864t, 3-bet pot cutoff v. button

actually, i changed my mind again. i'll get back to the question of whether we need/want a oop 3b calling range, but i want to keep going on this flop for a bit. so, this situation is basically the same as what i looked at yesterday, but i now want to consider btn's optimal c-betting range...

3b ip w/ initiative, cbet or no?:

• co opens top 25%,
• btn 3bets 10.5% of hands: [TT+, AQ+] + 40% of [Axs, KQs, QJs, KJs, scs, ATo-AJo, KQo] + 25% of [other suited broadways, suited gappers, offsuit connectors],
• co calls 25% of [55-QQ, ATs-AQs, KQs, AQo] + 10% frequency for [AA-KK, 22-44, 54s-JTs],
• co checks,
• btn cbets [tp+, fd, oesd, var3% of all other hands], EV (var3=25%) = +11.3bb
• co shoves [tp+, fd, oesd, 1pr+bdfd, 1pr+gutter], EV(25%) = +7.3bb
• btn calls [tp+, fd], EV = +27.1bb

if we then vary var3 (btn cbet 'air' %), and plot the ev of the btn cbet (blue points) and co c/r w/ a pure value/semibluffing range (red) and value+50% air (orange), we get the following chart:

this is probably largely intuitive, but cbetting air is -ev, and the value of co's c/r increases rapidly as button makes that mistake. obvious conclusions are:

1. btn would benefit from a check-behind range v. aggressive opponents (see blue points), and 
2. co needs btn to be cbetting air to turn a profit on his c/r (see red points),
3. co does not need to c/r w/ air,

basically, this is a flop that both btn and co should play very honestly, but if the button cbets too much, co gets a license to c/r a ton of hands. other thoughts?

next i suppose i should look at those lines that start with the flop checking through...