If we have a big combo draw like an OESFD we are AHEAD of everything but sets.
Text results appended to pokerstove.txt
38,610 games 0.005 secs 7,722,000 games/sec
Board: Ad 8h 9h
Dead:
equity win tie pots won pots tied
Hand 0: 51.901% 51.90% 00.00% 20039 0.00 { AA, 99-88, AKs, A9s-A8s, AKo, A9o-A8o }
Hand 1: 48.099% 48.10% 00.00% 18571 0.00 { JhTh }
... and in this particular case, we're actually a dog to AQ (since one of our queens is dead). But that's neither here nor there.
The only part of his range that we actually beat is AK. The rest we're a dog to. I've noticed in several threads the trend for people to treat combo draws as if they have 60%+ equity, and it's just not true. The reason they can be pushed hard is because they do usually have decent equity (~50%) but also because they have a lot of fold equity.
And although folding out top pair type hands isn't great, since we just got a worse hand to fold
And to clear up a misunderstanding about fold equity: We don't need him to fold "the best hand" for there to be fold equity. Fold equity is the money we gain from him folding a hand that isn't drawing dead. We have fold equity vs. a gutshot straight draw when we're holding a set if we push. Quite possibly not enough fold equity to make a push worth it, but fold equity nonetheless.
Case in point:
Pot is $30, My opponent I have both have $90 stacks. I push with 51% equity. I really want him to fold the worst hand.