POT ODDS

[RJT]

I have read through a number of books on Hole ‘em: SSHE, Super System, etc. I like to get an overview of most that needs to be learned, taking in concepts as I go and items that are easily grasped and then go back and start with the basics. Well I am back to basics and I read a recommendation here for Winning Low Limit Hold ‘em, by Lee Jones (hadn’t heard of it).
So, I picked it up today and started reading it. Barely into it, I read a concept that I had not thought about nor read about. The author was talking about pot odds. Now this is one of the first things we learn, yet his example was new to me. He writes: “…For instance, suppose after the river card is turned up…” Then he goes on to talk about pot odds relative to his example after the river. In his second paragraph under POT ODDS he writes: “Pot odds also apply to draws….”
This POT ODDS section was a real surprise to me. First, by talking about pot odds after the river (this is my main question which I address shortly) and second by the way he wrote relative to draws instead of discussing this first.
Here are my questions. I can understand a concept pot odds after the river but:
1) Is there really such a thing? Odds are expectation of future events. The cards are all dealt. I can see what the chances are that an opponent has a Q in his hand when I have none and none on board – 4/45. But isn’t it really a 50-50 chance (from my point of view)? He either does or doesn’t. And a 100% chance (from his point of view) – he know if he does or doesn’t. Therefore pot odds after the river either doesn’t exist and I understand that my move is based on what I have, possible hands, what I think he has based on his prior plays, his betting on current hand etc. or if it does exist:
2) Please explain it a bit more to me and how to bet or not bet accordingly.
3) Is it of much relevance (at least compared to pre:flop, turn,river) in play, if so how much? In limit and in NL, too.
4) Was it just a poor example and I am making much ado about nothing?
Thanks again, all, you are a big help to me.

[MycroftX]

Use paragraphs.
I don't really know what that post means, I think you are confused as to what Pot Odds are...

but people will be happy to answer my friend

[RJT]

Sorry, I did use paragraphs, I failed to indent. My point is I think the author gave a bad example of pot odds by talking about pot odds after the river -that makes no sense to me - I understand pot odds to be in relation to future cards, i.e flop, turn , river. Either you are right and i don't fully comprehend pot odds or the author is wrong and my post can be ignored.

[Mangatang]

Pot odds simply tells you the ratio of money you can win (in the pot) versus the amount it cost you to call. On the river, you compare the pot odds you're getting versus your estimation of your chance of winning.

Pot odds are more clear when it comes to draws, because you know exactly what the odds of you hitting your hand are, but on the river, it's up to you to make a best guess as to your chances of winning a hand.

Example:

On the river, you have top pair top kicker, and someone has been calling your bets on every street. You bet again on the river (after a third flush card fell). This time your opponent raises you. At this point, you count the pot odds to be 8:1. Even if you're pretty sure he has the flush, you have the pot odds to call here. You only need to have the best hand in this situation one time in nine, for it to be a profitable call. It's up to you to determine if you have a 1 in 9 shot or not.

In general though, on the river, once the pot is big, it's worth a call with almost any hand you have (except a missed draw).

[AngryCola]

You can't know for sure what your opponent is holding on the river. Indeed, it's true your exact odds are known only to the cards, themselves (and a player holding the nuts).

If the pot is laying you 10:1 on your river call, you would know that you must be right about your hand being the best only 1/11 times. If you think your hand is good enough to win the pot more than 1 out of 11 times, you can call profitably. Likewise, the bigger the pot becomes, the more inclined you should be to throw in a call.

If a pot was laying me 15:1 (a big pot indeed) on a river call, I would be very likely to call if I felt I had any kind of chance to win the pot. I would only have to be right 1/16 times.

These kinds of calls are estimations, plain and simple. However, just because it's an estimation doesn't mean it doesn't hold value. Just think about all the pots I win slightly more than 1/16 of the time. /images/graemlins/smile.gif

[RJT]

Thanks Mangatang, you answered the question I was trying to ask.

Your example gave an easy explanation for me to see the relationship of pot odds after the river against one opponent. Taking your same example does the 8:1 change with more than one opponent?

Also, with a different board, not so obvious - do you actually compute pot odds after the river vs the way the betting went and one figuring what your opponent(s) probably has?

I can't imagine being able to compute all the possible hands that can beat mine and the respective odds of those hands so quickly after river and prior to showdown. I understand for now to refer to your last sentence. But are you saying eventually I need to have all the outs of the opponent figured too?

For example: Board 2 3 7 10 Q - with no flush possible.
I hold pocket 8s (I know I probably wouldn't still be in at this point with 10 Q on board). How can one compute all the possible hands that can beat me so quickly? Perhaps a few more examples and how the computation is done might help.

I do understand pot odds and the computation relative to draws (don't have it all down pat yet, maybe that is the problem?).

p.s. I did indent my first post, didn't realize computer changes it and to do paragraphs one needs to double space.

[AngryCola]

[ QUOTE ]

Thanks Mangatang, you answered the question I was trying to ask.

Your example gave an easy explanation for me to see the relationship of pot odds after the river against one opponent

[/ QUOTE ]

/images/graemlins/tongue.gif I gave you the same example! No love for the late poster. /images/graemlins/grin.gif

[AngryCola]

[ QUOTE ]
I can't imagine being able to compute all the possible hands that can beat mine and the respective odds of those hands so quickly after river and prior to showdown. I understand for now to refer to your last sentence. But are you saying eventually I need to have all the outs of the opponent figured too?

[/ QUOTE ]


The more you can figure out, the better, but you don't need to make it that complicated. I still think you are looking for real numbers to incorporate into your river pot odds, but most of the time it's just going to be your gut estimation of your chances. As you said, determining every possible way you could be beaten is rather difficult. That's why it's simply a complete estimation most of the time.

You probably don't need to compute the chances the other player has the best hand, etc, etc. All you need to do is decide for yourself, mostly based on reads, if your hand will be good more than say 1/11 times when the pot is offering you 10:1.

Its generally a lot less about math, and a lot more about gut instinct and reads.

[RJT]

AngryCola - actually I was writing my respond to Mantatang and posted it after your response but prior to my reading your response. How can I ignore your help? You have some great replies on this board? You have never been anything but helpful. Not to mention best avatar I have seen.

Ok, here's one for you (an extreme example to make the point of my question)keeping in mind my question of pot odds post river:
board is 2s 4s 7s 9s Qh - I have 3s Jd.

I am heads up and we raise each other ad infinitum. Well the chances of the other guy having a spade is 8/45 (plus whatever odds is for having 1 or 2 spades). Well my chance of having the winning pot is 37/45. But obviously I probably don't have the winning hand -he almost certainly has a spade, ergo one higher than mine.

How is pot odds relevant here? That was the other thing I was trying to ask.

[AKQJ10]

RJT,

Not to butt in here when Mangatang and AngryCola are doing such a great job answering your questions, but it sounds like you may be subtly misunderstanding the way pot odds apply on the river.

SUBTLE MISUNDERSTANDING:

You need to calculate all possible hands that could be out against you and, based on that calculation, determine the odds that you would need to call a bet. Then compare the odds the pot is laying you and call if appropriate.

SLIGHTLY REFINED MISUNDERSTANDING:

You need to weight all these probabilities of different hands being out against you by the likelihood that your opponent would actually get to betting the river with each of them -- no doubt you'd need to use Bayes' Theorem for this, although now my head is spinning -- and then weight all the different possibilities to come to the probability that your hand is good. Now compare the odds the pot is laying you and call if appropriate.

VAST SIMPLIFICATION (which i believe is what those guys are saying):

Using your poker intution, make an estimate of the probability you think you'll win. Compare the odds the pot is laying you, and call if appropropriate.

/images/graemlins/spade.gif /images/graemlins/diamond.gif /images/graemlins/heart.gif /images/graemlins/club.gif /images/graemlins/spade.gif /images/graemlins/diamond.gif /images/graemlins/heart.gif /images/graemlins/club.gif

So to use your very good example, i would just "guesstimate" the probability of your 3-high flush winning to be 0.03. (Others might set a different probability based on more poker experience, better knowledge of the opponent in question, etc.) In odds terms that's 32.3 to 1. So if the pot size is, say, 20 big bets the correct play is to fold.

Although as i think about it again, maybe if the player has been known to be a compulsive bluffer, the probability of your flush being good could be as high as 0.05-0.10? That's where the tricky part comes in, knowing your opponents.

[RJT]

AngryCola - again my last post was after yours - "...a lot less about math..."- - Thanks.

[AngryCola]

[ QUOTE ]
Well the chances of the other guy having a spade is 8/45 (plus whatever odds is for having 1 or 2 spades). Well my chance of having the winning pot is 37/45

[/ QUOTE ]

I'm pretty sure those odds are not correct, but to be honest with you, probablity is not one of my strong suits. It's something I'm still working on. In the example that you gave, your chances for having the best hand are not good (regardless of the exact probability).

In that example, I don't think I would have ever put money in the pot to begin with, because it's not a favorable board for the hand you specified.

Look at it this way, you know that in that spot the chances of you having the best hand are extremely low. Therefore, in this example where you somehow make it to the river, you would need big big pot odds to support a call being the right play. You still may have to call, however, as all the raising you were envisioning built a huge pot.

Ed Miller and Gary Carson both advise you to call a bet on the end in big pots, even when you feel there is little to no chance of your hand being the best. The reasoning behind this suggestion is that it may be a mistake to call with the worst hand, but it is a far greater mistake to fold the best hand in a large pot. So much so that you must often make crying calls in huge pots.

Honestly, yours was not that great of an example, because once you have already done a lot of raising in this hand, pot odds almost require you call 1 bet on the river. Personally, I don't see how to get away from this hand after it has been raised as much as you are suggesting.

I think the big point to absorb about river pot odds is when the pot is large, you don't have to be right (have the best hand) very often. That's where pot odds come into play on the river.

The math of it all (not your specific example) becomes very complex to think about and to try calculate at the table. I still think your reads on your opponents are your largest source of information.

For instance, if in your example the other player was the biggest rock known to man, that would sure change things. Now what are your chances? They are most certainly lower, because it's unlikely the rock would be raising you or betting the river without the apparent best of it. In fact, if you had a read that this player would never do such a thing, your pot odds on the river would not matter one bit, because you are estimating your chances of having the best hand as zero.

Still, be careful when thinking about making a fold like this. As I already mentioned, costing yourself the whole pot is a much larger mistake than costing yourself one bet.

Looking at the possibilites of your opponent holding a spade is completely legitimate, but then you have to start factoring in other things to your decision. You have to start asking yourself questions like this:

What are the chances my opponent holds what he is representing?

What are the chances my opponent would be playing it this way?

How tight/loose is my opponent?

There are more things to consider, of course. Regardless of what else you have to ask yourself, you have to add all of these factors up into one number. Obviously, with so much estimation going on, it's not going to be completely accurate. Still, it's all us players have to go by. Go ahead and make your estimation of whatever is appropriate for the situation.

When it all comes down to it on the river, there is really only one final question you have to ask yourself with a pot laying you 10:1.

"Will I be right about this call more than 1/11 of the time?"

You use all of your abilities to come to your own conclusions. If the answer is yes, you call. If it is no, you fold.

Sorry I wasn't more helpful with the exact probability of your opponent holding a spade. Your question reminds me that I still need to study a few things.

Just remember, the estimations you make are a combination of several factors. The chances of your opponent holding a certain hand is just one of them.

Also, you say you have read SSHE, and I believe you, but I would still consider going over it a few more times. I learn something new every time I read it. Good luck.

[AngryCola]

btw, I was j/k about the "no love for me" comment. /images/graemlins/grin.gif

Hopefully I answered your question, though. /images/graemlins/smile.gif

[RJT]

Course I knew you were joking. And definitely am re-reading SSHE.

The way I figured opponents odds was 8/45 - 8 being the number of unknown spades. 45 = 52-2(my pockets)-5 (board)
37/45 I used because in heads up hand - the odds of me winning vs opponent should add up to 1(100%).

But in reality he either has me beat with a higher spade or is bluffing or is a bigger idiot than I for staying in the hand that long.

I would never have raised,I would have checked/called to begin with (assuming in limit game)pot odds at that point were worth a small risk hoping for a bluff by him,and wouldn't have folded for same reasons you stated).

[AngryCola]

[ QUOTE ]

The way I figured opponents odds was 8/45 - 8 being the number of unknown spades. 45 = 52-2(my pockets)-5 (board)
37/45 I used because in heads up hand - the odds of me winning vs opponent should add up to 1(100%).

[/ QUOTE ]

I don't have the answer for this, because I am fairly ignorant about cretain probabilities like these. I see how you got the numbers, but I'm not sure how they apply here.

I mean, sure there are 8 unknown spades left in the deck, but that does not equal the probability that he is holding one (from how i understand it).

I really don't know. I could be wrong about that.

I'm going to go do a little reading, but that's a fairly interesting question that "gaming_mouse" in the probability forum could almost certainly answer.

Who knows.. maybe you know more about probability than I do. hehehe. /images/graemlins/grin.gif No matter, hopefully a few of us got you thinking the right way about river pot odds. At least we accomplished that much. /images/graemlins/blush.gif Good luck.

[RJT]

“I mean, sure there are 8 unknown spades left in the deck, but that does not equal the probability that he is holding one (from how I understand it).”

That is one of my points – pots odds post- river and pot odds pre-river are two different things. The probability of any one opponent having been dealt a spade is one thing – the probability that one player has a spade who is still in river with that board and keeps raising ad infinitum to my idiotic raises is almost a certainty (again disregarding bluffs). And the probability that he has the ace of space is most likely (otherwise he would have just called me at one point, figuring I had it).

[AngryCola]

[ QUOTE ]
And the probability that he has the ace of space is most likely (otherwise he would have just called me at one point, figuring I had it).

[/ QUOTE ]

I have to disagree here. Your example was a heads-up pot. Why are you sold on him having the Ace?

Personally, I would be re-raising you with a few more hands.

You must not assume the player always holds the nuts when he re-raises you here, unless he is a complete rock.

However, you are definitely starting to understand the kind of thinking you have to do on the river. You reduced your own chances of having the best hand based on your read of the situation. Still, there is a way to mathematically determine the probability of your opponenent holding a spade. As I said, both the true mathematics and your read of the situation are combined to give you the final estimate of your own chances.

Just remember, your example was a heads-up pot. The vast majority of the smaller games are going to have larger pots with a lot more money lying in the center. It's going to seem silly to be calling based on pot odds in some hands, but because your hand has to be the best only a small amount of the time, it's usually profitable to call with a hand that has a reasonable chance to take the pot

Let me give a short and rather sparse example.

You have just made a Q high flush on the river. The A and K of the suit are not on the board. The pot has developed in such a way that there is a lot of money lying in the center of the table.

Even if the action is a little scary when it gets to you, most of the time (against average small-stakes opponents) you should be making the call. It may look bad, but often you will be very surprised when the cards are turned over. Because of the pot odds, it's usualy a big mistake to fold in that kind of situation. Folding the best hand in a large pot is simply too big of a risk if you have any reasonable chance of holding the best hand.

I purposely did not post any numbers or hand "action" in my example. I think the concept of the example is more important than the specifics of it. That is the kind of situation where pot odds become more crucial. If it had been a smaller pot, you might have considered folding, because your margin for error was smaller.

Yep, I think that's about it. (exhales)

[RJT]

The reason I was so much sold on the the ace of spade is the premise "ad infinitum" (to infinity) which really can't be true (only used it to illustrate my point) because there is a finite limit (the one who is shorter stacked would at one point be all in). What I meant is that unless one has the ace of spade after a number of raises-re-raises - one is going to say ok lets stop this and see who wins. If one had the ace then there would be no reason for him to ever stop and call other than boredom.

[RJT]

I also assumed heads up there is no cap on raise-reraise.