Lets say I push allin on BU, SB calls and then BB overcalls?
How do I calculate the percentage that I will lose e.g. to SB but win side pot against BB (or vice versa)?

I am looking into ICM calculations and see pokertracker taking these scenarios into account in the quiz but I have no idea how the come up with the numbers.

For simplicity I'll ignore the probability of chops and consider equity to be the probability of winning. It shouldn't be too hard to add in, but more work.

P(beat BB) = P(beat BB but lose to SB)+P(beat SB and BB)
P(beat BB but lose to SB) = P(beat BB)-P(beat SB and BB)

Example: We shove 55, SB calls with KQ, BB calls with AK.




P(beat BB) = .5622
P(beat BB and SB) = .3968
P(beat BB but lose to SB) = .5622-.3968 = .1654

I don't get it, your numbers aren't adding up. Using your example and lets say SB is small stack.
BU win 39.55%
BB win 34.63%
SB with BU side 25.23% *0.5594
SB with BB side 25.23% * 0.4351

is that correct?

No. You can find the probability of two events both happening by multiplying their individual probabilities, but only if the events are independent! That is not the case here, because the probability that BU beats BB overall is different from the probability that BU beats BB given that the BU loses to SB.

Think of it this way if it helps. If you are given the information that BU's 55 lost to SB's KQs, do you think the probability that BU has beaten BB is still 55.94%?

A different example may make it more obvious. If BU shoves with QQ, SB calls with KK and BB overcalls with AA, and I tell you SB beat BU, that means BU probably didn't hit a set, and is very likely to have also lost to BB, much more likely than the 80%-ish chance of losing independent of this knowledge. So you can't just say P(BU beats BB and loses to SB) = P(BU beats BB)*P(BU loses to SB)

so how do you get to unity if SB is short stack? Is it:

BU win 39.68%
BB win 35.09%
SB with BU side 16.54%
SB with BB side 25.23% - 16.54%

We need the SB vs BB heads-up matchup: SB's equity is 28.57%
We also need heads-up BU vs SB: BU=50.34%

Now we can fill in all 3! scenarios (not separately counting ones involving ties):

P(SB > BU > BB) = .1654
P(SB > BB > BU) = .4378 - .3509 = .0869
P(BU > SB > BB) = .2857 - .2523 = .0334
P(BU > BB > SB) = .7143 - .3509 = .3634
P(BB > BU > SB) = .5034 - .3968 = .1066
P(BB > SB > BU) = .4966 - .2523 = .2443

Those add exactly to 1.

If SB is short stack then he can't win any side pots or am I wrong?

Ah right, so then it's just:

BU = .3968
BB = .3509
P(SB > BU > BB) = .1654
P(SB > BB > BU) = .0869

Which I see is exactly what you said in your previous post lol