Quote:
Originally Posted by nolispeifaflaatoi
SB vs BB is the simplest case since we're the only player responsible for defending. So if SB is raising to 3 BB they're risking 2.5 BB to win 1.5 BB. Our minimum defence frequency is 1.5/(2.5+1.5) = 37.5%. If we're defending less than that, the SB can make an immediate profit by raising any two cards.
Against other positions it's a bit more complicated since the bet has to go through multiple players. For example, when the button opens to 2.5x they're risking 2.5 BB to win 1.5 BB, so the minimum defence frequency is again 37.5%, but this is now divided between the two players who are facing the bet. So if for example the SB is defending 15% and the BB 27%, the button cannot make an immediate profit by raising any two cards since their bet would need to get through 62.5% of the time and it only gets through 85% * 73% = 62.1% of the time.
Also, we need to defend more than the minimum frequency if we're ever defending by calling (ie. not 3-betting everything). The more we're calling, the bigger the defence frequency we need. This is because even villain's worst hands continue to have equity against us when we just call.
I am always a bit skeptical about the one street at the time calculations. In practice, one thinks further (exploiting) and as GTO, it might have a different opinion (one can buy or compute that info if one thinks it is worth it).
But interesting to think (if it seems worth it in practice) that one can play some fewer hands when one 3-bets more. Or plays more aggro postflop.
In tournaments, I often think about the other players who should be doing their share of defending, and I am not too fancy about the marginal hands (I read that from a book).
(An AT folding in BB vs. the button open raise. Likely not, as not too much in danger of being dominated).