Yeah that brings some clarity, thanks. What I'm still wondering is whether we can bring alpha back into the equation, by differentiating between 'full bluff-catchers' and 'partial bluff-catchers'. That's the gist of my post above. So let's say once again that Priv is 6 and alpha is 1/7, and let's suppose that 12% of the time we have a hand which falls inside the opponent's bluff range, and distributions are symmetrical so if we were always to call, we'd win half the time and lose half the time (vs his bluffs) with that subset of hands. Now to bring alpha back in, I'm speculating, we'd entirely remove from consideration those 6% 'can't-beat-a-bluff' hands, fold the 6% 'beat-a-bluff-despite-being-within-bluff-range' hands and then see how many extra folds we need to get up to .94/7 = 13.43% of our initial range, so an additional 7.43% of that initial range. Does that make sense?

In these simple cases where the only reason not to use 1-A is the equity of the "worst bluff" being higher than 0 I believe you could get a pretty good (or perfect in some cases) approximation by adjusting alpha as you suggest.

Cool stuff, thanks