Protecting marginal hands - just don't get it

[MrStretchie]

This is about the section in SSHE on protecting marginal hands in large pots. Instinctively I understand it. However, when I try to work out the rough math, it just doesn't seem to work.

I don't have it here, but the example is something like
Hero is BB with 7[img]/images/graemlins/diamond.gif[/img]8[img]/images/graemlins/diamond.gif[/img]
4 limpers, SB raises, Hero, limpers call (12 SB)
Flop: 9[img]/images/graemlins/heart.gif[/img],7[img]/images/graemlins/club.gif[/img],Q[img]/images/graemlins/diamond.gif[/img]
SB bets, hero should raise

So.. getting 13:1, obviously you should at least call with your pair + backdoor flush draw.. Due to the coordinated board, your hand works out to around 5 outs.

Their argument is that you should raise. The reasons are to fold out hands like A8, any ten or 6 (which would pick up an open ender if an 8 hits), possibly paired 9's, pocket 10's or J's..

However.. the most you could improve your hand is to 6.5 outs - if you count the two pair outs as full outs, and the backdoor as 1.5. So you increase your equity from 20.4% to 26.0%. If we ignore implied odds, that's an increase of 0.73SB. But you pay 1 SB to get it..

Now with implied odds.. If you don't raise, and we assume that devalues your hand, it means at least one other caller is going to the river. So let's say you get two callers going down to the river. You win 20% of the time, and to make it worst case, they both fold the river when you hit and they don't.
So 20% of the time you win the current 6.5BB, plus about 5 more (assuming the SB bets/calls down). The rest of the time you lose 1 SB on the flop and 1 BB on the turn.
Soo EV = 0.2*11.5-0.8*1.5 = 1.1. You expect to win 1.1 BB with this play.

Second case, you do raise. Both of those guys fold. So now you win 26% of the time, not 20, but your implied odds are lower. When you hit you win 6.5+2.5 = 9BB
EV = 0.26*9-0.74*2 = 0.86BB.

SO.. I believe S&M. I'm sure they know what they're talking about. And this whole 'calculation' was so full of assumptions, I know one of them (or more) must be wrong. What I'm wondering is: where is my gross mis-assumption.

To answer my own question: I'm thinking it's because I'm discounting the chance that I have the best hand after the flop. Probably if I Knew SB (or somebody) had a queen, this wouldn't be a good raise. But since I *might* have the best hand right now, or make a slightly better (but not TP) hand fold, it becomes worthwhile.
Is that it?
Whew..