Help with "Small Stakes Hold 'Em

[flavaham]

I recently posted this at the cardplayer forum and no one seemed to know what I was talking about so I'm going to post it here: (this is cut and pasted from the original post)

Okay, I'm reading "Small Stakes Hold 'Em" right now and I'm a little confused on the Pot Equity section. Let me see if I understand it correctly. If I am drawing to the nut flush I am roughly a 2-1 dog which means my pot equity is 33%. This is the portion of the pot that I expect to win and therefor my pot equity. Here's where I get confused:

Suppose in the next betting round the pot is $60. The first player bets $20 and everyone else folds to me. I'm 2-1 to make my flush so the pot odds say call (4-1). The problem is that I am putting in half of the money that is going into the pot with pot equity of 33% which tells me that I am giving up 17% by calling (or, put another way, I'm putting 50% in and expecting only 33% back). Does the money that is already in the pot make up for this? With pot odds of 4-1 it would seem that I'd need to call this every time but I don't know if I just lowered my EV by making the call.

Maybe I'm making this harder than it needs to be.
(end of original post)

Any help on this would be great. Between pot odds, implied odds, reverse implied odds, and pot equity, I'm not sure which to apply and how. I'm rather good with the pot odds and implied odds, but the equity thing is a little squirly still.
THANKS!
-g /images/graemlins/grin.gif

[That guy]

you call because its +EV... it doesn't matter if your EV just went down or up... it only matters if it is +EV or -EV.

Pot equity is best described as the average result your hand would get if you did it hundreds or thousands of times.

In your example, you are getting 4-1 and correct to call. In fact, as stated in SSH, whenever you have 8 or 9 clean outs in limit hold em, you will nearly always be correct to call.

[flavaham]

Okay that's about where I am. Thanks for clarifying. It just seemed to contradict when I first read it.

Can you give an example of when I should use Pot Equity in making a decision during a hand?
Thanks again,
-g

[Deorum]

In your example, with your equity at 33%, you are giving up
33% of the $20 call, or $13.3 of your $20 call. However,
you are also gaining 33% of the $80 pot (60 + the 20 that
your opponent put in there) for a gain of $26.4. You are
giving up $13.3 to gain $26.4 for a net gain of $13.1. Of
course, this assumes that you have two cards to come, but
only have to call one bet (as you are slightly better than a
2-1 underdog to complete your flush with two cards to come;
you are about a 4-1 underdog to complete it with only one
card to come, and so you must adjust to that, ie. if you
only plan on calling to see one more card, you are closer
to a 4-1 dog than a 2-1 dog, but if you plan to see both
cards, you need to include the turn bet into your pot
equity calculations, as well as how many bets you think you
can get on the river if you make your hand).

[That guy]

Can you give an example of when I should use Pot Equity in making a decision during a hand?

when you talk about 'outs' -- you are assuming that you are currently behind in the hand and need to hit certain cards to take the lead.

when you talk about 'equity' -- you are talking about the combination of the chance that you are currently ahead + the chance that you improve.

so say you call a late position raise with JT-s from the BB and there was an early position limper who also calls the raise.

the flop comes J/images/graemlins/diamond.gif 2/images/graemlins/club.gif 2/images/graemlins/spade.gif and you check, thinking about a check-raise... now, say the early limper bets and the late position player raises. You have top pair and a marginal kicker. You appear to have ~3 good outs (the 3 remaining tens) + you may have the 2 remaining Jacks. You also might be ahead in the hand.

Now you have to think... with that kind of action, what is my pot equity? If you had this situation come out hundreds of times, how much money would you make on average (per hand)?

well, there is a mathematical way to come up with this by putting each player on a range of hands and counting the combinations of each possibility. that said, this is highly subjective and quite math intensive.

I would guess that given the action on the flop, calling a bet here is probably a -EV play. But maybe not hugely so. What this means is that the times you win is offset by the other times where the cost of putting in more bets yields nothing.

You will be ahead some of the time but you will be beaten somewhat often. What hands do you beat here? You are ahead of overcards and you are beating J9 -- and you are ahead of a bluff. But one or both of the other players could easily have AJ or KJ... the late position player could have an overpair (QQ KK AA).

So there are a few hands you beat and many that you are behind.

If you are ahead, the other players likely have overcards that can beat you -- so you can still lose. If you are behind, you are a longshot to draw out (spike a ten).

Let's say you are ahead of the other players 15% of the time. Let's say when you are ahead, you opponents will outdraw you 25% of the time. When you are behind, you are drawing to 3 tens which you will hit 12% of the time if you stay to the end (see both cards).

Using these assumptions, your pot equity is:
(.15 x .75) + (.85 x .12) = .215

So your pot equity might be something like ~20% here.

So if you are playing 5/10 hold em and pretend that you will be 'all-in' if you call the bet. the pot now has ~$45 in it (in the scenario above) and it is will cost you $10 for you to call the raise. 10/45 = ~22%. So it would look like about a neutral equity decision (you will average out about zero/slightly negative over the long run).

(note that if you were not all-in, it would cost extra bets and you would be putting in 33% of the incremental money for 20% winning chance, swinging this decision more -EV)

comments from others welcome as it is getting late and I am not editing this yet....