Had a 4bet flop spots that filled me with total ambivalence yesterday, but I have found kinda interesting subsequently. I remember finding it interesting trying to puzzle out in real time whether it was better to fold or to shove. 

Shoving didn't feel insane due to all the backdoor equity and obviously the TP to get us started. However, I felt you could be just as easily one side or the other of the required equity to go with it.

Turns out it was literally a close call. We need 36.5% to shove, and PPT tells me we've got a neat 36.5% against AAxx. 

So what with rake + assumption that villain has BDFD a minimum of 50% of the time = fairly sensible fold. right?

Questions:

1. Interested in polling who would shove here (instinctively, rather than hindsightedly, if you know what I mean)? Villain was approx 20/5 over 20 hands at the time.

2. When I asked PPT how it would change if villain had KK, I assumed our equity would stay the same or go down slightly as KK blocks a small proportion of BD straight outs. However it apparently goes up to 39.2%. I can't work out why, can anyone explain?

3. Is there a way to work out percentage likelyhood of villain having at least one BDFD on this board with: aa; aa+KKds; top 2%?

Thanks folks