to finish my thoughts

[jyms]

In my thoughts on devs response cna someone explain this if I am wrong.

when a hand is 35% to win you have 35% equity in the pot.
When you have 35% fold equity, you have a 35% chance of the opponent folding and winning the pot.

If you have a hand that has 35% equity and you "think" you have 35% fold equity,

This means that if you bet $10 into a $25 pot you earn 35% of $45 pot when the opponent calls or $15.75.

If the opponent folds 35% of the time when you bet $10 into a $25 pot you will earn 3.5 x $25 pot or $87.5

When he calls your bet the other 6.5 times you will win $15.75 based on the equity per hand, or $102.37 and will lose $190.12

Total win $189.87 and you will lose $190.12 for basically a break even play.

How can we sacrifice equity if FE is high.

[bjsaust]

I think its a strange way of saying we can make up for not enough hand equity with fold equity.

[DemonDaze]

Assuming you mean 35% Equity against his calling range.

Really need to know your equity against his entire range as well, to know if you are losing EV by betting.

[loonychune]

This is how you would work out your expectation value for each time you make this play.

Expectation when leading: <Jyms> = <Jyms Bets $10 into $25 pot with 35% equity expecting opponent to always call>

<Jyms> = 35% of New Pot Size - Cost of a Bet (1)
= 0.35($45) - $10 = $5.75

But if we introduce fold equity now, we have

<Jyms got FE> = 0.35($45) + 0.35($25) - $10 = $14.50 (2)

This is interesting me since our expectation value when we don't bet and opponent just checks is

<Passive> = 0.35($25) = $8.75. (3)

So we'll always make more by betting in this spot. In fact, going back to (2), if we make it

<Jyms> = 0.35($45) + p*($25) - 10 = $8.75

and we solve this, then,

p = 0.12

So we always make more betting here than letting our opponent check behind us if we have >= 12% fold equity.

EDIT:

Let me know if this is useful (/correct). I could re-write to be more explanatory if it just looks like a bunch of numbers thrown in to an equation (which it isn't).

Fold equity expectation value:

<Jyms with FE> = (probability of winning)*(size of pot after bet and call) + (fold equity as a probability)*(size of current pot) - (size of bet)

There is so much room for analysis here it's ridiculous. What about if opponent raises some of the time, what about if he doesn't check behind when we check, etc.

[DemonDaze]

When you have 35% fold equity, you have a 35% chance of the opponent folding and winning the pot.

Your definitions are incorrect. If your opponent only folds hands that you already beat (assuming the river), you have zero fold equity.

http://en.wikipedia.org/wiki/Fold_equity

[loonychune]

Glad you posted demon.

SOME OF MY PREVIOUS MATHS IS WRONG.

If we look at it another way though: we know he's going to fold 35% of the time and he's calling the other 65% of the time.

I mean, does it not make sense to say: he'll fold here 35% of the time and he'll call 65% of the time.

> Our EV is as in (1) 65% of the time.
> Our opponent folds 35% of the time and we win a $25 pot.

Possibly:

<jyms> = 0.65*{0.35*($45) - $10} + 0.35*($25)
<jyms> = $3.74 + $8.75 = $12.49

If he folds 35% of his range that beats us, then he folds 22% of the time so the second term above would be 0.22*($25). BUT then what is our equity against his range the other 78% of the time now that he's folding some of it?

Maybe it's just the same:

<jyms> = 0.78*{0.35*($45) - $10} + 0.22($25)

When we're in a spot though, we're usually gonna say: he folds here x % of the time and he calls y % of the time and because we win a different sized pots when he calls or folds i think we just use the new ('possible') equations above.

It'd be nice if you looked at the maths and how it applies as opposed to the nature of definitions...