[vmacosta]

I like your passive play on flop+turn here. On the river, I think a check/call is still the prudent thing to do.

If fish is getting out of line with some random PP or even AK (which is what many fishes do), there is some chance of you being raised by a worse hand on the river--either as a bluff or cuz fish doesn't understand hand values.

Plus, CCer has done nothing but call on a drawless board so you can hope to pick up his call as well if fish bets again.

Furthermore, sometimes fishes shut down and don't bet on river with AA/KK/AQ cuz they're scared or the pot's big enough or whatever.

Finally, even if fish gives up with some PP, there is still some chance CCer will bet a wrose hand or already had you beat.