The following hand came up tonight and was wondering how to do the math properly.
In a limped pot pre (~$25) the board came out QcJc7h and the following action happened:
Villian 1 - Shoves all in for 320 postflop into a pot of 25 and I assigned him the following range partly based on what I thought he had (mainly flush draws because he had done this earlier with a flush combo draw) and what he actually ended up having (which was Ah,Ad): KK+,AQs,Ac9c,Ac8c,Ac7c,Ac6c,Ac5c,Ac4c,Ac3c,Ac2c,KQ s,9c8c,8c7c,7c6c,AQo,KQo

Villian 2 - Thinks for a bit and calls for his last 220 and I put him on the following range: 77,QJs,Q7s,J7s,QJo,Q7o,J7o

Hero has KcTc (and covers both villians) and ponders and ends up folding which I later found was a mistake. Was wondering if someone could show me the math on how big of a mistake it was with my ~40% equity vs both ranges. Thanks!

You have 41.9% equity in the main pot, which is $465 before you call. So you have to pay $220 to get into that pot which will then be $685. Your share of that pot is $287 (685*.419), so you have a +EV of $67, given those ranges.

The side pot would be $100, plus your $100, and your equity in it would be 53.4% so your share would be $106.80, or a positive EV of $6.80.

Therefore, your EV of calling these shoves would be +$73.80.

You need to pay 320 to win a total final pot (including your chips) of 885.

Your pot odds are 320/885 = 36.15%. Your equity in the pot needs to be bigger than that to justify a call.

There are some hands that crush us such as A9 and 77. Obviously we have a monster draw but I don't particularly like calling in a spot like this. If they're shoving 320 into a pot of 25, there will probably be better spots where we can narrow their range better and where we're the one with the lead and fold equity.

Garick - Thanks. Your explanation of the math was very straightforward and easy to understand. I got similar numbers but the way I did it was much more confusing and time consuming.

Nogyong - Yeah I agree with you and that's what I was thinking at the time. But when I looked up my equity, I was surprised at how big a mistake it was mathematically. I guess it's because my equity doesn't change a whole lot in a 3 way pot compared to a 2 way pot, since one of the villians is now crushed by the other guy. Thanks for your input

I assigned slightly different ranges that may or may not be more accurate:

ProPokerTools Hold'em Simulation

643,839 trials (Exhaustive)

board: QJ7

Hand	Pot equity	Wins	Ties
KcTc	42.46%	272,949	912
Ac*c, QJ, Q7, J7, AA, KK, QQ, JJ, 77, 9c8c, 9c7c, 8c7c, 7c6c, 7c5c	20.39%	120,641	21,301
QJ, Qs7s, Qd7d, Js7s, Jd7d, Ac7c, 77	37.14%	228,948	20,389