Quick math lesson about Folding Equity for all the n00bs

[punter11235]

Hey all,

I think it may be useful.
Here is the problem we often see : We have a hand, we want to push. We know approximately what will call us and we wonder how often Villain needs to fold for our push to be profitable.
Here is quick course how to do it very fast. I am able to do that calcs in about 15 seconds and I am not even that quick with teh numbers. So here we go.

a)First everybody here is (I hope) familiar with standard calculation of the type : "we have pure bluff and the pot is 100$, we bluff 50$ so we need to win 1 time in 3 to break even). This will be basics for :
b)We have some chances if called !
Here is what we do :
- we run pokerstove with our hand vs his calling range (unfortunately we have to estimate it properly);
- now we calculate FINAL pot (after our call) and see how much is our equity there ( [win % we get from PStove * final pot).
- we calculate :
(our contribution to the pot) - (our equity in final pot). Call this number P.

-Now we treat it as pure bluff problem (like in A) with our bet size being P and pot staying the same.

Simple right ?

Two examples :

1)we have 35% to win if called (say flush draw). There is 100$ in the pot. Opponent bets 70$. We have 400$ more, he covers.
We push.
Our equity is 35%. Final pot if called is 900$ so our equity in final pot is 35% * 900$ = 315$.

We need to invest 400$ so the number P is :
400$ - 315$ = 85$.

Now its like betting 85$ into pot of 170$ with no chance to win.
Everybody can calculate needed FE now in just 2 seconds... (I hope). Just in case its (1/3).

2)Cole vs Yvesaint thread from MSNL. Here of course we cant know the exact Cole range.

Just summary : 4k stacks. 5handed live 10/20 game.
Cts opens for 100$, tourists call, Yvesaint make it 450$ with A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img]
Call makes it 1100$. Tourists folded and its up to Yvesaint.
We wonder how often Cts needs to fold for our push to be profitable.
We assume that his calling range is QQ, AK.

Lets do our steps :

-Text results appended to pokerstove.txt

143,833,536 games 0.032 secs 4,494,798,000 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 58.096% 38.81% 19.28% 55825068 27736416.00 { QQ+, AKs, AKo }
Hand 1: 41.904% 22.62% 19.28% 32535636 27736416.00 { AKs }

So our equity in the pot is 41.9%.

Final pot will be 8100$. 8100$ * 41.9% = 3393$.
We need to put 3550$ more.
There is now 1100$ + 100$ + 450$ = 1650$ in the pot.

Number P is 3550$- 3393$ = 156$ or about 150$.

So its like betting 150$ into the pot of 1650$ without no chance to win.

So we need to win it now 150$ / 1800$ = 1/12 of the time to break even.

Its all pretty simple and intuitive if you understand that number P is our REAL cost of the bluff (as we got something back from final pot).

I hope it will be helpful for some people.
Feel free to comment ask questions, point mistakes if you feel like it.

[BobboFitos]

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[therockofgibraltar]

very nice! thanks!

[Freelancer]

Awesome !!


(I never get a single calculation done in time on the tables so this might help me out [img]/images/graemlins/tongue.gif[/img])

[SABR42]

[ QUOTE ]
Loc: Poland

[/ QUOTE ]
Mówisz po polsku?

[Mossberg]

Nice post.

Re-up.

[dardo]

Thanks, good trick.

dardo

[andyEB]

Very useful -- thanks!

[Mossberg]

master sticky?