Is this a specific spot or just a generalization of several spots? Did we x/c twice? Did we probe turn after he checked back flop? Did we call a x/r on flop, faced a check/check turn line and deciding on river?

I like your thought process with the pool likely not bluffing enough on rivers.

In general, when we have x/called twice, I lean more towards checking. Problem here is that many opponents will check back TPGK on river. If we x/call twice then lead, I feel the hand is pretty easy to play for him (especially on equity shifting rivers).

If flop went check/check and we probed turn and now have a river decision, I would lean towards betting. I think the ev of the bet turn/bet river line is going to be higher than probe turn and hoping they will bet river vs check.

If we c bet flop OOP and c bet turn, I would mostly just continue betting.