So balancing river bets is easy from a theoretical standpoint. Offer villain odds and bluff at that frequency. If you bet pot, bluff 33%.

I've never really thought about optimal chk call frequency. I know that we have to call at a certain threshold to stop villain auto profiting. So if Villain bets pot and is perfectly balanced then we need to call 50% of the time to stop him auto profiting. So from a gto perspective are we putting our chk raises within the 50% threshold? i think we are. but im abit iffy on this subject.