[jcm4ccc]

I disagree that you can count your Aces as good. They might be, but in terms of decision-making, I think you have 9 outs (AK does not always reraise, BTW). You should be conservative when estimating whether or not you have a legitimate out. A9 is too poor to expect to win if an Ace hits on the turn or river, especially since you have 2 preflop callers who have yet to act on the flop.

So I'm assuming that you have 9 outs. The BB has made a pot-sized bet. If you put him all-in, you should assume that the SB and button will fold, since they have yet to enter the pot. Again, you should be conservative when estimating what will happen. You have little indication that the MP or Button will call a raise of 1100 chips when they have only invested 90 chips so far.

So what kind of FE do you need to make this break-even, chip-wise? You have 1110 chips if you fold. You will have 1830 chips if you push and BB folds. You will have 2580 chips if you push and BB calls and you win. So the formula is this:

1110 = (x * 1830) + [(1 - x) * .35 (2580)]

1110 = Chips if you fold
x = Folding Equity
1830 = Chips if you push and everyone folds
.35 = Chance of winning if you push and BB calls
2580 = Chips if you push and BB calls

Solving for x, you get:

1110 = 1830x + [(1-x) * 903]
1110 = 1830x +903 – 903x
207 = 927x
207/927 = x
22.3% = x

So you need him to fold 22.3% of the time to make this a break-even push. You want better than break-even, so let’s say that you need him to fold 25% of the time to make this a good push.

I’m assuming this is a low buy-in tournament. If it is, I would expect the BB to fold around 0% of the time. Okay, maybe 2-3% of the time.

This next statement will sound like I am calling you a donkey, and I’m really not. Nonetheless, I think it is the mark of the donkey to overestimate his outs (when he thinks about them at all) and to assume a favorable situation for acting aggressively (such as getting 2 or more callers to your push).