I'm not sure about the answer to this, but it's one I've posed in multiple forums without really a clear resolution.  It relates (mainly before the final draw) to a spot where we're 3 ways and the round went 1:1:2 (or some permutation).  Should we, if we don't think the 1cd that has position on us is good enough to always bet when we check (or even if he is) be betting to get value from the 2cd (and I guess also for some kind of balance since we'll lead our pat hands here).  About 55 minutes in Triple the Gold episode 3 DeathDonkey suggests we bet to get value from the 2cd -- is it really worth it?

There are a few possible outcomes based on how our opponents draw when we bet.

1. Both opponents get pat (I'm assuming pat here means 8 or better which is obviously tighter than they'll be in reality most likely) -- this will happen probablistically somewhere around 2-3% of the time assuming the 1cd will get there about 1/4 of the time and the 2cd will get there around 1/10 of the time.
2. One pats -- this will happen about 30% of the time -- 1/4 the 1cd will get there 9/10 the 2cd won't, and 1/10 the 2cd will, 3/4 the 1cd won't.
3. 1cd unimproved, 2cd improves to 1cd -- this will happen about 36% -- 3/4 when the 1cd doesn't improve, 5/10 the 2cd imrpoves to a 1cd.
4. Both unimproved -- this will happen about 32% of the time based on the fact the 1cd won't improve 3/4 and 2cd won't improve about 4/10.

So what happens in each of these cases?

1. Here we lose 1BB and any equity (which is going to be fairly small most of the time) we had in the pot most likely since it's going bet/raise/3bet back to us and we're not even closing the action.
2. Here we lose some fraction of 1 BB (over checking and calling) depending on the smoothness of our draw and the pot odds we're getting (plus how often he's doing this with things like breakable Ts/9s) or relinquish equity based on our average equity in this spot.  I'll assume against a pat hand we have something like 15% equity on average (sometimes we'll be splitting our equity with the other 1cd when it's the 2cd that pats).
3. We get marginal value at best depending on the smoothness of draw.
4. We fold out 2cd and the equity he folds (which I think is going to be around 18%) is redistributed to Ivey and us (so we pick up something around 10% of the current pot size in value).

So what's our EV from each situation look like?

1. -1BB + ~0 (we'll just assume we're drawing dead or would never draw here).

2. -0.85BB

3. ~0

4. 10%*Current pot size

Taking into account the relative occurence: EV = (-1BB)(2%)+(-0.85BB)(30%)+(0)(36%+(10%*POT)(32%)

So if the pot is 5BB, EV ~ -0.12BB, 10BB, EV ~ +0.05BB

So maybe we should only tend to be doing this when the pot is big?

How important do we think not always having a pat when leading is here?