Equity Calculations?

[Acemanhattan]

How do you do an equity calculation based on your opponents suspected range of hands?

[mvdgaag]

You try to determine your chance of winning of his range and multiply by the pot. Sometimes this is easy (example 1), sometimes a bit harder (example 2).

Example 1: you hold AsJs, the board is KsQc7s. You have 13 outs to the nuts (9 spades and a T) I'm ignoring your overcard atm).
That makes around 13*4 = 52% to win. If there is a pot of $100 your equity is $52 at least, regardless of your opponents hand. If he hit nothing it's a bit higher because you'd win with A high, I'd overestimate my equity here, because you also have an overcard you might catch and a very small chance to win unimproved (especially if you get him to fold, this is called folding equity). So I'd go for $60 or so.

Example 2: You have AK on a board of JTAr. Your opponent could hold several hands that beat you, several draws that might beat you by the river and several hands you've got beat. Determining your equity has become a lot harder. You'll have to put him on a range. For each hand in that range find your equity and add them all weighed using the probability he holds that hand.

- he has two pair x% of the time. You have 9 outs (A, K, Q) so 35% equity.

- he has trips y% of the time You have 6 outs (A, Q) so 25%equity.

- he has a J or T with a live card z% of the time, so 6 outs (J, X) so you have 100-25= 75% equity

- he has... etc etc


total equity = (x*0.35 + y*0.24 + z*0.75 + etc.) * pot
remember x+y+z+... must add up to 1, or 100%.

This is quite hard to do by in an actual hand, but some quick assumptions and knowing some odds by heart will get you a long way.

GL

[n4sty]

You can do all these calculations in PokerStove after a session to see if you were making the right moves. You can see you hand againts a suspected range of opponent hands, usuing this i have remembered a lot when on the tables.

www.pokerstove.com

[afadeyi]

When people then begin to refer to fold equity, would this mean you have 40% fold equity? I'm not real sure how to calculate fold equity or how to think about it intuitively. Someone help.

Thanks

[Tjorriemorrie]

[ QUOTE ]
When people then begin to refer to fold equity, would this mean you have 40% fold equity? I'm not real sure how to calculate fold equity or how to think about it intuitively. Someone help.

Thanks

[/ QUOTE ]

try searching some times

Example:
[ QUOTE ]
A holds A6. She is heads up with B, who holds 22. The flop is 973 rainbow (no cards of the same suit).

A has pot equity of 31.5% B has pot equity of 68.5%

(In other words, if there was no further betting, and the players simply turned up their hands and were dealt the turn and river, A is 31.5% likely to win.)

If B is 70% likely to fold, A's fold equity is 47.95% (68.5 x .7). Consequently, A can consider that her hand equity if she bets will equal 31.5 + 47.95%, more than 80%.

[/ QUOTE ]
The main problem you're facing is getting to a good read on the chance the villian will fold. That's where you start using SD%, F-T%, fold to riverbet, etc.

Also, in a multiway pot of 4 people, if you know you might have the 2nd best hand, your pot equity could be 20%. But you know the last 2 players will most likely fold to a bet, then bet, because when they fold you're equity can go up to 40%.

[mvdgaag]

Fold equity is quite easy to calculate and understand.

Equity calculations are only valid if you both see the river, because you calculate your chance of winning at the showdown.

For example: There is a chance someone will fold, let's say 33% of the time. And you have 50% equity (if he calls).

Now you lose the pot 33% of the time and win it 66% of the time (33% when he folds and 50%*66% when you win and he doesn't fold)

FE, at this moment, is the equity gained from the chance you give your opponent to fold. Which is equal to your equity when folding is taken into account minus the equity when it isn't = 66%-50% = 16%. This would be $16 in a $100 pot pure profit because he might fold to a bet.

Naturally this should be higher than the expected losses if he calls a bet times the chance that he calls that bet.

Also bear in mind that this is your equity at this point. Your EV can be different! For example you have 80% equity and a 50% chance of him folding here.

than its : 50% win pot when he folds
50%*80% win (BIGGER POT) when he calls and you win
50%*20% lose (BIGGER POT) when he calls and you lose

So if you have a large chance of taking the pot right there, but can win a significantly larger pot a large amount of the time if you allow your opponent to get to a later street than you should not take advantage of this folding equity. This is what slowplaying is all about.

Slowplaying is mathematically correct when your EV of checking is higher than your EV of betting. This means that the value of the bet (if you have the best hand) AND the added EV from folding equity AND the value of protecting your hand is lower than your EV given by your implied odds. Notice that these are quite some demands and you should harly ever slowplay unless your opponent will quite certainly fold to a bet and can only improve to hands that you would still have beat if he does.

GL