Theory: TPTK IP vs EP limp/call PF on dry board

[spoonitnow]

I bet here for mostly balance reasons. Standard line is to bet the flop, often check behind the turn (depends on the board + opponent) and tend to call a river bet.

Also, I'm not trying to be a huge winner with one-pair hands and betting the flop can get the pot way out of order. Just make sure you realize later in the hand that your hand is severely underrepped.

With both of these lines we're put in a spot where our hand is under-represented and we're checking one street to pick up bets on another. Also in both lines, the street we check has the effect of controlling the pot a bit. The differences seem to be kind of subtle, so maybe which play we choose in a given spot should be more based off of our opponent?

For example, I'd prefer to c-bet the flop and check behind on the turn against villains with a lower fold-to-cbet% and a higher later street aggression.

So then under what circumstances do we prefer to check the flop?