Ac7c. Cap or no Cap?

[ZOMG_RIGGED!]

so a 2+2 is claiming I'm a moron but my play makes perfect sense to me so I throw myself so the mercy of the 2+2 courts.

AP 5-T.

MP: God's gift to good players. VPIP: 90+% WTSD: 72+% PFR: 0% AF: .4ish Only time I've ever seen him raise PF was a stone cold bluff. No idea how he plays big starts pairs, so they are in his range.

MP+1: me. Ac7c

SB: Fish I have friend listed. In a 500 hand sample I have him running at -7.4 BB/100 with a VPIP for the SB at 80%. Horrible player, but smart enough to reraise here with the top of his range. No PP AA-TT or AK, AQ, maybe AJ or AT.

BB: 2+2. His claimed Range. AA-TT, AK, AKs, AQs, AJs

MP limps. I raise to isolate. SB calls. BB 3 bets. Mp calls. I cappies. All call.

With a rough estimate as to what a 80% range is with no top hands PS gives me:

equity win tie pots won pots tied
Hand 0: 23.583% 23.40% 00.50% 4748398503 102069370.50 { Ac7c }
Hand 1: 46.083% 46.53% 00.19% 9440653136 37619574.00 { TT+, AJs+, AKo }
Hand 2: 12.298% 12.18% 00.29% 2471116882 58234387.00 { random }
Hand 3: 18.037% 17.46% 00.82% 3543425023 166388636.50 { 99-44, AJs-A2s, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 53s+, 43s, 32s, AJo-A2o, K2o+, Q2o+, J2o+, T2o+, 94o+, 85o+, 75o+, 65o, 53o+ }

If we loosen up BB's claimed 3 bet range to a still realistic one:

equity win tie pots won pots tied
Hand 0: 30.577% 30.04% 00.66% 15110427404 333929777.25 { Ac7c }
Hand 1: 31.996% 31.73% 00.40% 15961674248 199395740.25 { 99+, AJs+, KQs, AQo+ }
Hand 2: 18.102% 17.78% 00.40% 8942612041 200856014.25 { random }
Hand 3: 19.325% 18.16% 01.25% 9132933430 628403425.25 { 99-44, AJs-A2s, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 53s+, 43s, 32s, AJo-A2o, K2o+, Q2o+, J2o+, T2o+, 94o+, 85o+, 75o+, 65o, 53o+ }

So realistically I lay somewhere in the middle.

So my claim is my cap is fine becuase it preserves a little mystery to the BB with the intent of gettting a 4 card flop if I want one. If I just call I think BB bets his range 100% on the flop but a cap gets me some leeway. I have no plan on the betting the flop unless I catch. SB and MP provide HUGE implied odds, and I feel not only is my hand extremly easy to play but BB is extremly easy to play against at this point.

So 2+2, does a cap have merit here? My claim is that its probable close to even but at worst only slightly -EV, BB claims is burning money