[Nick C]

Okay, I'll assume we have complete rags like 84o, so Button will have at worse two overcards versus us.

AA-JJ = 24 combos that make us about a 5.5 to 1 dog.

AK = 8 combos (discounted, because Button is so incredibly tight) that make us about a 9 to 5 or 1.8 to 1 dog.

So that makes us, what, about a 4.5 to 1 dog on average?

We do have one postflop advantage, which is that Villain's range is so narrow that we know we're behind on any flop that contains an ace or king and doesn't give us two pair or trips. Then again, usually we're going to need two pair or trips, so I'm not sure how much what we know really helps us. I think we're in a reverse-implied odds situation most of the time when we flop a pair and in fact we're doing worse than the hot-and-cold equity suggests.

We'll catch something on the flop about 1/3 of the time, but that will usually just mean we're chasing versus an overpair and will need to check-fold the turn UI if Villain bets again (or, if we think our tight opponent will second barrel with UI AK, we can call again and usually lose that BB on the turn but sometimes end up taking the pot either because we improve or because Villain checks the river and lets us win). Anyway, catching just one pair on the flop won't even be particularly profitable. (Basically, we're relying on implied odds on good turn cards, and we should have some of those, but it's not as if we're going to make a fortune when we flop a pair, and in fact usually what'll happen is that we'll just lose more.)

Okay. We'll flop two pair about 1 out of 25 times. We'll flop trips or better, what, 1 out of 150 times or something? These are the only hands that will actually be profitable for us postflop, and we're only going to get them about 1 out of 20 times (assuming my quick math is correct).

So . . . about 2/3 of the time we're simply check-folding the flop and making a 1 SB donation.

About 1/4 of the time we're still practically just breaking even postflop (that's my approximation of what happens when we flop a pair), just like we did when we check-folded. But let's be generous and say we recover our full 1 SB preflop call of the 3-bet when we flop a pair.

So for 19 of our 20 preflop calls, we're going to lose about 13 SBs. That means we need to win 6.5 BBs that other time when we flop big. 3 of those BBs are already in the pot preflop, so we need to win about 2.5 BB postflop on average with our big hands. Which I'd imagine is in fact approxmately what we can hope for.

Can all of this be right? It seems to me that if Button offers us anything back at all, we should take it. Calling the 3-bet seems roughly break-even to me, and I suspect it might not even be that. I wonder if we should just fold whether Button offers us a rebate or not.