[iron81]

I think you're being too generous with 2.7:1. If we're breaking a 9 its because we're pretty sure an 8-7 is no good so we need to make a 7. If we need to make a 7, its a small pot so we don't have the odds to break. Personally, I'd rather 3 bet/pat round 3 than call/break because villain will likely break an 8-7 if we 3 bet/pat.

The problem with 3 betting is that then we have to check the river which turns our hand face up as weak regardless of whether we got villain to break. This means we have to pay off a bet