Evidently, a couple of my calcs were wrong. These are snippets of a PM between Chipp and I regarding the comments he left on that page.
C (blog comment):"What this means is that even if when you call you automatically win the pot, [button] is still profiting [immediately] if you fold over 30% of the time." (edited for clarity)
...is off- c y?
N: Is this right?
0 = -3f + 12 - 12f
15f = 12
f = .8 = 80% folding is breakeven....
...And if we only win half of the pot...
0 = -3f + 12((1-f)/2) - 10.5 ((1-f/2)
.2 = 20% folding is breakeven? Is that right?
C: Yeah, that works.... I think we need to be looking at the bigger picture here. This guy is raising us with some distribution- if he's raising atc we clearly have > 1/2 the pot when we take a flop [blogger's note: this is re the assumption made that we're entitled to 50% of the pot when calling]. If he's folding some hands, we "buy the button" and face two random blinds w/ our (here) 3otb distribution. There's lots of possibilities, but my point is that if he's not raising atc, we need to consider the value gained from these other poss in determining whether we're being exploited. And again, if he is raising atc we should def have more than half the pot, despite being oop.
So like the more hands he raises, the more our showdown equity increases when we call, and conversely the fewer hands he raises the more often we "profit immediately" (in this case the "profit" being a shot at the blinds otb w/ your 3otb distribution). In theory we want to construct some distribution balanced such that he can't increase his equity by shifting his strategy towards either of these extremes.... Anyway, to my point w/ the c y- opp doesn't necessarily profit immediately there cuz there's still two opps behind that can wake up and pick him off.
Obviously, the last part I left off for simplicity sake, but it's definitely something that still needs to be taken into account. Additionally, another way your preflop raises can be exploited is if someone is smooth-calling often behind you so that they have position on you PoF (Gavin Smith has mentioned this a lot in old Circuit episodes).
I might try to do more with this in the future, but Christ, I make enough minor mistakes with my math (no formal math training in +3 years, nor past Calc I, plus I usually do this shit really late at night) that I don't know if I'll be able to approach any real solution, but hopefully something worthwhile can be intuited from it. If/when I do this, I'll keep you posted (awful pun intended).
Also, congrats to Roddy who cashed onto UB again like two days ago and has already made like... twelve-thousand final tables. He might have all the money, but I can drink legally and he can't.