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. [img]/images/graemlins/spade.gif[/img]

[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. [img]/images/graemlins/spade.gif[/img]

[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. [img]/images/graemlins/smile.gif[/img]) 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. [img]/images/graemlins/confused.gif[/img]

[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