Do you have a plan for this hand? Because it really sounds like you should fold pre. Hoping he checks 3 streets and we show down the best hand isn't a good plan.
This is a clear-cut case where if you're planning on calling any street you're better off betting.
Oh no Im bluff catching the river with it on non BW board
Im also value betting the same river if he checks.
I assume that you think you need around 30% fold frequency here to make betting +EV.
However hands that you beat dont count towards that frequency.. you gain no EV by folding out anything you beat.
If villian checks the turn with small PP and will call just a 1/2 pot bet on the river you need around 85% fold equity (hands you beat dont count) for betting now to be higher EV
Plus you give villian change to bluff, you have about 96% equity against anything he bluffs on the turn and 100% equity against anything he bluffs on the river.
your bet dosent even makes sense here in terms of fold frequency, If we give him a range of all PP All BW and some SC you need your bet to work 35% of the time ish (taking into acount you could improve to a set) You probably fold out 25% on the flop.
On the turn you would need 35% again, you probably get around 20% max
On the flop most of the hands you fold out you beat so there is little fold equity (value gained from the fold)
On the turn there is more FE as you are now folding our things like weak aces, but even so the total frequency of hands that you do now fold is still well short of your goal of around 45% to make it +EV
Start thinking about ranges etc.. this just is never +EV
However if the flop and turn gets checked through it is HUGELY EV to bet or call
If villian bets turn and gives up on river its hugely EV
If vilian bets both turn and river its marginal. The key to making money is to avoid marginal situations; you dont profit from them however you play them, yet by checking the flop and turn you allow yourself to play a hugely profitable river.