[joker122]

"So what is he value betting here that you beat and that he would have folded to your bet? Or that he will b/c with, but would have only called if you bet?"

ok so what hands make up his range? ace high, 88-44, TT/QQ/JJ, JT, QJ, 89s/T9/J9/Q9/A9.

with ace high and 88-44 he can't call a bet on that river so I'm not missing value from those hands by checking.

if he has paired a jack on the river with AJ/QJ/JT or his he has made 2 pair with J9 he will surely bet trying to extract value from a 9, and he only has to call the CR half the time for it to be profitable, which i think he does given that we don't know anything about eachother. if he has QQ this reasoning also applies.

against QT i don't think he can 3bet a cr, so against that hand 2 bets are going in anyway. same goes for JJ.

so really the only argument for betting is that checking lets a 89s/T9/A9/Q9 and TT take a free showdown.

when considering combos, it appears as though he has a hand that can bet/call or a hand that should fold to a river bet the vast majority of the time.

I guess a key assumption is that he folds ace high or 88-44 to a river bet...but if he has the slightest ability to read hands how could he call with those hands?