What is Expected Value? (EV)

[dranger7070]

*Disclaimer*

I realize there is a thread in the Digest for EV, but it has examples for SNGs and talks about comparing $EV and cEV and it looks like a wall of text and that's just gay for a beginning poker player to look at. So I thought I'd write my own.

I'll do my best to keep this as simple and straightforward as possible so that someone just starting out can read and absorb it quickly and with as little pain as possible.

*/Disclaimer*

Positive Expected Value will now be known as +EV and Negative Expected Value will now be known as -EV.

So what is EV?

To put it quite simply, EV is what you expect make on average for making any play in a given hand.

Example:

PokerStars No-Limit Hold'em, $0.10 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

saw flop

Hero (UTG+1) ($10)
MP1 ($10)
MP2 ($6.25)
MP3 ($11.98)
CO ($12.72)
Button ($9.61)
SB ($4.09)
BB ($10.04)
UTG ($10)

Preflop: Hero is UTG+1 with A, A
UTG bets $0.30, Hero raises to $1.20, 7 folds, UTG raises to $3.10, Hero raises to $10 (All-In), UTG calls $6.90 (All-In)

Total pot: $20.15

Sweet! We got it all in pre-flop, ship the mannies, right?

Sort of.

Let's say Villain has KK in this exact hand.

According to Pokerstove, AA vs KK AIPF, AA has 81.946% equity.

What does this mean?

Basically, that we don't win 100% of the time we get it AIPF here.

More specifically, in this 200bb pot, we EXPECT to win 63.892bbs* (rounded up for simplicity) on average.

*To determine this, we use the equation (100bb * our equity) - (100bb - villain's equity) = EV

So. (100 * .81946) - (100 * .18054) =
(81.946) - (18.054) = 63.892

This is probably the simplest example I could give to show you what Expected Value is. Let's delve a little deeper.

The problem with the above example, is that we knew the villain's hand. As we all know, this is rarely (never) the case when playing a hand. We need to put villain on a range of hands, determine our equity vs given range, then do the equation to find out if the play was +EV or -EV.

Another example:

Too lazy to look up a hand in my database for this, so I'll just type this one out.

100bb stacks, Hero raises 4bb in MP1 with TT, TAG regular flats OTB with a range of hands.

Flop comes (Pot is 9.5bb)

Hero cbets 7bb, Villain raises to 21bb, Hero jams, Villain calls

Here, we need to determine a range of hands for Villain. {JJ, 77, AcKc-AcJc, KQs, JTs, 98s}

Was this shove profitable for us?

According to Pokerstove, our hand vs this range on this flop has 56.106% equity, resulting in an averageprofit of 12.212bbs.

(100 - .56106) - (200 - .43894)
56.106bb - 43.894bb = 12.212

The thing to note here, is regardless of what hand villain shows us, we still make on average 12.212bbs every time we make this play vs this range of hands. It doesn't matter if she shows us JJ for top set and has us crushed, or 77 and we have him dominated. The actual results of the hand DO NOT MATTER. We still won, 12.212bbs.

This is where EV graphs, etc come into play, as inaccurate as they are.

Also, just because you have < 50% equity in a hand doesn't mean your play wasn't +EV. The amount of dead money also influences this. That's kind of outside the scope of this post, but I (and I'm sure others) will be more than happy to prove this if you ask ITT or IRC.

Another thing to note is, the closer to 50% your equity is, the more variance you will experience in your results in the short term. If you're only a 51% favorite in a hand, you would have to run the simulation infinite number of times before your winrate in that spot = EV.

Keep that in mind the next time you want to rant about losing a coinflip PF.

To win at poker, you want to make +EV plays in every hand, in every spot, and never, ever make a -EV play. Obviously, since we are human, this is impossible. However, the closer we can come to playing 'perfect' poker as possible, the higher our winrate, the moar mannies we get to cash out and rub on our titties.

I've probably left out a ton of stuff that should be included, but I'm brain dead from working all night so cut me some slack. If you see anything that needs to be edited, things to be added, just post in the thread and I'll add/remove/edit as needed.

GOGOGO!

Edited for math errors. Ty spoon.