Simple calculation

SlowHabit · #1 11-23-2007, 04:36 AM

It's quite embarrassing that after so many hands of poker, I don't know how to do a simple equity calculation. Can you guys enlighten me?

Problem 1
Money already in pot: $1000
Villain's stack: $900
Hero's stack: $800

Villain's equity: 75%
Hero's equity: 25%

I make it hot on the flop and pushed. If Villain folds, I win $1000; ez moneys.

If Villain calls, his hand has an equity of $600. My hand has an equity of $450. Total, I lose $150 every time Villain calls.

So, the question is "what percentage of the time should Villain go away so I can break even?"

I use the following formula. Please correct me if I'm wrong. Thanks.

0 = 1000x + (1-x)(-150)

Problem 2:
Money already in pot: $1000
Villain's stack: $1000
Hero's stack: $1250

Villain's equity: 75%
Hero's equity: 25%

Problem 3
Money already in pot: $1950
Villain's stack: $1000
Hero's stack: $1250

Villain's equity: 75%
Hero's equity: 25%

Once again, thanks!

sixhigh · #2 11-23-2007, 05:03 AM

Well your formula is correct and your equities in the first problem are also correct. What's the question?

SlowHabit · #3 11-23-2007, 05:15 AM

[ QUOTE ]
Well your formula is correct and your equities in the first problem are also correct. What's the question?

[/ QUOTE ]
If the process I used to derive the equation to figure out X is correct. I have never done this and just want to make sure before I start adjusting my game [img]/images/graemlins/cool.gif[/img]

Fabian · #4 11-23-2007, 11:25 AM

The way I think about it is this:

Every time you push instead of checkfold (assume 0% fold equity here), you lose $150. Every time you push and make him fold, you win $1000. To make up for the $150 losses, you need to make him fold 150 / (150+1000) = 13ish% of the time. Intuitively this makes sense to me, and the math checks out too of course. Also not sure what the question is exactly so maybe this reply was useless.

SlowHabit · #5 11-23-2007, 05:24 PM

The question is "are the hands' equities correct?"

sixhigh · #6 11-23-2007, 05:57 PM

Yes they are.

Say the amount in the pot is p, the amount required to push is a and your pot equity when called is e.

Then your EV in case he calls you is

EV_c = (p + 2*a) * e - a

...... = (p + a) * e - a * (1 - e)

Now if your fold equity is f. The EV of pushing now is

EV_push = f * p + (1 - f) * EV_c

........... = f * p + (1 - f) * ( (p +2*a) * e - a )