Equity, Equity Edges, Pot Odds, Implied Odds, and EV

[DavidC]

It's been a while since I've read Small Stakes Holdem, and I didn't realize that these topics are already covered (and better) in that book. Get the book.

Theory of Poker is also good for this stuff. Get that book too.

If you don't have access to the book, though, here's a few things about Equity, Equity Edges, Pot Odds, Implied Odds, and EV.

They're all different. In particular, DO NOT confuse Equity with EV: that's the single largest recurring theoretical misconception that I've seen on this forum.

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Equity is your chance to win a hand.

Equity Edges are when you have a greater chance to win than the average player.

Pot odds are the amount of money in the pot, as a ratio against how much money you must put into the pot.

Implied odds are the amount of money that may be put into the pot, as a ratio against how much you have to put in.

EV is the expected profit or loss from taking a particular action.

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Equity:

Say you have a FF on the turn vs a single opponent with TPTK (AK).

You therefore can't win other than by making the flush.

You have 9 outs, there's 46 cards. That gives you about 20% equity in the hand.

If there's 15BB in the pot, you "own" 3BB.

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Equity Edges:

Since there's only two of you, every further bet that enters the pot is profitable to your opponent and unprofitable to you.

He's making (E * N * B - B): His equity * the number of opponents * the number of bets they all put in - The bets that he's put in.

We'll assume 1 bet: 0.8*2*1-1 is: 0.60 bets in profit for every bet that goes into the pot.

How can he make only 0.60 bets in profit if he's got an 80% equity? Easy: he takes 0.8 from your bet, but gives you 0.2 from his.

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Pot Odds:

If there's 15 bets in the pot, and your opponent bets into you, the pot is offering 16:1 odds.

Keep in mind that our equity in this hand is 1/5.

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Implied Odds:

Unless you're calling all-in, there's the possibility for more action in the hand.

Assuming you've actually seen this guy's hand, and know that he has top pair, there's little reason for you to call his river bet.

However, assuming that he hasn't seen your hand, he may give you action if you hit your hand.

Assume the pot is 16BB after he bets the turn. Assume you're acting after him. Assume that he will call a river bet by you 100% of the time if he checks, that he will bet out on a flush card 75% of the time, and that he will call a river raise 75% of the time.

Your pot odds as stated earlier are 16:1.

However, your implied odds are at the very least 17:1, but actually work out to 17.6 BB.

While implied odds can make a play attractive, it doesn't necessarily make it +EV.

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Expected Value:

Keep in mind that the EV of calling, folding, checking or raising can be evaluated independently.

You should always strive to make decisions that are the offer the highest possible expected return.

Of course, it doesn't always work out as planned, but that's poker: This isn't an essay on variance. [img]/images/graemlins/smile.gif[/img]

It's necessarily to understand pot odds, and implied odds, as well a equity edge, to understand EV.

In this hand we have implied odds of 17.6:1, and if we call, we will own 20% of the 18.6 BB that will theoretically be put into the pot.

Keep in mind that even though the river bets are being made when we have 100% equity, since we'll only get to make them 20% of the time, they're being discounted just like the rest of the pot.

The difference between your portion of the implied pot (18.6*0.2 = 3.72) and the cost to get there (1 BB), is your expected profit: 2.72BB.

Note that if you could check through this, with 15 BB in the pot, and the same 1.6 BB implied odds, your expected value for checking would be: 3.32 BB.

If you don't have an equity edge, then raising isn't a good idea, if you know that he's going to call you or worse, raise you when he has the edge.

You would have to put in 3 more bets if he raised you, and you would lose almost all of your positive expectation.

--Dave.

[QTip]

Thanks for the hard work in this post Dave. I've only read it once, so I'll have to take time to check it out again to really digest it.

[AdamL]

Makes the pass!

This is a great post!!! [img]/images/graemlins/mad.gif[/img] GRR! [img]/images/graemlins/mad.gif[/img] [img]/images/graemlins/mad.gif[/img]

Makes me want to chuck molten tnt at chipmunks and bunnies!!! [img]/images/graemlins/mad.gif[/img] [img]/images/graemlins/mad.gif[/img] [img]/images/graemlins/mad.gif[/img]

[DavidC]

I'm still working on these concepts myself, but I'm getting closer to understanding them.

This isn't 100% true, and After I've polished up a little bit of Theory of Poker I'm going to fix a few small errors.

I'm not even going to be touching effective odds. [img]/images/graemlins/smile.gif[/img]

In my humble opinion I'd say it's not terribly wrong though.

[@bsolute_luck]

i'd have to say equity and betting for value are the 2 hardest things for me to get any kind of understanding on. this post will help, but a question:

in equity you say "say you have a FF on the turn...". what is FF?

[Isura]

Nice post. I have also found TOP really good for this stuff. It really ties in nicely the stuff used in SSHE withough much explanation. TOP's chapter on playing the river has helped me immensely. Probably my favorite chapter from the book.

[harmonjh]

I'm going to guess that FF is four cards to a flush.

[DavidC]

[ QUOTE ]
i'd have to say equity and betting for value are the 2 hardest things for me to get any kind of understanding on. this post will help, but a question:

in equity you say "say you have a FF on the turn...". what is FF?

[/ QUOTE ]

One of the things that I was going to edit.

I suppose I could actually put up two hands and the board as well. I'll get to it eventually.

TPTK (top pair top kicker: AK pairing either card and not pairing both)

FF = four-flush: between your cards and the cards on the board, though you can qualify it by saying "one-card four-flush" (three are on the board) or "four-flush board" (the board shows four of a suit).

[DavidC]

Don't discount future action by your equity in the pot. Consider it to be part of the current pot (actually, consider only THEIR contributions to future action into this).

Sorry.

--

If you hit the river, and bet out every time, and he'll call every time, you have implied odds of 17:1.

If you try to checkraise all the time, and he'll bet 75% of the time and call a raise 90% of the time, then:

0.25 * 16:1 odds (4)
0.75 * 0.1 * 17:1 odds. (1.275)
0.75 * 0.9 * 18:1 odds (12.15)

This works out to 17.425:1 odds, making it better, in this case, to checkraise. This would change if he's going to fold to every checkraise or bet less often, etc. etc.

Also, This has to be balanced against the probability of him raising and calling a three-bet when you bet out on the river.

--Dave.

[DavidC]

[ QUOTE ]
I'm still working on these concepts myself, but I'm getting closer to understanding them.

This isn't 100% true, and After I've polished up a little bit of Theory of Poker I'm going to fix a few small errors.

I'm not even going to be touching effective odds. [img]/images/graemlins/smile.gif[/img]

In my humble opinion I'd say it's not terribly wrong though.

[/ QUOTE ]

... or reverse-implied odds, or bet odds, or folding equity...