on this board, but using pre-flop ranges based on an approximation of what Snowie usually does, it's surprisingly close.

Pre-flop: Button has something like...
22+,A2s+,K2s+,Q6s+,J6s+,T6s+,96s+,86s+,75s+,64s+,5 4s,A4o+,K9o+,Q9o+,J9o+,T9o (38%)
BB 3-bets pretty wide, but usually calls with...
99-22,A9s-A6s,A3s-A2s,KTs-K2s,Q9s-Q7s,J9s-J7s,T8s-T7s,97s+,86s+,75s+,64s+,53s+,43s,AQo-A8o,KJo-KTo,QTo+,JTo (23%, a cold-calling percentage that would terrify most nits).

Pre-flop, the BB's calling range has 48% equity vs the BUT, and he's getting a discount. (When you consider he can 3-bet too, being in the BB isn't as terrible as some people seem to think!)

On AK2r, the button's range has a shade under 53% equity. It's risen a whole 1%.

I would have assumed that the Button can c-bet at a high frequency, but much depends on the sizing chosen. With a bet-size of pot, Snowie would actually check back 74% of its range, for reasons I can't fully understand or explain. If half pot is chosen, then betting 67% of the range is deemed optimal. The checking range includes a lot of top pairs with bad kickers along with queen high and total air. The betting range includes monsters, all draws, and indeed any two cards that have a backdoor flush draw or better. There's a mixed strategy for many of the air hands without BDFDs, with many having an EV of about 1.5bb (which is only 23% of the pot).

If the button bets half pot, the BB folds 41% of its range. It basically continues with a pair or a better, or a gutshot. The BB folds often enough for a 1/2 pot c-bet with ATC to be immediately profitable, but GTO isn't concerned with making immediate profit. It's concerned with maximising profit (or minimizing losses, if you want to think of it that way).
Without putting every combo in the calling range into Equilab and evaluating random turn cards, I'm pretty confident that the 60% continuance range of the BB will have a significant equity advantage over a 100% betting range for the Button.
Whether the BB can realize that equity OOP is a different matter entirely, but it should be obvious that hands like 99, QJo are already beating 76s and other random junk in the button's range, whilst AT is completely crushing it.

In short, the BB can defend 60% of its range, and go to the turn with an equity advantage if the button bets the flop too often or with a sub-optimal range. Or to put it another way, the BB can make an "exploitable fold" with some of its range on this board, because it will more than make up the EV with hands that continue.

I might look at the other flop texture tomorrow, but whenever I've done this sort of thing before, it's pretty amazing to see what happens. Not only do an optimal raiser and caller's ranges have close to 50% equity pre-flop and on the flop. On most runouts, they have close to 50% equity on every street.
I guess the old cliché that "Every hand is fifty-fifty" might actually be true.

Thank you very much for the analysis. It makes me wonder why I can't just bluff all of my junk on the flop though. If my opponent knew my strategy and made the adjustment of calling and raising more often, then my bluffs will fail but my value hands will benefit. Perhaps the value hands don't benefit enough to outweigh this possible loss of bluffing ev. I don't know.

If the big blind is making exploitable folds, then why would we choose not to bluff with all of our junk? You say that the big blind will gain ev with the hands that continue, but if I'm giving up on my pure bluffs on the turn, then what's to stop me from being bluff heavy on the flop? Is it simply because those potential flop bluffs earn more by checking?

The folds are only "exploitable" in the sense that he's not defending enough to prevent you making an immediate profit based on the pot odds and the basic fold equity equation.
But villain's aim isn't to prevent you making money though. He just wants to maximise his own EV, which is why he folds non-profitable hands.

A real-life player that folded (much) more often than a GTO bot would be more directly exploitable, because if he folds too often, then more of your air hands would gain EV by bluffing. If someone folds too often, then you exploit his imbalance by bluffing more, ldo. Working out how much more to bluff is the tricky part.
Yes, this. They earn slightly more by checking against an optimal defence. Against an optimal player, you can't just bet ATC every time and expect to make a ton of money, because his continuance range will be optimal, and your betting range will contain too much junk, meaning any money gained from folds on the flop is cancelled out by the EV you lose from villain's calls.
Some hands need to be put in the "give up" bucket, such that the EV of your entire range is maximised. (Clearer example: We might loosen our opening ranges pre-flop because villains are folding their blinds at "exploitable frequencies", but we don't start opening 100% of hands UTG, because only some hands become +EV opens, not all of them.)

It should be mentioned that the EV difference between checking and betting your air won't be a lot on most flops, but it will add up over time. On the AK2 example, all the air hands (undercards without even a backdoor flush draw) have roughly the same EV whether they check or bet, so it's not a blunder to bet them.
In addition, it should be pointed out that betting the air doesn't necessarily lose money. It just doesn't "win" as much as checking back.
More obvious errors occur when you start betting too often on boards where you will get called (or check-raised) at a high frequency and have even less equity. In those spots, betting too much air could actually lose money, as it would essentially be firing it into the abyss.

I was trying to wrap my head around this and I couldn't come up with a reason for why the hands without backdoor flushdraws would win slightly more by checking back. That is until I thought about how these hands would win pots. The backdoor flushdraw is strong and will retain that equity even when called. The hands without backdoor flushdraws basically have no chance of winning when called because when we bet these hands and our opponent calls, our pair outs are ruined. So by checking we keep our pair outs strong and we bring more value to our range by keeping our opponent's range as weak as possible.

If we get called by one pair, we can backdoor trips or two pairs whether we have a BDFD or not. (Most of the EV comes from fold equity, however). The hands with BDFDs also have a smidgeon of additional showdown equity gained from potential runner-runner flushes, so they have slightly more EV than offsuit undercards, which could make two pairs but lose to a backdoor flush (or better). Apparently this extra smidgeon of equity is enough to turn the BDFD hands from checks into bets at some frequency. (The EV difference between betting 76s with BDFD and 76 without a BDFD is incredibly small, like 0.1bb or something, but it's enough to make the former a better hand to bet with than the other. Since we're going to bluff with some "trash" hands, we may as well do it with the best trash.

That's 10bb/100hands, which is hardly a small difference.

/nitpick

Update time.

I think pure bluffs would be really bad on a dynamic board for this very reason, which is why I give up on the low equity hands on dynamic boards.

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I haven't made any progress since posting this thread regarding range construction, but I've had good results. I booked my first ever losing year in 2015, but I think I played better than ever. Go figure. My loss for the year can be chalked up to both playing few hours live and shot taking. I probably have a positive winrate if all stakes are considered equal, but due to a few shots that went badly, I lost money this year. The heads up no limit holdem battles against a tough tag didn't help the winrate, but I think I learned a lot from playing him.

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Now, with regards to range construction against humans, I still follow the guidelines that I set in the original post in this thread. I mix it up a bit with key draws and hands that I think are on the margin of bluffcatcher/value hands and I think it benefits my strategy to do so especially against good players. However, without reads I just assume that my opponents are terrible at poker and I'll not play mixed strategies unless I have a good reason to do so.

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I think the topic of range vs range advantage is very interesting and if we can make strides towards maximizing the advantage when we have it, as well as minimizing the disadvantage when present, we can get a little closer to the goal, which is of course to play solid poker, whatever that means.

Here's my response to a private message that I received the other day regarding range vs range advantage and the question "can we over fold with a range advantage?" In a nutshell, I don't like it. However, live low stakes no limit holdem players tend towards having a hard time putting in big bets as bluffs, so there's definitely room for exploitive folding here. How much of your range you can safely fold depends on the quality of your reads. Readless? I don't give people much credit, but with solid reads that have been confirmed over and over again, I'll fold big chunks of my range. Here's the question:

I responded:

63% according to equilab after betting, but to my surprise the big blind has ~49% equity after the flop falls, which is an improvement from the ~45% equity that the big blind has after calling preflop. Of course, my equity goes up against bad players that call too much preflop, which is my excuse for being way off.

Also, I accidentally left out AKo from the big blinds 3 betting range, which brought his equity down to 46% on the flop. If I take out A5s-A2s from his 3 betting range and put them in his calling range, that only helps my cause as far as raw equity goes.

After giving the big blind a looser defending range that included the likes of 74s, T6s, etc, that brought my pre betting equity up to ~60%, which is more my to my liking of course.

Given my exp lately playing LLSNL most opp. who bet/raise when they have a range disadvantage usually don't show up with the "nuts" (like top set or top 2pair etc...) they will show up with random baby 2pairs or trips on boards that smash our range or are way better for us.

Yeah we will have more nutted/value hands overall which is a good thing, but when we do get x-raised (which is never a bluff at LLSNL) i think we can exploitatively fold even to like a few combo of nutted hands
honestly...

BUT the real question is does this turn their range face up in this spot which allows us to over-fold/exploitatively fold most of our range... Or am i just wrong in this sense^

You're not wrong as long as you keep in mind that you're both exploiting and exploitable. How many times does your opponent have to check raise you before you start calling him down? Live low stakes? You can probably fold huge chunks of your range without reads or worrying about it. Online? Not so much.

Yeah your right i agree... tbh if you are exploiting anything in general you are exploitable...

I don't think many players at LLSNL until maybe 2/5 look to "exploit my leaks/tendencies (like folding the top of my range too often)" or try to make "plays at me because they think im capped here etc..."
I just think they DON'T adjust correctly and realize im bet/folding or that my betting range is too light in this spot etc... stuff like that.
In addition to that point they can only technically exploit us if they know what we have/have a lot of info like our range is face up here so they can maximally exploit that (and being completely value heavy in spots can be turning your range face up that's why i will bluff very often from time to time with the top of my range as long as it is a +EV spot to do so).


(Digress) Does "adjusting" mean if you are 1 step ahead of your opp. = adjusted to his strat by building an appropriate range? And how often do we need to "adjust" is this a myth or some psychology stuff like leveling...

At live low stakes no limit, I think it's good to make preemptive adjustments because opponents are almost always value heavy. I value bet thinner and bluffcatch less often live than I do online because of this.

Against better players, particularly online tags, I tend to call down more often when I have strong hands in my range and my opponent has few. It goes back to this:

I'd much rather avoid leveling wars whenever possible. Sure, using your reads and your opponent's tendencies against him is great, but if you're throwing hay makers, you become vulnerable to the uppercut, so to speak. Here's my take on leveling wars:

I'd like to talk about dynamic boards. Here's an example:

100bb effective no limit holdem

cutoff raises 3x, folds to the big blind, big blind calls.

567r

big blind checks, I do what?

I have this loose theory that the dominating draws, such as A8, A9, T9, T8s, Q8s, Q9s, J9s, and J8s should be bet at a frequency approaching 100%. I think the easily dominated draws such as A3, A4, K4s, K3s, and Q4s, should be bet at a frequency approaching zero.

Another example:

100bb effective no limit holdem

cutoff raises 3x, folds to the big blind, big blind calls.

467

Following the trend set above, I'd bet here with Axo, Kxo, Qxo, Ax5, Ax8, T9x, Tx9, at frequency near 100%. I'd bet with A3o, A5o, A8o, Q5s, Q8s, J8s, T8s, T9o, 98s, without hearts at frequency approaching zero.

I like to think that this gives my bluffing range some variation, and maximizes equity when called or raised, which will happen quite frequently on such dynamic boards in my experience.

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This would be incomplete if I didn't talk about my value hands. I have pretty tight value betting ranges on both boards because of the strength of my opponent's range. I'm currently betting 1/2 pot with my whole betting range in both examples without a read that the big blind likes to pay off big bets.

I just ran the first example through Snowie, and your theory seems to check out reasonably well. Snowie half pots about 30% of its range in that spot (it has a lot of overcards that missed completely), and to balance the straight, sets and two pairs, it definitely seems to prefer betting combos that are drawing to the nut straight with an 8. (A backdoor flush draw is also pretty essential). It's not quite so keen on 9x hands, although it does bet K9s, Q9s, J9s, T9s at some frequency.
There aren't a lot of combos in its range that are drawing to the idiot end of the straight (only A4s and A3s, but not K4s/Q4s), and again it bets those sometimes. I think part of the reason for this is that they can fold out better Ax hands.

The situation might be a bit different on the button. I'll have a look tomorrow if I get the chance.

My understanding is;

Static usually refers to a board state in which the player whos ahead now is unlikely to change.

Volatile boards are ones where relative hand strengths are more likely to change on future streets

wet boards tend to be volatile and static tend to be dry but boards like 732r may be dry but volatile becayse over cards are likely to come on turn/river

Thanks for the help. I think it's odd that Snowie doesn't bet A9.

Yeah, that all makes sense but I think we can simplify the problem by eliminating the terms dry, wet and volatile. It goes back to this:

This way, depending on the ranges in question, we can draw a line in the sand separating dynamic boards and static boards. Of course there will be exceptions, like against a player that calls too much in general. Against that opponent, our bluffs may not earn the immediate profit on static flops. Against the player that folds too much on the flop in general, our low equity bluffs may earn immediate profit, even on dynamic flops. However, I believe these to be the exceptions.

My mistake. I forgot to list it. A9s with BDFD gets bet 94% of the time. A9o is at 22%.

For completeness (all combos with BDFD as well as straight draw):
A9s 94%, A8s 100%
K9s 62%, K8s 100%
Q9s 35%, Q8s 100%
J9s 0%, J8s 77%
T9s 33%, T8s 100%
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A4s 80%, A3s 20%

It seems pretty clear (and intuitive) that the hands with the most raw equity against the likely continuance range are more likely to be bet. OESDs are better than gutshots, obviously.

Thanks again Arty.

I think it's odd that the J9s doesn't get bet at all even with the backdoor flushdraw. That's probably the hand that benefits most from getting folds from better hands, so I think it lends some credibility to my theory that it doesn't matter if better hands fold the flop.

Also, I was thinking about possible deviations by our opponents, particularly those players that call too much with weak draws getting a bad price. My strategy on dynamic boards will likely perform much better than a strategy that builds it's bluffing range from the bottom up on dynamic boards.

Then when we get to the river with our checking range, we have a good mix of hands that can bluff the river and get better hands to fold. If we were to build our bluffing range from the bottom up, then our checking range would be left with a bunch of middling hands with lots of Jack and Queen highs that probably can't get better hands to fold on the river after checking down the flop and turn.

One of the problems with betting so many hands is that the 765r is going to get check-raised by a nicely balanced range, and 9xs can't continue vs a pot-sized check-raise. Amusingly, the hands that Snowie most likes to check-raise with as semi-bluffs are J9s and T9s. It tends to check-call with the better 9xs.
Oh, and now I've double-checked, this is one of those rare spots where Snowie actually likes donking (23% frequency, which is huge by Snowie's standards. This is clearly a very "interesting" flop). With K8s, Q8s, J8s and T8s, it leads out almost always, and it donks with 9xs occasionally too. The donking phenomenon makes the situation even more complicated, since it's really hard for the CO to design an optimal c-betting range if the BB has a donking range as well as check-calling, check-folding and check-raising ranges.

Makes sense to me if you think back to the AKx board we talked about upthread. There, the preflop raiser had a profitable bluff with the low equity hands because he had the range advantage on the flop. Here on the 567r board, the big blind has the advantage and can make more low equity bluffs.