Nashpoint

So IP can still value bet/bluff normally OTR, but if IP has a "zero-bet"/min bet range OTR IP has to add some stronger hands to that range too to defend against check raises.

My knee-jerk reaction is that this would lower my EV because I would have to move equity from my betting ranges (I usually use two sizes) to zero-check. Im especially worried about the EV wasted in the line check zero-check check.

My first exploitative response to the bet-or-zerobet strategy (playing OOP) would be to check 100% of my range OTR.

Can you give an example situation OTR (with ranges) that we can run a sim on?

So OTR, oop will never ever have to worry about facing a bet if he checks because under the law of the zerobet IP is not allowed to bluff or valuebet when checked to? I doubt that is a great self inflicted limitation on IPs part :)

can you explain this in more detail?

In a mathematical sense there is no conformal mapping of range vs range equity to ev and absolutely no linear relationship between ev and equity.

Its better to have 57% equity in a 2k pot than 67% equity in a $300. When you opt to bet you are forcing a transformation to a lower spr branches.

Your EV will be extremely dependend on the specific distribution of blockers et.c. which skews the overall range vs range equity when you start subgrouping ranges into betcall betfold, checkcall and checkraise strategies by equilibrium bruteforce calcs.

It is easy to construct river games where a "weaker" range defends more successfully than a "stronger" one due to the specific composition of the combos. This is also an argument against polarization. 

With a wider villain range we have a higher relative equity that is true. But the pot may or may not be smaller which may or may not boost the relative EV (pot*riverequity*riverbettingstrat).

A higher relative equity does not automatically yield a higher relative EV.

If villain decides to go x ip OTF we still run into some bad runouts on later streets.

That said, I check this flop 100%, mainly because my range is in some serious shit on this texture against a wide CO defense in a 3bet pot and I would have a hard time defending a lead on later streets with regard to spr (normal depths).