50% equity is irrelevant, realized EQ for oop is probably way lower, so OOP will be forced to fold (too) many hands if IP bets big. The smaller bet collects more money (for the strong hands) and gives more possiblities to bluff on later streets.

But at the end it's simple. Betting small withi entire range has higher EV. :) Try the same model with a higer betsize (only) and you will see the difference.

Hi BigFiszh
Thanks for your answer. Have you seen Bens Video

http://www.runitonce.com/poker-training/videos/piosolver-analysis-akhh-on-kq2ssh-btn-v-2/

where he was c-betting his whole Range with a small betsize and realized that he was wrong.

That's why I'm still unclear about the situation I posted above. Equity and Equity Realisation are in both situations quite similar but the outcome is not the same. Can you say what factors lead to a complete different betsize and c-betfreq. ?

On this Board Texture Kh Td 2h oop has almost only Bluffcatchers in his Range. Would a higher betsize not be more useful to damage the amount of EV of this hands ?

Maybe that depends on de portion value / bluff in your range.
I mean in nuts/air vs bc scenario bet big seems ok, but if your value combos grow up we are able to bet lower?
Im not sure but try adding some bluff to your pf range and see what pio does

Anyway being ip here as bigfish said makes us materialice better and 1/3 cbet 100% helps more than split our range and in that range you dont have much mid value hands forced to check since his best hand is JT

Might also highlight the differences between a KQX tt board vs a KTXtt board? I would imagine the draws have much more equity on KQx than KTx...

Also, by betting smaller, we get to bet our entire range perhaps, which should make our execution of the hand play out closer to EV expectation

TK