[DanZ]

As alluded to in my post, you can get 4 more outs when the cold caller mucks aces up on the turn. 4 outs is not worth 2 big bets, since the pot is not going to be 20 big bets. But, the pot is very big - about 10 big bets before the turn action.

So, let's anaylze the following in a fantastically crude way:

You are against a straight and set. You will likely pay 1 bet and fold when it is 3 back to you. You cost yourself 1 out in a pot that would otherwise project to be about 14 big bets. However, you will likely lose that same bet on the river, and will save perhaps calling 2 on the river - though you could safely fold to 2 on the river here, or fold if a k or j comes. Let's approxiamte and say that this costs about 1/3 of a big bet on average over checking behind, but is not the case all that often - say it's 20% of the time.

let's say you are against a set from the cold caller and 2 pair from the BB. This is analagous to before, except there is danger the higher set will not raise, and you get trapped for paying off twice. Give this another 20%, and it will, on average cost more, but you get your 1 out draw much of the time. Call this scenario a 1.5 big bet loser.

Cold caller has KQ or KK, BB has straight - well, you get check raised and may lose someone drawing dead. This is a cost of about 3/4 of 2 bets on the turn, with no upside real upside. Call this 10% of the time.

Let's say you are against aces up twice. Now, you win 2 extra bets twice as they likely both call you down. Since they are drawing to very little, we can call this a 1.8 bet profit or so, and say this happens 10% of the time.
Another 10%, you are against aces up and a draw of KK or KQ, and this is worth roughly 1.6 big bets to get called on the turn in 2 spots. If the BB rasies aces up, this is even more profitable for you, so let's stick with the conservative number.

Let's try this one - BB has J9, and other player has aces up. Same as above, but your hand is worse. call this 5%, and profit is about 1.4 BB.

Now the most likely scenario - 25% for straight in BB, aces up in cold caller. We get raised on the turn, which costs us about 1.6 BB since we have at most 8 outs, however, this bet saves us a 12 big bet pot by buying us 4 outs. This is worth about 1.2 big bets. In other words, this scenario has a very small cost.

In a nutshell, 35% of the time, the bet is very profitable, 45% of the time, it's slightly unprofitable, and 20% of the time, it's very unprofitable.

This makes the bet correct. Notice the really bad outcome is when you are against a higher set and for whatever reason cannot fold, and this only happens when the BB does not have a straight. Since the BB has a straight is only about a small bet loser on your bet , you would need to weigh the other scenarios against that, with the good scenario more profitable than the bad by a half bet, and the good about a 2-1 favorite over the truly bad, you have this:

-slightly bad*.4 + (1-slightly bad)*2/3*1.7 - (1-slightly bad)*1/3* -1.2 =
-slightly bad*.4 + (1-slightly bad) *.8 =
break even is 7/12 or about 66%.

The most contentious assumption among these is the likelihood of set over set being so high. This translates to a much higher % of "BB has straight" for a break even point. If we reduce that figure to half of what I have, the bet break even % for BB has straight is around 75%.

Dan Z.