It is well played.
The flop bet is a must really. You have 9 nut outs + 3 more and should build the pot. This would be true even if you don't have the rundown equity (the number Equilab would give) necessary for a value bet, but I think you are close have to it. In essence, you make the bet to increase your winnings when you hit. It is much easier to win a big pot with initiative. By contrast, if checking and calling, or worse, if it goes check-check-check, do you think you would get paid a single dime when the board shows a 4-straight and you come out betting?
To reiterate, a flop bet makes the final pot double or triple in size compared to if it goes round-check. That big final pot you almost always win because you have nut outs. So those 6 bb is an investment. Effectively, it much less than 6 bb you invest since you'll have to call a bet anyway and you have equity in the pot. In isolation (say you'd be all in with the bet), it might have an EV of minus a fraction of a bb. Here, we get paid big dividends by betting and increasing the final pot size.
The exception to betting flop would be only if the button is likely to fire flop and turn whatever peels off. I don't see that happening.
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Originally posted by nitrol
Still push on river has max EV.
On the river, it is not the time to make an overbet. All draws got there and we can't trust villain to be an idiot. There's no room for him to have a decent hand. Overbets with nuts are best when we make unexpected nuts, like backdooring a straight on a 2-flush flop + turn.
The reasoning you have presented on this issue may work at playmoney tables, and maybe, just maybe, at an unusually fishy NL2 table.