So this hand came up and I was unsure of the best way to proceed on the flop.

Range Distribution

I figure that I probably have something like 4% 4b here (a little wider since position/relative position is the nut worse when I flat).

I am really thinking about this hand in two ways. First what is best for our range. As you can see from the link we hit this flop OK with our range, trips or better 15.6% of the time, Over pair + FD 18% of the time, Bare OP 55% of the time, and spade another 4.5% of the time. This makes everything else ~7%.

So from a range situation, do we really need to be shipping all of our hands. If we can get just as many folds with a smaller bet size with our over pairs (the bottom of our range), this seems like the best way to proceed.

Opponent's Range Distribution

Villain is going to miss the board a lot, if we get played back by KK+ and/or ss then we are getting near 45% folds from villain. So since he is going to fold so often do we really need to ship, also doubt that he picks up on us cb/f this board and we are actually rarely cb/f (I think we have one bet size on this board either always GII, or always less).

In a vacuum I have AdAsXdh, I thought that this would be a hands that I might want to check. I could get action from his air and I am WA/WB at the moment. Also villain has a fold to cbet on paired flops of 100%. I have the backdoor nut flush draw so I don't need to worry about the diamonds rolling off am him improving that way. I could get him to check and improve to a hand that has <335% equity on the turn that he commits with (wraps, GS+FD)?

I also think that QQx, JJx flops are probably the best for his 3b range since he will have more bigger broadway cards and think that if we find that betting less and constructing a b/f b.gii range. FWIW the Ev of a shove versus a calling range of KK+,ss is $27.36 so we should be trying to figure if we can perform better then this.

EV of Shove