Idiots Guide to Schwza's Math Test

[A_PLUS]

A few days ago, Schwza posted a quick poker math quiz. Most of us can do the math when we have 5 minutes and a pad of paper, but estimating these numbers in 30 seconds under pressure is tough. Very worthwhile excercise
Math Quiz

I made a major mistake on question #1, and realized that the way I calculate the % of time that I need an opponent to fold is way too detailed to be done in real time. So, I came up with a quick little short-cut that can be done in a a real hand.

Question
On the turn, it is my turn to act. I know I am behind. What % of his hands, would the villan need to fold, for a push to be correct by me?

Quick and Dirty Answer

1.) Calculate the total pot if you push, and he calls.
-Ignore the last 2 digits (10,000 ~ 100)
-multiply by you outs (100 x 8 = 800)
-double it (800 x 2 = 1600)
-subtract you current stack from this number
(1600-4000=-2400)
This number (-2400) is your EV when called [EVc]

2.) Look at the current pot relative to EVc (drop the
negative)
-Fill in the blank. Pot is ____ times as large as EVc.
-Pot (4000) is 1.66 times as large as EVc (2400)
-Add 1, and we have our answer (1.66+1 = 2.66)

I need my opponent to fold 1 of every 2.66 hands for this push to be profitable.
OR
I need my opponent to fold (1/2.66 = 37.59%) of the time.

Work through this a few times, and coming up with estimates becomes really easy. They arent exact, but close enough for me.

**If you are on the flop, rather than turn, multiply by 4 instead of 2 in step 1

[Matador225]

Nice post A Plus. I'm sure this will help a lot of people.

[Matador225]

Also just out of curiosity, how did you come up with this shortcut?

[A_PLUS]

I just set up the equation that I would use to solve it.

(% of time he folds) x (pot size + my stack) + (1-% he folds) x (showdown pot x equity) = my current stack

I substitutes 2 x (# of outs) / 100 = equity, which is a good guestimation method.

Then I just started rearranging things until something jumped out