Mathematical analysis of push fold mode
This is going to be a long post so bare with me. I was wondering if my shove stealing moves when I'm short stacked are +EV, so I decided to do a mathematical analysis.
First of, I made a calling range for the average opponent I play against. Note that a calling is player and image dependent so it's not a fixed number, but I'll assume it is for this post. This is the calling range I gave them:
Poker stove told me that a person will get one of these hands 12% of the time.
I then compared every hand against villains calling range. I round it up to 5s to make it easier. Here's the hand vs. their range data:
These will win 25% of the time: T2-T5, 92-94, 82-83,72-73,62,52,42,32,J2-J6
These will win 30% of the time: K2-K9, Q2-Q9, J7-J9, T6-T8, 95-98, 84-87, 74-76, 63-65, 53-54, 43
These will win 35% of the time:A2-A9, KT-KJ, QT-QJ, JT, T9
These will win 40% of the time: AT, KQ, 22-55
These will win 45% of the time: AJ, 66-77
These will win 50% of the time: AQ, 88-99
These will win 60% of the time: AK-JJ
These will win 65% of the time: QQ
These will win 75% of the time: KK
These will win 85% of the time: AA
I didn't use suited cards as the relationship between win rate and suited or not was not clear; I thought I'd ask you guys instead of trying to figure it out. It seems that I can add 3.5% for low suited cards and 2% for high, something like that.
I'm not sure if the formula I made is correct. Anyway, here it is:
= chance to be called X [(chance will win X amount gained) + (chance will lose X - current stack size(calculated in M))] + chance will not be called X amount stolen( calculated by percentage of stack gained)
EV= 0.12P X [(W X (1+2M)) + (1 - W) X M)] + [(1 - 0.12P) X 1/M]
P= Players left to act, W= win percentage, M= effective stack size, calculated in M
Add the numbers into the equation and if it equals greater than 1, it is +EV. If this formula is accurate, I could memorize the numbers for when I play live poker, so that I know if the move is + EV or not. I might even be able to calculate it in my head with some practice/tricks.
However, just because the shove is + EV does that necessarily mean I should make that move? This formula doesn't consider the idea of "waiting for a better spot." It also sort of assumes that increasing my stack by x% means that I will increase my equity in the tournament by x%, which is not true. Just because I double up does not mean I doubled my chances of winning.
I'm not sure if the first part of the formula is correct: 0.12P part. What if there is a 10 handed table and I'm UTG. Does that mean I will be called 108% of the time??