Thanks mongidig. I found the post where I'd done the math a few years ago:
https://forumserver.twoplustwo.com/s...4&postcount=36
My estimate, based on the math in that post, is that you're confident that you're going to collect 8BB+ EACH time you flop a set if you cold-call pre with a pocket pair. If 5 people see the flop for 2 bets, 4 off them call a bet on the flop, 2 on the turn and 1 on the river, that's 9BB. Obviously if other villains in the hand are willing to raise pairs and draws, getting to that 8BB is that much easier.
I didn't do the math for cold-calling with hands like 87s-QJs or A8s+. It's pretty complicated since a lot of the time when we flop one pair, we have something to go along with our 5-out draw to 2 pair or trips like a gutshot or flush draw. Now, in stark contrast to when we flop a set, we DON'T want villains in the hand who are willing to raise - we want to make our hand as cheaply as possible, which in turn makes it harder to grow the pot.
I'll take a stab at estimates with the following math-simplifying assumptions:
- We'll say we'll flop either a pair, a flush draw or an OESD about 40% of the time.
- we make a hand that holds up (whether it's two pair, trips, a straight or a flush) when we do see a flop 30% of the time that we see one (30% of 40% is 12%).
- when we see the flop but miss our hand, we put in 1 sb on the flop and 1BB on the turn
so 60% of the time we put 1BB in preflop and fold the flop.
28% of the time we put in 2.5BB and fold the river.
60 + 28 * 2.5 = 60 +70 = 130
So for the 12 times out of 100 we're assuming we'll win the hand, we need to average pot sizes of 130/12 = 10.8BB. That's VERY high! Table conditions need to be VERY optimistic to think that's going to happen very often.
Feedback on my (over)analysis welcome.