Well if thats the case, then why in Polks hand does he state bluffing 4 or 5 combos out of 26, meaning only bluffing 15-19% on a pot sized bet when youre stating you should have 33.3% bluffs in a pot sized bet?

Also, on the flip side what is the math behind over-calling?

For ex, with top pairs\mid pair\low pair etc, youre going to call some but fold others, examples of better ones to call with may be higher kickers\blockers etc,
But how can we figure out the math behind the total amount needed to call before one can claim youre over-calling?

Thanks for your response

" Do keep in mind that this does not keep in mind future play. If these betsizes are done with more action possible (such as on the flop) then the frequencies are not so easy to calculate. "

If turn and river bet are both full pot bets would it just be .33x.33? ....... (11%)??

" However, his main concern (at this point in his explanation) was to avoid ending up at the river with a range that contains many more bluffs than he can profitably bet. "

Well how is he figuring this out ? Is this just manual math hes done in specific spots over and over and just memorized it or???

Do you know the formula to go about figuring something like this out?

If both turn and river bet is full pot would it just be .33x.33? ....(11%)?

There isn't any useful minimum defense frequency on the flop or turn since range interactions with the board evolve when more community cards are dealt. Range and nuts advantage shift or get equalized, and there is no useful approximation to a multi-street static polar v bluff catcher situation. This is why solver study is useful for trying to devise simplifying heuristics applicable to broadly characterized spots : e.g. how to double barrel on paired board in single raised pots in position against loose callers, etc. A short and enlightening explanation why the minimum defense frequency formula is very limited in its applications apart from some specific river spots (or some toy games with numbers, with no card removal effects) has been given by punter11235 (who is a developer of Pio Solver) on the 2+2 support thread for the software:

Punter11235 on MDF

Figuring out exactly the math of what those calling or betting frequencies ought to be can't be any easier than computing the Nash equilibria (GTO strategies). The algorithms for approximating those aren't very complex (although they require many iterations) but they don't reduce to simple formulas except for the case of some simplified toy games. At best we can find some heuristics, or simplified rules, for determining how many bluffs, or semi-bluffs, or bluff-catchers, we can have on the flop or turn, and what hands are the best candidates because of their implied odds, blockers, need for protection, etc.

I'm pretty sure when strong players give advice about over-calling or over-bluffing (or under-bluffing) they don't base that on mathematical formulas but rather on their experience toying with solvers and anticipating how their range constructions will carry them to reasonably well understood and favorable river spots. Ben Sulsky and Uri Peleg (among others) have some videos that explain how to use solvers efficiently to build such intuitions. If your subscription is 'Essential', look at the videos of Peter Clarke and Qing Yang. For the theory, you can delve into Andrew Brokos "Plays Optimal Poker 1 & 2", or Will Tipton's "Expert Heads Up No Limit Hold'em 1 & 2". In both of those you will find formulas that apply to more complex toy games giving insight into real hold'em poker situation if that's what you're looking for.