Ok, 6 max trny.

hero: bb, 35 bb's
utg+2 : 100 bb's
btn: 100 bb's (eff. stacks 35, w/e)

utg+2 opens with minraise, btn 3 bets to 5 bb's, so about 10 bb's in pot.
I have Ac2c. OR opens 30%, btn 3bets 5%. I want to jam but like to do the math first (hypothetically)

How do we quantify the times both players fold or call to get our fold equity?

I know how to do this heads up but get a lil' lost when it's multiway.

for short, I'd like to get the average FE amount when taken every outcome in consideration.

dunno, makes sense?

TY!

Here is how you do it. Consider all of the possible scenarios.

Scenario 1: You shove, and both players fold.
Scenario 2: You shove and CO (you called him UTG+2 which is weird in 6 max) calls, while button folds.
Scenario 3: You shove, CO folds and button calls.
Scenario 4: You shove and both players call.

Technically there are other scenarios (e.g. CO calls, button shoves and CO folds; both call but one folds on the flop) but I will ignore those for simplicity.

You need three pieces of information about each of these 4 scenarios to calculate your EV. First, you need to know how large the pot will be in each scenario. For example, in scenario 1 there are 8.5BBs in the pot (why did you call it about 10; are there antes?) in the pot when you shove. Your shove adds 35BBs for a total of 43.5BBs. No other money goes into the pot.

Second, you need to know your equity against their hand ranges. In the first scenario it is easy. They have no hands, so you have 100% equity. You multiply your equity times the size of the pot. So 1.0 * 43.5 = 43.5BBs. From here you probably want to calculate your "gain" so you subtract your starting stack of 35BBs to get +8.5BBs.

Third, you need to know the probability of each scenario. For scenario 1, you want to know how many hands in the CO's top 30% of hands he will fold. Let's just say that is 80% of his hands he will fold with. Then you need to know how many hands in the Button's top 5% he will fold with. Let's say he will only fold with 10% of those. So both players fold .80 * .10 = .08 of the time.

Now you multiply each scenario's gain/loss times the probability that it occurs and add up all 4 of the results. In the case of scenario 1, it is .08 * 8.5 = 0.68BBs.


The real trick to this if figuring out which hands in each players' range that he will fold to your shove, and which one's he will call with. In reality though, this will be even more difficult to estimate than usual because the Button's calling range might change based on what the CO does. If the CO calls (or shoves) for example, the button might be more likely to fold. But once you have their calling/folding ranges figured out, you can easily figure out what percentage of their opening ranges they are calling/folding with and you can figure out your equity against whatever hands remain.

If you just do the problem one step at a time you can solve it. I have my doubts about the precision of the answer in practice though as it will be largely determined by your assumptions.

Ty sherman, it was this part I was a little unsure about, although it's logical enough. Yes there were antes, so bout 10 bb's. also, cutoff, yes of course.
ty sir. Guess that makes this a pretty easy shove then

Isn't there a math rule that you can quantify any probability as long as they are not independant? What is a simple way to determine if something is independant or not? #mathnoob.

They are independent if the outcome of one event does not depend on the outcome of another event.

For example, the second hand you are dealt in a hold'em game does not depend in any way on the first hand you were dealt. The hands are independent.

In your situation, you can assume independence even though there is not. The Button's decision will depend on the CO's decision at least some of the time. So their decisions (whatever they may be) are not independent. However, to make the math easier it is often useful to assume they are independent...particularly when the dependencies are small (as in this case).

Here is an example of how they are not independent though. Some players like to "keep players honest" so if the CO folds, the Button might decide to widen his calling range.

For what it is worth, I am pretty sure the play is going to be -EV without doing the math. If the button is only 3 betting 5% of all hands he is dealt, he already has a very narrow range. Therefore, you will not get them both to fold very often. In addition, his narrow range probably crushes your A2s hand. So you will have little equity when called. Little equity from folds and little equity when called = probably a -EV play.