Suppose the Button opens to 3 BB's and the blinds defend by either 3Betting or Folding.  To keep the Button indifferent to opening the worst hand in his range (which we assume BTN will fold to the 3bet), we have the following for this model:

Optimal Blind Defense = 1 - (Frequency Which BTN Needs Blinds To Fold For An Immediate Profit) = 1 - (3/4.5) = 1/3

Thus, the combined 3Bet percentage of the blinds, if they chose to either 3Bet or fold, would be .33333

Suppose the SB 3Bets a range of ~14.5%.  The BB would then be required to 3bet the amount which satisfies the equation:

.3333 = (.145) + (.855) * (BB 3Bet)

This implies the BB would 3Bet ~22%.  Seems like a lot.

Of course, this model does not take into account things like pot odds of the Big Blind to call the BTN Open when the Small Blind folds, and I think we see that the BB should certainly have a calling range versus the BTN Open.

The first question is how wide to make the calling range versus a 3X Open.  While it seems intuitive to defend any two suited and an extremely wide range versus a BTN minraise, I'm less sure how to construct the calling range versus a 3X Open but the SPR seems drastically affected on the turn and river with this extra big blind added to the preflop open.  Furthermore, even after we do solve for a plausible calling frequency, I run into the following problems constructing a range:

1) If we start going super-linear then it seems most flops will give us hands we're forced to play passively since our equity on turns and rivers will often be non-robust.

2) Because of (1), we let the BTN realize tons and tons of equity with draws.  He also gets to play these in position against a fairly condensed range on our part on many boards, and this doesn't bode well for us.

3) If we start going non-linear and adding more suited hands off-suit connectors, then we should gain some robust equity-share on many flops, but we end up with more dominated holdings.

Do any of the coaches have input on this?  Specifically, how wide to make the BB Calling Range Versus a 3X BTN Open, and secondly how to construct it?