
Ryan W. answered 11/19/21
Professional Poker Player
This depends entirely on the specifics of the flop (what is the paired card, what is the third card, is there a flush draw, are the cards connected, etc.) and the ranges of the players that entered the pot. Some general heuristics we can use on paired boards as the preflop raiser is to bet frequently for a small size (33%).
For example, as the BTN vs the BB in a single raised pot on QQ2r, we can bet our entire range for 1/3 of the pot (https://imgur.com/a/OHvs418) and the BB is forced to overfold because they simply have so many hands that completely missed.
However, on 665 with a flush draw, the BTN has to proceed more cautiously. We are still using the small sizing because the BB has just as much 6x as us if not more. The difference is that we are checking about 40% of the time (https://imgur.com/a/8D3D8xd). Some good hands to check are hands that totally whiffed, like hands with two overcards, no straight draw, and no heart. To protect our checking range, we should also check hands like AA, KK, and QQ. We prefer to bet the lower overpairs like TT and JJ because they need more proection as they are more vulnerable to overcards coming on the turn.
Lastly, there are some spots to size up on these paired boards. Specifically, larger sizings are used as the 3bettor in spots where neither player is going to have trips very often. For example, as SB vs BTN in a 3bet pot, the OOP 3bettor should be using a half-pot size and never opts for the 33% sizing (https://imgur.com/a/ZNlve84). OOP never has trips and IP only has a few combos of hands containing a 3 (1 combo of quads, 2 combos of A3s). As a result, OOP has the nut advantage due to all of its overpairs that IP does not possess, and the larger size is used to leverage that advtantage. IP is forced to make some ace high calldowns on brick runouts that players are certainly not finding in practice, so taking large sizings and bluffing three streets in these spots will be highly profitable.