another 2/5c blog

Suppose we have raised a hand preflop 3x OTB and get one caller from the SB with no limpers or anything:

Pot size = 7bb

When we miss and cbet the flop for ~ 2/3 psb say (for 4.5bb)

In this situation when we ask "how much does he have to fold here for this move to be profitable by itself?" usually people say "well obviously when he calls, we lost 4.5bb and when he folds we win the pot, at 7bb. So -C*4.5 + F*7 = 0 for break even means that he needs to fold 39% of the time for this to be +ev".

Now unless I'm just plain wrong with this, that fold percentage seems to be way too low. If you only take situations in which you get to the flop, cbet and lose, this kind of calculation doesn't seem to take into consideration the fact that some of the money in the pot was yours to begin with in a global hands kind of sense.

As far as I understand, this is only 0 ev given that this is the specific situation that we are in (i.e. we are plonked into the chair with a missed hand on the flop and what is the best play from here) however in terms of overarching preflop -> flop strategy this is a losing play!

If this guy folds 39% of the time to cbets (supposedly 0 ev), then only looking at situations in which we miss the flop and continue to bet 4.5bb, this leads to a net loss of 1.45bb every time we do this, and so instead we need a fold of 48% to break even.

It is just this difference of about 10% that I am confused about, obviously the percentages change as you change different parameters (PFR size and cbet size) but this discrepancy has got me wondering.

Its kind of like the same thing as why folding is always EV 0 even though you would lose money if you only folded (or would globally lose is you fold in big pots all of the time), which I have also never particularly understood. I know that the money in the pot is not seen as yours any more, but it still seems to affect total profits?