Problem: In Pot Limt Omaha, we need to protect our check back range, because if your opponent sees you value bet too much on early streets, he will start betting every time you check. Working from river backwards, you must find bluff range corresponding to flop that allows us to bluff more EARLY in the hand when the opponent hasn't defined his range. As we see his strength on the flop when he calls approximately the top 50% of his range, we have defined his hand as above average and NOW WHAT? Of course! We don't want to bluff as much on later streets - but what is the function that can make this range combination stuff fall into place ON THE TABLE?!


Assumptions:
1. On a 3/4 pot size cbet, we know that the river value/bluff ratio that makes villain INDIFFERENT to calling (0 EV) is 35/15. PROOF: 75 bet into a pot of 100. If this ratio of 35/15 gives us a villain ev of 0, we have proven our case if 1. we win our value bets and 2. villain wins all of our pure bluffs, and .30(bluff)*175(pot) - (.70*75)= 0. And it does.
2. Using the bluff range and sizing of assumption #1, we further assume for simplicity that river CB =50, and fold to cb =50 all streets.

These assumptions are very close to optimal and represent close to average population data. Assumption 2 gives us a mathematically sound starting point for Cbetting in a balanced way. 15% of my range that I started the hand with is bluffing river-theoretically.


My idea was : why not bluff about 1/.7162, the inverse of what I bluffed river with on the turn, because that was EXACTLY HOW OFTEN the population went to the river after seeing turn. What better metric do we have to make our cbetting range to be AS UNEXPLOITABLE as possible?
To this end, I used database data which shows that in raised pots 57.8% of turns are seen by 2+ players and 71.6% of rivers GIVEN that turn was seen(data from 230k hands, all players in my small database).
Working backwards from river play, I wanted to ADD BLUFFS IN DIRECT PROPORTION to how many more turns and flops are seen by actual players (moving theory to reality) and examine a potentially solid mathematical basis for providing A SIMPLER WAY of estimating bluff ranges on the fly under given assumptions.
I'm posting this here now to get more feedback, because when I finished the math on this to get full cbet ranges for each bet size, I estimated that my theoretical value range is nearly identical to monkersolver range of about 15% value to CB 54% of A high flops (actually 13.7v/36.3b for 50%cbet on my chart translates to 13.7/50=x/54, x=14.8%). I haven't crossed checked anything else, as I only had notes from a video in Fernando's MM course- no solver.


Appendix:

Working bluff range back, we take the inverse of 71.6% of rivers (dividing sawturn% by sawriver%, as represented by the population average).

Secondly, we take 57.8% of turns (when flop seen) and invert this fraction to directly add the appropriate amount of bluffs based on TURN- (standard model) 15% bluff range on river * (1/.71626) = 21% turn bluff (given 50% cb would amount to 29% value bets)

thirdly, the FLOP cbet range= 21% * (1/.578) = 36.33% flop bluffs, 13.66% value.

Now, we have bluff range on flop (ex: 36.33%) which declines IN PROPORTION to the frequency in which the population reaches the turn and river to 21 and 15% . As a check, you can see that 15 is 71.6% of 21, because we wanted to increase our bluffs working backwards to make our opponents EQUALLY INDIFFERENT.

Is this slightly wrong, perfect, or perfectly crazy? Even if you tell the fish about this, he won't care anyway. LOL

In hold'em, it's usually bad practice to model the flop as a value/bluff scenario. The solver shows us that polarizing on the flop is very often a bad idea because the polarizing action gives away too much information. It's better to keep villain in the dark for another street about what our plan is for our range. It'd actually be very easy to know how many bluffs you should have on the flop if you play under a value/bluff model but this doesn't maximize ev in reality. I could try to find a way to explain this better if you want.

Now, omaha is very different, but with equities running closer I'm sure that early polarization is even worse. In other words, finding a balanced bluff ratio on the flop is worthless, it won't look anywhere to what a solver might and it won't teach you anything practical. On the flop we usually try to find ways to deny/realize equity and extract/deny informational advantages.

Another issue is that you are using population frequencies as some sort of way to calculate your desired frequencies. This again doesn't work. From a polarized point of view, if villain overdefends, even slightly, we never bluff. If villain underdefends, we always bluff. There's no inverse of his defense as correct bluffing frequency. You also don't want to use the population frequencies mixed with some gto concepts that require your opponent to be playing optimally to work. You shouldn't be playing in a value/bluff mentality anyways and merged betting is probably more important in omaha

You have some interesting thoughts on this, but I don't see much theory or anecdotal evidence in your refutation of my application. I understand the role of exploits, but GTO remains important when you are playing against thinking players. In the PLO100 games I play, about 65% of the pool are decent enough to notice when you value bet too much on flop. This way, they can jump on the turn (WITH SIGNIFICANT equity outside of fold equity). If you aren't bluffing enough flops, THIS NECESSARILY screws up turn bluffs AS YOU STRUGGLE TO ADD ENOUGH TURN BLUFFS as board changes and you have to drop some. This is the thrust of what caused me to reconsider how precise I am making this. After all , it affects 18%pfr*50%(cbet at least once), OR about 9%of hands

So just so I understand the methodology you used population data to substitute in for actual folding frequencies then used that in conjunction with an EV equation to derive value bet/bluff ratios over multiple streets?

Derived from the price given to villain, we have a known value/bluff ratio given sizing at the river (static board-assume polarized betting wins vb's and loses all bluffs).

Then, the known population rates determine the rate at which bluffs increase toward the flop. It seems to check out with what monkersolver and PPT are telling me about bluff and value ranges back on the flop based on standard RFI and cold calling ranges.

So still not quite sure what you did here. You just took the base derived from the river and inflated it based on population tendencies to derive prior street bluffing freqiencies only?

Or overall valuebet/bluffing frequencies? I just don't quite understand what you did based on how you explained.

You understand me correctly, but overall, 48-50% is the average Omaha cbetting by monkersolver in a heads up, SRP. Bluffing frequency and the corresponding value range falls into place based on an average 50% cbet. If it is 70% recommended, I just inflate value and bluff ranges by 40% each.