Equity

I have a couple of questions regarding equity.

Firstly, is total equity simply (the equity of my hand against an opponents range) + (the fold equity) .

So equity against an opponents range can be determined by using pokerstove.

Is fold equity simply the percentage of folds the villian likely to make against the next bet.

So may opponent folds preflop 33% of the time against a 3 bet then do I use 33%. If he calls then is the fold equity then the percentage that he will fold on the flop.

Now, if my hand has 25% value equity and 35% fold equity I have 60% equity... what do I actually do with that infomation? How does it effect my bet size etc etc.

I'm not entirely sure about how to use the information and everything, but one thing does stick out at me. You don't actually have 60% equity. You have 35% equity based on fold equity. Right there you win 35% of all hands. You also win 25% of the remaining 65% of hands.

So your total "EV" so to speak is:

.35 + .25*.65 -> .35 + .1625 = 51.25%

This number though is not, in fact, expected value. It is merely the total percent of all hands that you will win. To find EV, we must weigh the various outcomes by the size of the resulting pots for each outcome.

Assuming 100bb effective stacks, and standard 4bb open from villain.

If we're just getting it in with this (to simplify the equation) then you win the 4bb immediately 35% of the time. The other 65% of the time stacks are contested and you win 25% of those.

.35(4) + .65*.75(-100) + .65*.25(100) -> 1.4bb + (-48.75bb) + 16.25bb = -31.1bb

As you can see, the EV of getting it in here is still negative even though we will win over 50% of all hands. This is the simplest equation as there is no postflop play occurring. Perhaps I'll take a look at those situations in more detail.

Since I gave you all that rambling, I guess I'll try to give you something useful as well. I have a feeling this may be more what you were looking for to begin with, but I love numbers so I got caught up with all the previous stuff.

You only need the fold to 3bet variable for this one.

Anytime you make a bet there is a formula to find the break-even point, the percentage with which a bet needs to take down the pot to break even. If you win any more than this %, you will show a profit.

For example, the 1/2 pot cbet. A lot of people know that this bet only has to take down the pot 1/3 of the time to break even. If you bet $5 at $15 three times you spend $15 in bets. If you win one of them you win $15 for a net profit of $0. If you get any more than 1/3 folds, over a larger sample size, you'll have a nice profit.

The formula to find this breakeven point is:
Bet / (Bet + Pot)

The previous example would be: $5 / ($5+$10) = .333

In the case of 3betting here, you already know how often your opponent will fold, 33% of the time. (Lots of opponents will have a larger % than this) Let's look at a standard 3bet against this fold %.

Villain raises to 4bb, and there are 1.5bb starting in the pot. We'll 3bet from 3-4x his initial raise. I'm not going to show all the math, but breakeven points for each raise size are as follows:

Size of raise in X*opening raise | In total bb's | Breakeven %

3.00 | 12 | 68.5%
3.25 | 13 | 70.3%
3.50 | 14 | 71.8%
3.75 | 15 | 73.2%
4.00 | 16 | 74.4%

As you can see, you need the player to fold the vast majority of the time to have a 3bet show an immediate profit. Luckily there are other ways in which a 3bet can generate you profit, such as an increased likelyhood of successfully cbetting, being ahead of villain's range to start, etc.

VEry interesting mate, gives me some things to think about

Hey Mase. You like numbers..

absolute value means if its negative drop the minus sign to give a positive result so the absolute value of - 10 is 10.. I think its called absolute value.

Anyway could total equity actually be the absolute value of :-

value equity - fold equity

So if the value of a hand is 50% and the fold equity is 65%.. rather adding 50%+ 65% to get 115% (I know I know)

the value is the absolute of 50 - 65 = 15%

Then if you consider the fold equity of the hand.. it means this the villian will fold to most bets.. so a bet is in order.

If the villian calls, the value of the hand drops from 50% to 15% because the call or raise combined with that fold percentage means the villians hand is increadibly strong.

Just an idea that poppped into my head.

That doesnt sound right to me. Stu, I've been reading alot on this and im going to put up a post as soon as i get my internet fixed and dont have to post this from the schools internet.

But basically it's what was said above. You put your opponent on a range and based upon your perceived ability of him you decide how often you can get him to fold right there.

Then you use a program such as pokerstove to evaluate your all-in EV which is your value equity in the hand based upon your opponents range and the board texture.

From those two you can figure out your total equity in a pot.

Here's an example:

Lets say you get dealt KcQc in the CO, its folded around to you and you make a standard 3x raise. BTN and SB fold, but the BB is a decent LAG and elects to flat you OOP.

Board comes 9c 10d 4c

you bet out pot, 7bb, he raises to 35bb, and you shove.

its a good decision because your WAY ahead of everything in his range except sets.

at this point your Equity is 57% vs his 43% if you put him on sets, any 10, overpairs and other combo draws, or a little better than a coin flip.

However, lets say you get him to fold 40% of your shoves, that gives you 49bb in dead money. so for a .50/1 game thats $49 you take down right there.

If he calls you're roughly a 60/40 favorite so your EV is $120 (assuming both parties had 100bb stacks).

so you get (and this is where im still learning so hopefully someone will check my math for me)

(49(.40))+(.57*200)=19.6+114=133.6 or +33.6bb EV

With the given numbers, $100 (100bb) stacks, 40% FE, and 57% chance to win, EV looks like this:

When he raises to 35 his stack is 62bb
Our stack is 90bb
Pot is 49bb

When we shove, and he calls, our EV is $24.57

$24.57 = (.57)($111) + (.43)(-$90)

When we shove and he folds, our EV is $49.

To get our total EV, we weigh each of these outcomes by their likelyhood.
As we've assigned a 40% chance of fold, our total EV is $34.34.

$34.34 = (.60)($24.57) + (.40)($49)

Stu, the use of absolute value in calculating EV is a very intriguing concept. I'm going to have to wrap my brain around it for a bit