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Old 12-28-2005, 02:33 AM
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Default odds vs odds vs... equity?

I have a question, and I think it's mostly a terminology question, although help with the basic concepts would be appreciated.

I think I understand drawing odds. If I have pocket aces, and one is a spade, and the flop hits 567 all spades, then I have to draw to the flush to be sure I have the nuts. There are 47 unseen cards, and my outs are the 9 unseen spades. 47 unseen cards divided by 9 outs means 5.2:1 drawing odds to make the flush.

(BTW, I usually just see this called "odds." I have seen it called "actual odds" a few times. So far as I know I invented the term "drawing odds," and that label makes the most sense in my head. Feel free to use my new poker term free of charge [img]/images/graemlins/wink.gif[/img].)

I also think I understand pot odds. Say I'm playing 10/20 after the flop in late position, with a bet and two calls ahead of me and two pre-flop betters to act after me. On my action the pot has $90 in it. I'll be getting 9:1 pot odds for my $10 post flop bet. That's plenty good pots odds for my flush draw.

I even think I understand implied odds. In the example above there were five players including myself that called the big blind. No one projected strength by raising pre-flop (although I SHOULD have if I were holding pocket aces [img]/images/graemlins/wink.gif[/img]). Then the small blind bet, and it was called around to me with two people yet to act.

With no one projecting strength either pre or post flop, there's a very good chance that the two players yet to act will also call. In that case, I can add their $10 each to the $90 already in the pot for a whopping 11:1 implied pot odds. In this case I'm buying that turn card wholesale.

The rule of thumb here being that, all other things being equal, if your pot odds are better than your drawing odds you should bet and in the long run you will make money.

I think I've got a handle on things so far. Now comes the part I'm shaky on.

Say the two players to act after me both fold. With $100 in the pot the turn comes an ace. The small blind bets $20 and the other players all fold around to me. His $20 plus the $100 already in the pot give me 5:1 pot odds if I bet, and that's near exactly my drawing odds.

BUT..

From this point on in the hand it's just me and the small blind heads up. That means for every bet I put in the pot I'm only getting one other bet to go into the pot, rather than the five bets I got both pre and post flop.

What is the name for this? Is this called "pot equity," or is that something else?

Regardless, I have read that I should fold here, since my turn bet and inevitable river bet will only be getting 1:1 "what ever this is called" and my odds for making the flush on the river are much higher than that.

So, my question is can someone please tell me the correct name for "what ever this is called" and direct me to a good treatment on how it relates to drawing odds and pot odds?
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  #2  
Old 12-28-2005, 11:43 AM
SheridanCat SheridanCat is offline
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Default Re: odds vs odds vs... equity?

Okay, let's see if we can clear this up.

[ QUOTE ]

I think I understand drawing odds. If I have pocket aces, and one is a spade, and the flop hits 567 all spades, then I have to draw to the flush to be sure I have the nuts. There are 47 unseen cards, and my outs are the 9 unseen spades. 47 unseen cards divided by 9 outs means 5.2:1 drawing odds to make the flush.


[/ QUOTE ]

Actually, it's 4.2:1 against making your draw. 47/9 = 5.2, but remember that nine of those cards are yours, so you get 1, thus 4.2:1. If you're prefer, you can divide the number of cards that don't help by the number of cards that do help to get the odds against directly: 38/9 = 4.2:1.

[ QUOTE ]

(BTW, I usually just see this called "odds." I have seen it called "actual odds" a few times. So far as I know I invented the term "drawing odds," and that label makes the most sense in my head. Feel free to use my new poker term free of charge [img]/images/graemlins/wink.gif[/img].)


[/ QUOTE ]

Those are the odds against making your hand. You can call it drawing odds, if you like. "Actual odds" is okay too, I guess, but it's not that commonly used, I don't think.

[ QUOTE ]

On my action the pot has $90 in it. I'll be getting 9:1 pot odds for my $10 post flop bet. That's plenty good pots odds for my flush draw.


[/ QUOTE ]

Correct. It doesn't even matter what the stakes are, just how many bets are in and how many bets you're going to have to call to see the next card. With two players yet to act, in your example, there is also the possibility of a raise that you need to take into consideration. You might have to pay 2 bets to see the next card.

[ QUOTE ]

With no one projecting strength either pre or post flop, there's a very good chance that the two players yet to act will also call. In that case, I can add their $10 each to the $90 already in the pot for a whopping 11:1 implied pot odds. In this case I'm buying that turn card wholesale.


[/ QUOTE ]

Not exactly. Implied odds represent bets you expect to win in later betting rounds if you hit your hand. We're assuming your aces are not a lock in this hand.

What you've actually described here is pot equity in action. With pocket aces and four to the nut flush, you have a very high pot equity, in the neighborhood of 48-50%. Of every bet going in the pot, you own about 50% of it. Since there are four other players in, every bet makes you money.

[ QUOTE ]

The rule of thumb here being that, all other things being equal, if your pot odds are better than your drawing odds you should bet and in the long run you will make money.


[/ QUOTE ]

Not necessarily. Pot odds, when compared with the odds against making your draw, only tell you whether a call is profitable or not. They don't really tell you much about betting or raising.

[ QUOTE ]

Say the two players to act after me both fold. With $100 in the pot the turn comes an ace. The small blind bets $20 and the other players all fold around to me. His $20 plus the $100 already in the pot give me 5:1 pot odds if I bet, and that's near exactly my drawing odds.


[/ QUOTE ]

You're calling one bet ($20) to win six bets ($120), which is 6:1 pot odds. Assuming you really think your set is no good, then you're still getting 4.1:1 to call the bet. It's an easy call since your pot odds are 6:1.

Not to mention, he has been showing strengh, so if you should make a full house or the nut flush you can expect an extra bet, maybe two, on the river. That's implied odds.

[ QUOTE ]

From this point on in the hand it's just me and the small blind heads up. That means for every bet I put in the pot I'm only getting one other bet to go into the pot, rather than the five bets I got both pre and post flop.


[/ QUOTE ]

It was certainly better before, sure. But still, you're going to have to see the hand through to the end.

If your opponent has a made flush already, then your pot equity is only about 40%, which is bad for you, of course. If he has a straight already, then you're in about the same boat.

If you are 100% certain that he has a hand like this, then you're right to fold. Say your opponent turns up his hand or exposes his cards by accident. But barring that, you'll never be that certain. I don't know anyone who could lay down top set with a four flush on the turn for a single bet. That would be terribly weak play.

[ QUOTE ]

What is the name for this? Is this called "pot equity," or is that something else?


[/ QUOTE ]

You should have an idea of what pot equity is by now.

[ QUOTE ]

Regardless, I have read that I should fold here, since my turn bet and inevitable river bet will only be getting 1:1 "what ever this is called" and my odds for making the flush on the river are much higher than that.


[/ QUOTE ]

When evaluating if you should make a call, you need to take into account the entire size of the pot, not just the fact that you've only got a single opponent. By the time if comes to you for a river call, there's going to be eight big bets in the pot, right? If you hit your hand you can raise and extract an extra bet. The pot is going to be pretty large.

Say you miss your monster and have "only" a set of aces. Your opponent bets on the river. There are eight bets in the pot, you're getting 8:1 to call. If you think you have a chance to win this more than 1 in 8 times, you must call. You will rarely have that much certitude.

[ QUOTE ]

So, my question is can someone please tell me the correct name for "what ever this is called" and direct me to a good treatment on how it relates to drawing odds and pot odds?


[/ QUOTE ]

If you want to learn more about when to call on the river, you should read Ed Miller's Small Stakes Hold'em. He treats this and many other concepts that are essential knowledge for a winning poker player.

I hope this has been some help. I'm sure there are errors in here - hopefully no huge ones.

Regards,

T
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  #3  
Old 12-28-2005, 11:46 AM
Kurn, son of Mogh Kurn, son of Mogh is offline
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Default Re: odds vs odds vs... equity?

There are 47 unseen cards, and my outs are the 9 unseen spades. 47 unseen cards divided by 9 outs means 5.2:1 drawing odds to make the flush.

Wrong. 47 unseen cards, 9 that make your flush is 38:9 or 4.22:1
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Old 12-28-2005, 04:19 PM
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Default Re: odds vs odds vs... equity?

Thanks SheridanCat. That helped.

And don't worry. I wouldn't lay down three aces with a nut flush draw. Not even for a Bunny Ranch token. [img]/images/graemlins/wink.gif[/img]
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  #5  
Old 12-28-2005, 07:20 PM
AKQJ10 AKQJ10 is offline
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Default Re: odds vs odds vs... equity?

I'm glad it sounded like SheridanCat's reply helped you; I'm just going to pick a nit here.

[ QUOTE ]
I think I understand drawing odds. If I have pocket aces, and one is a spade, and the flop hits 567 all spades, then I have to draw to the flush to be sure I have the nuts.

[/ QUOTE ]

If the flop is 5 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] and you have A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img], you can never have the nuts by the river. The nuts on that board is 9 [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/spade.gif[/img], or if you have it, 8 [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/spade.gif[/img]. It's unlikely you'll make an ace-high flush and lose, but you don't want to be the person who goes 20 raises on the river and pays off the straight flush! You could also make a flush on the turn but see the board pair on the river. Both possibilities of losing with an ace-high flush are worth noting, though not obsessing over -- if you make your ace-high flush, you probably have the best hand.

Moreover, on a 5 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] you still have a very strong hand with AA. Although you may be losing to a flush, straight, or two pair, none of those hands is guaranteed to be out against you. Furthermore the flush redraw makes your hand very strong, so even if you are behind, you still (per your OP and the subsequent corrections of the math) have about a 1/3 chance of drawing out. If you're losing to a flush, of course, that's two less spade outs left in the deck, but a lot of hands like 9 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/heart.gif[/img] or 6 [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/diamond.gif[/img] should bet aggressively on this flop, so even if you feel the betting makes it likely you're behind, you can't assume you're behind to a flush.

Anyway, I just felt these considerations were worth pointing out. The big picture issue is, you're interested in your probablity of winning the pot, not your probability of making the stone-cold nuts. With AA even on such a highly-coordinated board, and even if you don't improve, there's a decent chance you're still ahead so your decisions should reflect that consideration.
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  #6  
Old 12-29-2005, 11:44 AM
Songwind Songwind is offline
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Default Re: odds vs odds vs... equity?

Also, if your turn card is a flush, don't forget that in addition to your 9 spades for the flush, any 5, 6, 7, or A gives you Aces full or better, which beats the flush.

Your # of outs went up to 19. (3 each for the board to pair the low cards, 1 ace, and 9 flush cards.)
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