Question: Expected Value, Equity

ive been a member here for a while ...though im not real active here...i think this is the place to ask my questions.....since my question at another forum was answered with a post from here i believe

i see alot of players talkin about +/- EV...and equity....can someone break it down for me....

i dont ask many questions...ive learned through playin ...but when i ask a question i expect a good answer please dont act like im stupid...any help would be wonderfull

thxs
Brandon

bookmark, as I don't have much of a clue about equity +/-EV either and would love to know.

I'm going to move this to Poker Strategies. Hopefully F Paulsson, Dorkus, or any one of our other members well-versed in this topic will chime in (and I know they will ).

Heres a good start . https://www.cardschat.com/poker-odds-expected-value.php

EV = expected value = Your expected return on a wager.

Taking a simple example...

You push preflop for 1000 chips total from the small blind, Villain has 100 chips also in the big blind and calls, and it turns out you are a 70/30 favourite. You work out your EV by multiplying the possible outcomes by the probability of that outcome and adding them together. So in this example...

EV = (0.7*2000) + (0.3*0) = 1400

Here, the 0.7*2000 reflects the 70% chance you will double up to 2000 chips, likewise the 0.3*0 reflects the 30% chance you will bust. As you can expect to finish the hand with 1400 chips on average, the EV of your push given that villain called is +400 chips. Constrastingly, Villain's EV (assuming he has 100 chips like you) is (0.3*2000) + (0.7*0) = 600 = -400. On average he will have 400 less chips than he started the hand with (which makes sense, as your +400 EV has to come from somewhere ).

This obviously gets a lot more complicated once you start calculating for ranges of hands that villain can hold, probabilities of villain folding to bets, and so on and so forth, but that's the basic premise of EV. I can do a more complex example if you like, just let me know.

Fold equity is the extra value you get from making a bet if your opponent(s) fold. If you're shortstacked and have say 3 big blinds and push from the small blind into the big blind who happens to be chipleader, your fold equity is very small, as it is very unlikely he will fold. If you raise 4BBs preflop UTG on the bubble of a tournament, for example, your fold equity is considerably larger.

go ahead and lay it all on me....im pretty well versed in most of the numbers in the game....but i need toknow how important it is to be able to use this

Nice Chris. Now for equity. This should be easy to understand for anyone who owns a house. Actually, you usually dont own it. You share ownership with the bank and of course your equity is your share of the value of the house, whatever principle you've payed in + any increase in value since you bought it. In poker, it has become fashionable, thanks to poker software like Poker Tracker and Poker Stove, to refer to your share of a pot as your Equity and it cooresponds fairly closely with your mathematical probablity of winning the pot.

The best way to understand it is to pretend for a second that after the flop, everyone turned over their hands so that all players involved in the pot could see the hands of everyone else. They could then reconsider the values of their own hands against those of the others. If a decision were made to divide the pot between the remaining player, or continue on to the next round of betting, your equity would be the amount you would be willing to settle for assuming you had perfect understanding of your odds of winning or splitting.

But we all know that this is not the way a hand is actually played, so why use this terminology at all? Does it serve any purpose other than sounding real complicated. Well, it does. Sometimes we forget that when we're making bets, we're actually making investments based on the "assumed" value of a particular hand. We also forget that every hand has value, even the lowly 72o, and as long as the value, based on it's equity, exceeds the bet size, you're making a sound investment. This concept apply's more to ring games than to tournaments where the value of a hand rises and falls depending apon your relative stack size and the size of the purse.

For some reason I read "equity" as "fold equity" in the OP.

so dork....is that little ev equation work always........like the 4/2 rule...or is that just for example purposes

More complex example

Your stack: 2000
Villain's stack: 1500

Blinds: 25/50

You have QQ in MP. Villain is SB. Folded to you, you raise to 150 preflop, folded to Villain who calls, BB folds. Two players see a Ts8s4c flop. Villain checks, you bet 250, villain checkraises all-in.

What's the EV of folding? What's the EV of calling? The EV of folding is easy. If you fold you lose 400 chips, so EV(fold) = -400

Working out the EV of calling is more tricky. First we have to assign a range of possible holdings to Villain. Let's use something like this. We're assuming Villain is a reasonable player for the sake of simplicity.

(I got the win %s from PokerStove. If you're serious about stats in poker, get it, it's free)

AA, KK - Unlikely (surely villain would have reraised preflop), but maybe Villain has played AA/KK trickily.
5% chance, Hero is 10% to win.

JT+ - Plausible, makes some sense given the action and there are many possible combinations of top pair hands.
30% chance, Hero is 80% to win.

TT, 88, 44 - Again, reasonable possible holdings. Fewer combinations, but it's probably more likely villain plays a set like this on the flop than top pair.
25% chance, Hero is 10% to win.

AsJs+, KsJs+, QsJs - Again, reasonable to assume villain would call with these preflop and semibluff your c-bet with a flush draw and overcard(s) on the flop.
30% chance, Hero is 70% (average) to win

Nothing - Harrington says allow a 10% at least that a player is totally bluffing. We'll use the minimum here, as it's unlikely Villain would want to commit all his chips on a total bluff.
10% chance, Using AJo as a 'control' hand (as the probability of villain bluffing with total junk {53o etc} is tiny), Hero is 82% to win

So...

EV(call) = (1550*(0.05*0.1)) + (-1500*(0.05*0.9)) <--- This is for the occasions Villain has AA/KK
+ (1550*(0.3*0.8)) + (-1500*(0.3*0.2)) <--- If villain has JT+
+ (1550*(0.25*0.1)) + (-1500*0.25*0.9)) <--- If villain has TT, 88, 44
+ (1550*(0.3*0.7)) + (-1500*0.3*0.3)) <--- If villain has AsJs+, KsJs+, QsJs
+ (1550*(0.1*0.82)) + (-1500*(0.1*0.18)) <--- If villain is bluffing (using AJo)

EV(call) = (7.75 - 67.5) + (372 - 90) + (38.75 - 337.5) + (325.5 - 135) + (127.1 - 27)
= +214.1

In other words you will end up with 214.1 chips more that you started the hand with on average if you call. If you compare with the EV of folding.

EV(call compared with folding) = 214.1 + 400 = 614.1

In other words you end up on average with 614.1 chips more than would have had by folding. Sometimes what seems like a -EV decision can actually be a +EV decision when compared with the alternative.


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Taking a look at a bit of the calculation in depth.

(1550*(0.05*0.1)) + (-1500*(0.05*0.9)) <--- This is for the occasions Villain has AA/KK

Here the 1550 (villain's stack of 1500 + big blind of 50) is your gain if you win, the 0.05 is the probability Villain has AA/KK and the 0.1 is the probability you win the hand (and thus gain 1550 chips). Constrastingly the -1500 is your gain (loss) if you lose, the probability villain has AA/KK is still the same, and the 0.9 is the probability that you lose the hand (and thus lose 1500 chips).

cant wait to continue this conversation but im play 5k gp on prima....

but i think im actually gonna understand and like what im seeing......probably wouldnt hurt me to invest in a couple of books

definetly pick up some theory books