KK vs overshove river

I would bet turn for value and protection an x back Rover. If he ships turn you have to let go

I would go for 2 streets of value with around 40% pot bet on flop and turn.

As played I would fold the river on the over bet shove. I expect villain isn't doing this as bluff and you win only against QQ or weird played AJ.

Cheers,
SDK1987

I`m going to go in to this a bit more out of curiousity, because I feel like I`m missing something.
If you play it this way, I either isolate against better or give draws the right odds to call.

Lets say I raise with 40% of pot on turn, that would be a 13BB raise.
Different options for him:
- air: he`ll fold
- pockets: below 88 he`ll probably fold. so only beat 99/QQ
- 2 pair or better: will flat or reraise
- flush draws: lets say without overcards is 1/4 odds. so he`ll have to call 13bb in a 45BB pot. with his implied odds, thats a call.
- straight made or draw: either already has me beat or gets right odds to call

so if I raise and he calls I can say that he has either beat me or draws to beat me (except 99/QQ).
If he reraises I would have to fold. Same what I probably should have done on river except without the extra 40% in the pot.

If I check everything above stays the same except his weak hands stay in his range and the pot is controlled more.
So while I agree I shouldnt have gone broke on river, check turn and fold against shove seems better.
If he makes a small river bet I probably should call.
Happy to learn here, but I dont see how betting 40% turn gives me any value. and if I bet more I might have to call river because of pot odds.

Or am I using some messed up logic here

Preflop i 3 bet to 6.5 or 7x in postition and 8 oop, flop bet less if he have draw or pair he never fold and u still have him in the pot with Ax hands maybe ,turn i am not sure but river is more of the time fold , he have 77, 88, 99, TT, maybe JJ when not 4 bet in his range even i open Q9s here