What is Expected Value? (EV)

*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.

Mistakes ITT.

Originally Posted by BooG690

Mistakes ITT.

STFU I edited

Originally Posted by BooG690

Mistakes ITT.

No big deal.

Edited again to fix mistakes.

The problem with ev of course, is that when we have blah blah in x position, and villain calls from wherever with whatever, we don't have time to open up poker stove, enter our hand, enter his range, work out equity, decide accordingly. This is where practice comes in. When we're not playing poker, when we're studying, we should play about with poker stove to see how certain hands match up against certain ranges. Some are obvious... if we have KK, and we know our opponent only 4bets us with QQ+, we should be able to quickly figure out that our equity is 50-50, that is, the probability of him having a better hand than us is the same as him having a worse hand, and when he has a worse hand, he's equally as dominated as we are when he has better hand. If we can add AK to his range, then this increases our equity, because it's a hand that is dominated by us. But say he's an uber-nit who only ever 4bets with KK/AA, suddenly our equity is very poor.

Very few ranges are this easy to work out, the majority of the time we have a board to consider too. KK vs a range of QQ+ is not 50-50 on a flop of Q63.

I try to explain ev to my friend by using dice as an example. I propose a game where we roll a dice, and he gives me £1 if it rolls a 1, 2, 3 or 4, and I give him £1.50 if it's a 5 or 6. He has a think about it and then declines. Why, I ask him? Because the odds are stacked against me, he says. I'll win £3 every 6 rolls, you win £4. And this, I tell him, is why he should fold when you are not in the lead unless the bet size is favourable in relation to the size of the pot we can win.

I tell him what about if I give you £2.50 when you hit your 5 or 6, and you still give me £1 when it's a 1, 2, 3 or 4... well, now I'll go for it, he says, because although the odds are stacked against me still, the prize for hitting makes up for the losses.

I think we're getting somewhere...

Of course, this is very good at demonstrating equity when we're behind and chasing the nuts, but not so good for when we have tens on a Jxx flop. I'll save that lesson until I understand!

I still have a great deal to learn about ev, but I am fortunate that maths comes fairly natural to me, so while I doubt I'm accurate in determining my equity against a range, I'm reasonably good at estimating, probability is something I understand. So while I've got work to do, I can still apply my estimates and be more accurate than most at my level.

nice informative post, add how to interpret EV graph?

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.

Should that be = +EV?

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.

TMI
But really, it is an important post for many, do we need the extra curricular advice?

TMI
But really, it is an important post for many, do we need the extra curricular advice?

Yes, we do

Originally Posted by Tasha

Should that be = +EV?

No, I meant it will take an infinite number of hands for our winrate in that spot equal our Expected Value for making that action.

Originally Posted by Tasha

TMI
But really, it is an important post for many, do we need the extra curricular advice?

Are you offended? If so, I apologize. It was meant as a joke from a thread on another poker forum that the majority of the posters here will understand.

Originally Posted by dranger7070

No, I meant it will take an infinite number of hands for our winrate in that spot equal our Expected Value for making that action.

Okay, now I see. Thanks.

Originally Posted by dranger7070

Are you offended? If so, I apologize. It was meant as a joke from a thread on another poker forum that the majority of the posters here will understand.

No, not all.
It just looked out of context to me but apparently I missed the reference. (And yes, I'm sure there are many of you who can put forward a variety of arguments as to why it is always in context no matter what the subject.)

Tits.

Spoon, please to make this thread NSFW. Tits have been demanded.

Well, there goes my shot at getting this in the Digest lol.

Originally Posted by dranger7070

Well, there goes my shot at getting this in the Digest lol.

Exactly my point to start with!