Mathematical analysis of push fold mode

[pat3392]

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:

66+,A9s+,KJs+,QJs,ATo+,KJo+

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:

expected value= 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)

Therefore,

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??

[revolvingiris]

Should have everything you need:

http://www.flopturnriver.com/pokerfo...se-136353.html

Also your calling range is way too tight for players calling out of the blinds in MTTs. Those look more like a calling range for STT.

Take every +EV spot you can find in MTTs. Most "waiting for a better spot" moments are players realizing they are beat and not wanting to chalk it up to that. Any time you add chips to your stack you increase your odds of winning. Just take your chipstack/ total chips in play and you have your "how often you will win" percentage (minus skill).