Old school me followed the logic of bet big to protect against the FD. Then as i studied solvers i learned that no its actually correct to bet small on 2 tone boards or wet boards in general. However solver likes to bet big in some spots. For example CO versus BB 3bp BB is pure checking which makes sense. Surprisingly though CO prefers to check or bet pot at a close to 50/50 ratio with a slight bias towards betting. MY when studying a sim i like to start with a several sizes like 25%/50%/1xpot/2X pot then trim of sizes the solver doesn't use or rarely uses. well the solver basically never uses any any other sizings when i give it those choices. So what gives.? the only thing that stands out so far is 3bettor bets more often and smaller on boards where it has more FDs and larger and less often on boards that naturally block 3bs FDs For example in comparison solver prefers to mix between 25/50% on J73 2 tone

FD don't effect flop sizes that much. They are very profitable calls vs both small and big sizes, you can't make them indifferent unless you bet huge.

With flop bets you usually put pressure (aka make them indifferent) on much weaker hands like one over card with BDFD or naked over cards. Depending on how much equity hands that you target have you scale sizing up or down. That's how I see it at least.

The problem with general statements like “bet bigger/smaller on twotone boards” is that they don’t consider what our betting range is built around.

Eg on low boards, the aggressor’s betting range is usually built around overpairs. So we do in fact see smaller bets on twotone boards, simply because these overpairs are worth less when the board is drawy. We would rather size down and get called by more low equity hands, instead of sizing up and getting called by a range that has so much equity against us.

That is, a small bet vs a weak pocket pair generates more EV than a big bet does against flush draws.

On higher boards however, we often bet bigger on twotone boards instead. This is because the types of hands we are betting are very different: we have more marginal hands like underpairs and middle pairs when the board is high, and these hands are more interested in betting when the board is rainbow - once again because they have better equity when called. So we carve out a small bet range around them on boards like KT5 rainbow.

On a board like KT5 twotone however, we are typically not that interested in betting hands like Tx. So there is no reason to use the small bet, and our betting range is instead built around hands like TP+ - hands that mostly want to bet big.

Try giving this a watch:
Why Good Players Don't Bet Big on Wet Boards
https://youtu.be/a1O75yVsa4M