Pot Odds/Effective Odds/Probability Question

[Dave H.]

I posted the following in the Poker Theory forum and was advised to post it here...

I have a thread in the Beginner’s section entitled “Yet Another Pot Odds Question” if anyone would care to refer to it. Mr. AngryCola (whose birthday is today!) has been trying very patiently to explain effective odds and I really thought it would be a great item for the Beginner’s forum. However, in his last post, he did indicate that someone else might need to get involved. I couldn’t think of anywhere else to go but the Poker Theory or Probability forums, so I will try my best to explain my problem and a couple of examples that we were discussing. If this post belongs elsewhere, please let me know. I DESPERATELY want to understand this. I should also mention that I have read and reread and reread (ad nauseam) the section in TOP about effective odds and I'm just not quite getting it.

Initially, with a four flush on the flop, I thought I needed pot odds of about 4:1 to call the next bet. I know that my odds of hitting the fifth flush card WITH TWO CARDS TO COME are about 2:1 so I couldn’t understand whether I needed 2 bets in the pot or 4 bets in the pot to make the call. The way I understand it, I only need 2 bets in the pot BECAUSE I KNOW I AM GOING TO SEE BOTH CARDS, i.e. I am going to the river for sure.

So the question I posed was: if I miss on the turn, do I then need 4 bets in the pot to all, or is it still 2 bets?

The answer I received, as I understood it, is that I need 2 bets, because (...this was the answer I received):
[ QUOTE ]



It's simply a matter of taking your odds for both streets combined, and therefore missing on the turn has no impact on the fact that you will make your flush by the river 1 out of 3 times. Think of the turn card and the river card as a combination. You are calling based on that combination, not the 2 halves of the combination. Get it? The point is your turn call isn't a seperate decision. It is a completion of your flop call. The money you put in on the turn should have already been factored in on the flop, when deciding whether you had odds to see both streets. just because you are throwing money in the pot on the turn does not mean that you are making an odds based decision at that point in time.



[/ QUOTE ]

I thought that the answer would be that I needed 2 bets to see the turn card but, if I missed, I would have to revert to 4 bets to see the river card.

So, given this answer, I tried to carry it further with this example, and I would like someone to PLEASE tell me where I’m going wrong, because it just doesn’t feel right! I’m trying to look at this strictly from a probability standpoint without regard to the texture of the game.

OK, let’s assume there are no cards on the board as yet and that I have been dealt a pocket pair. I know that I have about 4:1 odds to make a set or better by the river. Trying to follow the logic from the four flush above, that says to me that I simply need roughly 4 bets in the pot each time I bet to make my bet a profitable one. If that were the case, especially in microlimit games, it seems it would be a no brainer to bet or call to the river nearly every time I held a pocket pair. Again, that just doesn’t feel right.

Can someone please tell me what I am doing wrong?

Thank you in advance for your help!

[gaming_mouse]

I thought that the answer would be that I needed 2 bets to see the turn card but, if I missed, I would have to revert to 4 bets to see the river card.

You are correct and are doing nothing wrong. The quote in your post is making an astonishingly basic mistake. You should not ever listen to anything that person posts ever again.

Because of implied odds, it almost always makes sense to call a 4 flush down to the river except when you are heads up or when the board pairs and you have good reason to believe a full house is out. So just a general rule of thumb, prepare to call your 4-flushes down.

Also, as an aside (and I don't mean to be rude), you should not pepper your posts with unnecessary history and explanation. Just state the facts and ask your question. It's too hard (and boring) to read long posts.

HTH,
gm

[AngryCola]

An astonishngly basic mistake? I take offense given that your answer is definitely an astonishing common mistake. What you say about 2:1 on the flop and 4:1 on the turn is completely wrong. If you don't want to use effective odds, and just use 1 card odds, it would be 4:1 on the flop and 4:1 on the turn. He is asking about effective odds, please help him out as I am busy today.

Also your post seems to lack an understanding of what effective odds are. I am explaning to him his odds of hitting the flush on both streets. My recomendation is not that he should fold or anything of the like.

What you say makes no sense. You can't be getting 2:1 on the flop and 4:1 on the turn. That just doesn't make sense. You are getting 2:1 for the flop and the turn combined, which is pretty good (a strong draw) that you will almost always have odds to draw to.

4:1 to make it on the turn specifically, and 4:1 to make it on the river. 2:1 to make it by the turn or river. Please, try to at least deal with some of these problems, before going around telling someone the advice they are getting is wrong.

If you tell someone that they are getting 2:1 on the flop, and 4:1 on the turn, you would be very wrong. I'll let others on this forum elabortate. Please, anybody with a knowledge of effective odds (besides myself), help Dave out with his understanding of 2 cards to come odds. I have quoted Sklansky's descritiption of effective odds, and it doesn't quite seem to have sunk in with him. Any other way it could be explained to him, other than what I have tried would be appreciated.

Also, here is a repost of a quote from TOP, for those who are still a little fuzzy on what effective odds are:

"Figuring effective odds may sound complicated, but it is a simple matter of addition. You add all the calls you will have to make, assuming you play to the end, to determine the total amount you will lose if you don't make your hand. Then compare this figure to the total amount you should win if you do make the hand. This total is the money in the pot at the moment plus all future bets you can expect to win, excluding your own future bets. Thus, if there is $100 in the pot at the moment and three more $20 betting rounds, you are getting $160-to-$40. When you think your opponent won't call on the end if your card hits, your effective odds would be reduced to something like $140-$40. If, on early betting rounds, these odds are greater than your chances of making your hand, you are correct to see the hand through to the end. If they are not, you should fold."

[i]-David Sklansky pg.53 of The Theory of Poker[i]

[Dave H.]

HELP...PLEASE!!!!!
Obviously, this MUST be a difficult question. I don't want to cause problems; I just want an answer!!!

Thank you!

[AngryCola]

It really isn't a difficult question, which is why I'm beginning to get frustrated. It has been explained just about as well as it can be, but you still seem stuck on viewing each street individually. If you can't get your mind around this just yet, it's probably okay. In most small stakes ames , you have so much overlay it will rarely matter if you use 2 cards to come odds or single street odds.

So, unless someone can explain it in a better way than David Sklansky, or myself, you are just stuck having to try to figure out where your brain is getting blocked on this issue. But, dont fear! Until you have a firm grasp of effective odds, just use the 1 card odds, about 4:1 on the flop and the turn, in the case of the flush draw.

Again, I'm not sure it can be explained much better than how David Sklansky puts it. Your mindset of wanting to view each street seperately is what is keeping you from understanding this, IMHO. But, it's not as big of a deal as you may think at the levels you are playing at. I still believe you should pick up "Hold'em's Odds Book", by Mike Petriv. It should open your eyes a bit to the probability for all situations. It also has a detailed look at combinations, which are important in 2 cards to come odds. Good luck. /images/graemlins/spade.gif

[AngryCola]

Dave has just started a new thread, and it asks the same question I have already answered. I will answer it one final time. Dave, you are confused about how many bets you need to call for 2 cards to come odds and so forth. I already posted the method for figuring this. Pay careful attention this time. Here it is again:

Take the odds the pot is laying you on the flop and add the probable turn bet (from the flop bettor) to them. Compare this against what you have to call now (on the flop), plus what you will have to call on 4th street.

Current pot + future turn bet of original flop bettor = your 2 cards to come pot size.

Your current call + turn call = what you must compare against the pot when using 2 cards to come odds.

But again, this is the same way David Sklansky explains it. So, I don't understand why you cant get your brain around this issue as it's simply a matter of addition. /images/graemlins/spade.gif

[Dave H.]

Thanx again. I've tried reposting in Probability and eliminating some of the fluff...maybe that will get me more responses. I suppose I was too wordy. Let's see if it generates more responses.

I will DEFINITELY buy the book you suggested.

I HATE mental blocks...thanx for your patience!

[Kellon]

Before I got a chance to post this, I saw that AngryCola gave it a couple more shots. I would like to go ahead and throw this up to see if I've got it right myself.

I've been following this thread on the Beginner's forum. I have to admit I've been more and less confused, and back again, from post to post. At some risk, b/c I'm relatively new at this, I would like to throw out my thoughts (with apologies to gm for the uneccessary introduction. /images/graemlins/smile.gif) One assumption here: This is fixed limit HE.

When betting on the flop, you assess your odds based on the cards to come (2), the current pot size, and any reasonable expectation of future betting. The last consideration fits into the analysis of implied or effective odds, as I understand it. I think this is supported by the Sklansky comments about more rounds of betting, in AngryCola's quote. Thus, if you have a four-flush on the flop, you have 2:1 odds of making your flush by the river (if I have this piece of it correct). At the point in time of betting on the flop, you compare these odds to your pot (implied or effective) odds. It is very likely that the circumstances satisfy the "requirements" for a bet.

On the turn, however, things change if you did not make your flush. You now have only one more draw. Your odds of making your flush are 4:1. As for the bets, you must not forget that the bet size has doubled and you have only 1/2 of the number of bets you had in your earlier analysis. It is very possible that you might be in a situation of having to cold call 2 bets to a pot that only has 6 bets in it. Here you need to consider again the potential for future betting, as suggested by Sklansky, to determine what the effective odds are or are going to be to decide whether a bet is appropriate.

One of the confusing things, I think, in many of the posts in the other thread, seem to suggest that you make one basic betting decision and carry that through to the river. This just doesn't seem right. Each bet is a separate act. The money you have put in the pot is no longer yours and is not part of your new decision, per se, on the turn or on the river. What you do try to take into account, however, is what the other players are likely to do in your attempt to determine the effective odds. The bottom line to Dave's basic question has to be that each bet (after the flop, then after the turn) has to be analyzed as a relatively discrete event.

Thus, 2:1 on the flop; 4:1 on the turn if you didn't hit on the turn. Pot odds (implied or effective) may be considerably different on the turn.

I'm really curious if I'm even close here. /images/graemlins/confused.gif

[pittlaw]

OK, I'll take a shot.

To calculate the effective pot odds you are getting, you need to add up all the bets you will likely need to call to make your draw. On the flop, if you plan on seeing the river and your opponent will bet the turn, you will need to put in one small bet and one big bet, or 3 small bets.

So, if you are playing 2/4 limit and flop a draw that is 2:1 against by the river, how much would you need in the pot to call? If you figure that you will need to call 3 small bets, you would need the pot to be $8 (because if he bets on the turn, that will make the pot $12 and give you the 2:1 pot odds you need to break even).

Look, effective odds and implied odds are two separate concepts that complement each other. For example, if you were sure that your opponent would call a bet on the river if you make your draw, you would need smaller pot odds (or, rather effective odds) to make a call profitable.

So, in essence, you want to calculate the effective odds the pot will be laying you if you are going to the river. You do this by adding the total amount you will have to invest and compare the total amount you will probably win if you make your draw. If this ratio is greater than the odds against making your draw, you can call profitably.

[gaming_mouse]

What you say makes no sense. You can't be getting 2:1 on the flop and 4:1 on the turn. That just doesn't make sense.

You are getting 2:1 for the flop and the turn combined, which is pretty good (a strong draw) that you will almost always have odds to draw to.

Dave,

I truly apologize that you have had to read through so much about such a simple concept. Facts about probabilities:

1. On the flop, if you have a 4-flush, you are a 2:1 dog to make your flush by the river. This is simply a probability calculation and has nothing to do with your effective odds or any other kinds of odds. The CHANCE that another spade comes IN THE NEXT TWO CARDS is:

1 - (38/47)*(37/46)=.3498, about 35%, making a 2:1 dog.


2. If the turn card is a blank, the CHANCE that the RIVER CARD MAKES YOUR FLUSH is about 20% -- 9 spades left out of 46 cards total -- making you 4:1 dog against.

There is nothing paradoxical about these two facts. Once a blank hits on the turn, you have lost one of the chances that you had on the flop to complete, so your chances go down.

That said, the above two facts have nothing to do with your implied or effective odds. You cannot calculate these in general, because they depend highly on the number of players in the hand, how many raises you expect (if any), and the number of players you expect to stay in. For a specific situation, you can estimate them. But for flush draws you will rarely need to estimate them because you will almost always have correct effective odds to call. There are a few exceptions, which I noted in my original post.

gm

[Dave H.]

Thank you very much...what you said is how I understood it.

[AngryCola]

**DUPLICATE POST**

[AngryCola]

[ QUOTE ]
That said, the above two facts have nothing to do with your implied or effective odds. You cannot calculate these in general, because they depend highly on the number of players in the hand, how many raises you expect (if any), and the number of players you expect to stay in. For a specific situation, you can estimate them. But for flush draws you will rarely need to estimate them because you will almost always have correct effective odds to call. There are a few exceptions, which I noted in my original post.

[/ QUOTE ]

This is the key right here, what gaming mouse and I are telling you is actually the same thing, can you see why? He is simply asserting that you cannot estimate the action on the turn, so effective odds become difficult and inaccurate to calculate. While I may disagree with this aspect, it is a fair point. This is the reason people tell you to go with your immediate pot odds. As I told Dave before in many postds, if that is what he would like to do then go for it! But, he was still confused about what effective odds ARE. This has been the point of further discussion. Not how useful effective odds are, but WHAT they are. Thanks, and sorry for the confusion. /images/graemlins/spade.gif

[AngryCola]

9 outs - That is the number of outs you have with a 4 flush on the flop. So lets go from there.

Turn Probability and Odds
9 Outs = 19% probability
(47-9)/x:1 = 4.2:1 odds against

River Probability and Odds
9 Outs = 20% probability
(46-9)/x:1 = 4.1:1 odds against

Now lets look at odds for two cards to come, and I do mean both cards. /images/graemlins/smile.gif All of these figures assume 9 flush outs.

HIT ONE OUT = 31.6% probabilty or 342 combinations

HIT TWO OUTS = 3.3% probability or 36 combinations

TO HIT ONE or TWO OUTS =
35% probability or 378 combinations or odds against of 1.9:1

These figures are for 2 card combinations, which are used when determining effective odds. The point is you aren't getting 1.9:1 on the turn card alone. So, you can't say "Well before when i made that call on the flop, I was getting 2:1, and now I've missed so I'm getting 4:1." Which, as I understand it, is how Dave still sees it. 1.9:1 assumes you will see both cards. So therefore you can be getting nothing BUT 1.9:1 for both cards.

What you can say is, "Well, I made that 4.2:1 call on the flop, and now Ive missed so I'm getting 4.1:1." Of course now your odds are slightly better, because you have missed on the turn (1 less non-out that can fall off the deck). The point is, if you start thinking about it as 2:1 on the flop, and 4:1 on the turn, you will most certainly be wrong. If you must think about it in single street terms, think of it as 4.2:1 to see the turn, and 4.1:1 to see the river. /images/graemlins/spade.gif

[AngryCola]

Ding! Ding! Ding! Good job. /images/graemlins/smile.gif

[AngryCola]

One corection about my math in the previous post. x=9, the number of outs you have.

One more thing-

Gaming mouse is right about the probabilities, if you will look you'll find that both of our numbers are the same. What he doesn't understand is how you are thinking about the issue of effective odds.

These two comments:
"1.Do I only need 2 bets in the pot BECAUSE I KNOW I AM GOING TO SEE BOTH CARDS, i.e. I am going to the river for sure?

2. What if I miss on the turn? Do I continue to need only 2 bets in the pot or do I now need 4 bets in the pot to continue?"

..show me that you arent quite getting it.

2 bets for 1 on the flop? Why? Unless, you are all-in (and thus don't have to call any further bets), that assumes you will be seeing two cards. It's actually 4.2:1 to make it by the turn.

So if you miss on the turn do you need 4 bets then? Again, this leads me to believe you aren't thinking about it the right way. You would have odds of 4.1:1 of hitting your flush on the river.

So in both cases you wouldn't need 2 bets and THEN 4. You would need 4 bets for every 1 that you contributed, on that particular street.

The odds of 1.9:1 for 2 cards ARE used when determining effective odds. I have given you the formula for determining effective odds twice now, but you still seem to be caught up on missing the turn. Missing the turn has NO bearing when using effective odds.

Heres the just of it in terms of bets-

You need an overlay of 1.9 bets for every 1 of your bets, if you are using effective odds. But, effective odds go beyond what is currently in the pot.

The current pot + the future turn bet of the original bettor = your 2 cards to come pot size. Your current call + your turn call = what you compare against the previous answer.

So, you see that when you take effective odds, with 2 cards to come, you must look at your calls vs. pot in terms of both streets COMBINED. This is because you are calling based on a two card combination. That is why I told you to look at it in terms of just completing your flop call. I was attempting to get you to think about it in the right way.

Now, if you don't want to use effective odds (which apparently you don't given how caught up you are in missing the turn), then you must use single street immediate pot odds.

In that case, you aren't really considering the 1.9:1 chance you will make the flush by the river. Your only consideration is whether you will make it by the turn. The odds of that happening are 4.2:1.

But wait a minute, you make the call and miss on the turn. Damn! So, we must now evaluate the immediate situation all over again. The chances of making your flush on the river are now 4.1:1.

After reading all this, you should be able to understand the difference between effective odds, and immediate pot odds. If you can't, then I'm not sure what it will take, because myself and others have given you all the information that is available on this topic. /images/graemlins/spade.gif

[AngryCola]

[ QUOTE ]
1 - (38/47)*(37/46)=.3498, about 35%, making a 2:1 dog.


2. If the turn card is a blank, the CHANCE that the RIVER CARD MAKES YOUR FLUSH is about 20% -- 9 spades left out of 46 cards total -- making you 4:1 dog against.

[/ QUOTE ]

My only problem with this logic, is how it is presented. This could confuse dave, with the way he is thinking about it. Both facts are true, however.

Problem is, again, it's 2:1 by the river. While it's true you have missed one of your chances, that has nothing to do with 2 card combination odds and probabilities.
Last time I'll repeat this, i promise (i know mouse knows this):
It's 4.2:1 to make your flush on the turn.
It's 4.1:1 to make your flush on the river.
It's 1.9:1 to make your flush on the turn OR the river

When dealing with effective odds (as dave wanted to learn), you use the 2 card combination probabilities, and not individual street probabilities. Therefore, when you miss on the turn YOU DO NOT re-evaluate your chances, when using effective odds. You were always betting on the combination, not what would happen on individual streets.

I'm just saying you can't mix and match when explaining these things, as Dave is confused about when to use immediate pot odds and effective odds. I think for his sake (and mine), he would be better off using immediate pot odds. /images/graemlins/spade.gif