Talk:Pot odds

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This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2021 and 19 December 2021. Further details are available on the course page. Student editor(s): Editor794. Peer reviewers: J47211, Happyboi2489, Pinkfrog22.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 07:03, 17 January 2022 (UTC)

Article rewrite

I rewrote the article (again). I consolidated implied odds and effective implied odds since they are both the same basic thing and Sklanky's convention isn't universal (see Harrington on Hold'em). I tried to improve the examples and make the article read easier from top to bottom. The only potentially controversial statement I made is that the precise calculation of implied pot odds isn't well documented for hands that are not certain winners or certain losers depending on cathing an out or not. I'm pretty well read, but I haven't read everything. If anyone has knows of a verifiable reference that discusses it, please contribute!--Toms2866 00:03, 10 May 2006 (UTC)

Another bold rewrite. I found an example of implied pot odds for probable winners in NLHE by Sklansky & Miller p.163. Article probably should be better referenced (e.g., references for each assertion), but I don't have time right now. --Toms2866 02:49, 2 April 2007 (UTC)

Removed this Note in the intro -

Note: Pot odds are not a measure of probability, but a simple win-to-cost ratio to simplify expected value calculations in poker. Thusly, 10:1 pot odds are said to be lower than 20:1 pot odds, whereas a 10:1 probability is said to be higher than a 20:1 probability.

while it's valid information, having it so early on in the article is confusing.

i also added the "Converting Pot Odds to Percentage Values" because later, in one of the examples, that knowledge is taken for granted.

the article might benefit from some drawing odds/pot odds examples since that's the #1 use for pot odds for beginners. possible resource: http://www.turningriver.com/texas-holdem-drawing-odds.html (the bottom chart)

i changed the wording in the example about manipulating pot odds because it seemed peculiar to have a section heading about manipulating odds, then state that the optimal bet would be one that eliminates the difference that manipulating the pot odds makes.

the example in the bluffing section of the article could use some elaboration. added a link to the pot odds and bluffing page. Tgbob 02:25, 22 May 2007 (UTC)Tgbob

Old discussion

We should have something about implied odds... Evercat 19:18, 15 July 2005 (UTC)

Yep, I agree, but ... a seperate article.... ? I will try to add somethig.. -Abscissa 11:40, 18 February 2006 (UTC)

I added a weak discussion of implied odds (and also manipulating pot odds). I figure a weak something is better than nothing. Additional rigor illustrating the mathematics of how to compute (and not compute) pot odds/implied pot odds and how they are used in game situations would benefit the article. --Toms2866 14:46, 24 March 2006 (UTC)

We should add something about reverse implied odds, where your odds may appear worse than they seem.--Toms2866 13:42, 21 April 2006 (UTC)

I added effective implied odds (more than one card to come) and reverse implied odds, per Sklansky definitions of those terms.--Toms2866 13:03, 3 May 2006 (UTC)

Reverse pot odds

The explanation is bizarre. Summarising:

• Alice thinks that if her opponent bets on the river, she must be beaten.
• Alice intends to call on the river. (she's factored two $10 calls into her betting strategies)

What?? Anyone have a proper source for this? Stevage 07:58, 25 July 2006 (UTC)

I see no problem with either the explanation or the example. Your paraphrase is a bit odd: Alice doesn't not expect to to beaten if here opponent bets the river--she only recognizes that it's more likely. She calls because it's still quite possible that a river bet will be a bluff or a weak hand, but she has to factor into her pot odds calculation the fact that it's more likely that a bluffer will give up; thus, she needs a higher probability of winning than straight pot odds would imply. This is covered in many of the standard books. --LDC 16:06, 25 July 2006 (UTC)

?

"With two cards to come, the approximate percentage probability is: (number of outs) x 4 - 1."<-- Did you mean that post flop with the turn and river coming up your odds of hitting after both have occurred is approximately what you said above? You might want to point that out.

Probability calculation

Its pretty strange to express the "win-to-loss" ratio as it is in the beginning of the page. For one, i've never seen anyone express their odds as 1 to anything, its always along the lines of "I'm getting 5 to 1 odds on my money". Second, using the given formula with odds expressed that way, it gives you a lower percentage with higher odds. Ex: 5 to 1 = 1 / (5+1) = ~16% ; 7 to 1 = 1 / (7+1) = 12.5%. It just seems very strange and out of the ordinary to me. Static3d 19:32, 15 August 2006 (UTC)

Is this right?

The opening paragraph of this article is defining 'Return', rather than 'Pot Odds'. 'Pot Odds' are a consideration of the combination of 'Return' and the odds of improving a hand; Not just getting $100 back from a $10 bet.
This is a common misconception, and I hear it often as a professional dealer, most commonly pre-flop.
Rather than my drawing out a long explanation here, I refer to the URL at the bottom of the definition's page:

How to Calculate Pot Odds

This is an accurate, albeit brief, example.
BarryD9545 (talk) 12:06, 18 September 2008 (UTC)

The discussion at the introduction of the article seems to be mostly about probabilities of winning, not pot odds. Unless I'm mistaken, "pot odds" refer simply to the ratio of the pot compared to a given call or bet. Pot $50, call $10 = pot odds of 5 to 1. Expected value compares pot odds with actual probability: Pot odds greater than actual probability is positive expected value. Would it be possible to make this intro much more focused on just pot odds, and leave any discussion of probability to a later paragraph? Stevage 03:33, 2 April 2007 (UTC)

You're right, the first few paragraphs here are terrible, and don't really describe pot odds at all. I'll work on a rewrite today. --LDC 05:54, 2 April 2007 (UTC)

I rewrote the first part, but I don't have time right now to fix the latter parts--I'll get to them after I get back from work. --LDC

Reads much better now. Thanks!--Toms2866 14:42, 4 April 2007 (UTC)

Opening paragraph odds

Please stop "fixing" the math in the first paragraph that's already accurate. 1000-to-1 pot odds means that one must win the pot once every 1001 times to break even; once in a 1000 will be profitable, because one will win $1000 once and lose $1 999 times, giving an average profit of a tenth of a cent. Remember that "1000 to 1 odds" means the same as "1 in 1001", not "1 in 1000". --LDC 15:51, 5 April 2007 (UTC)

LDC is right. Player is contemplating a $1 call to win a $1000 pot. If probability of win = 1/1000, player puts in $1 1000 times, loses 999 times and wins $1001 once ($1000 pot plus his $1 call), profiting $1.--Toms2866 23:55, 5 April 2007 (UTC)

You're right, LDC. I knew I shouldn't have gotten that lobotomy. Sorry!Ronald King 02:56, 6 April 2007 (UTC)

Sure, the "math" is correct, it's the definition that is absolutely wrong! The absolutely correct definition of Pot Odds are as described in this link that is used at the bottom of the definition's page:

         "How to calculate Pot Odds"

As shown in this link as well as the other links on the page, Pot Odds are neither the amount of a bet into a pot, nor the number of times a called pot is needs to be won; The first is the typically incorrect understanding held by neophyte poker players, the second is an oversimplified version of a basic premise of Pot Odds, probably derived from improper understanding of these pages referenced at the bottom of the article:

         "Pot Odds & Implied Odds"
         "Using Pot Odds & Calling  Bluff"

I'd suggest reading those articles in full, as well the others listed:

         "Intermediate & Advanced Pot Odds Calculations"
         "Pot Odds vs Pot Equity"

The often misconstrued definition of "Pot Odds" should be corrected. All the more so because the correct definitions are linked within the very pages of the definition itself.

I'm surprised to an extreme this hasn't been corrected out before now.

BarryD9545 (talk) 10:48, 26 October 2008 (UTC)

The definition in the article is correct, and much of the information you've linked to here is misleading or just plain wrong. Most of your links, for example, talk about how to calculate odds of making a draw. That's useful, and is something that is often compared to pot odds to make a decision, but is totally irrelevant to the concept of pot odds itself, which is nothing but a simple ratio of pot size to the size of a contemplated bet. How one uses pot odds is a considerably more complex topic, and the various articles you link to offer more or less reasonable advice on the topic, but they aren't very good at explaining the basic concepts correctly. --LDC (talk) 15:44, 26 October 2008 (UTC)

LDC-

So, your understanding of Pot Odds is correct over the five links to the web on the definitions very page? All of those web pages - as well many, many others - are "misleading", but YOU are correct?

Sorry, but it is actually your interpretation of all those pages that is "just plain wrong". Pots Odds is a level up from bet-to-pot-size ratio (Return), not the other way around.

What I'm saying is that Pot odds includes the odds on making a draw, and that is compared with the Return on the "investment" of a single bet (the bet-to-pot-size ratio) to determine if a bet is worth making. But it is not the single factor of Return.

Most commonly seen at a Hold'Em table in Pre-Flop situations, your incorrect usage would be:

         Everyone else bet $10, so my $10 will
         get me $100 if I win with my 2-7 offsuit!
         I have to call, I have 10:1 pot odds!!!

This is often called "Playing the Pot" and while a player is typically thrilled with the short term profit, this misinterpretation of Pot Odds leads players into losing chips over time at a table.

Correctly thought out:

         I have an Ace-King flush draw after the turn
         (approximately 5:1 chance of improving), so
         if I make a $5 call into a $35 pot (8:1 Return)
         I'm getting the right Pot Odds to make
         this call.

Or, Conversely:

         I have an Ace-King flush draw after the turn
         (approximately 5:1 chance of improving), so
         if I make a $35 call into a $35 pot (2:1 Re-
         turn) I'm NOT getting the right Pot Odds to
         make this call.

It's the value of the Return being greater than the odds on improving your hand that makes the right Pot Odds. (Yes, the bet being contemplated is included in the calculation of pot size.)

The examples that you and Tom22866 cite (1 win in 1001 hands) are one of the long term uses of betting patterns that give Estimated Value (EV), and Pot Odds are indeed a portion of understanding EV, just as the Return (bet-to-pot-size ratio) is part of understanding Pot Odds. EV is a step up from Pot Odds, which is a step up from Return.

I'd suggest you do more research around the web, as well as in actual texts, accept the information given in all those locations as correct and adjust your understanding; Then, perhaps, you can aid in providing the correct definition herein ... if your arrogance doesn't interfere with accuracy.

BarryD9545 (talk) 11:45, 27 October 2008 (UTC)

You seem to be arguing a definition of "right" pot odds, and I might not disagree with that. But this article is about "pot odds", which is a simple term of art meaning nothing more than the ratio itself. I'd suggest you research something more reliable than the web, such as well-respected books by real experts like Sklansky, Caro, and others; they use the term exactly as it is defined here, even while they also talk about the kinds of topics you're talking about. Your interpretation of "right" pot odds (being a combination of pot odds plus odds of winning) is indeed a common shorthand expression, but it is not a good way of explaining the concept itself. You first "bad" example above is actually correct--the 7-2 player is getting 10:1 pot odds for his call; he just doesn't realize that his chances of winning are less than the 9.1% he would need to make the call profitable (ignoring the implied odds, playability, and position arguments which further complicate things). --LDC (talk) 15:36, 28 October 2008 (UTC)

My use of the term "right" in conjunction with Pot Odds is a fade from our actual discussion; It is just another way of saying that a player has Pot Odds or does not have Pot Odds.

Since you mentioned Sklansky first on your list, here is a excerpt from a posted review of Sklansky's book "Theory of Poker":

The basic example [Sklansy] uses of a coin-flip makes it easy to conceptualize Expectation - in the long run, a coin-flip is a 50-50 proposition, so an even-money bet has an expectation of zero. You will neither win nor lose money in the long run. But, if you are able to get favorable odds by finding someone willing to give you $2 for every flip you win against $1 for every flip you lose, you know have a positive expectation. In the long run, you will win money.

Applying this to poker, any time you get favorable odds on a bet, you are compelled to make the bet. Going back to our post about Pot Odds, you will see this concept in practice: If you’re offered the opportunity to make 4x your bet, and your odds of winning the hand are 3:1, you take the bet because mathematically, you expect to win money in the long run.1

How much more simply can it be stated that Pot odds are the combination of Return and improving a draw??

Now, I know it'll be tempting for you to twist this block of text and claim that the author is referring to EV rather than Pot Odds, but in reality the point being made is that Pot Odds leads into EV; Pot Odds refer to the hand at hand (excuse the pun), and EV is a long term prospect. The author is also saying that understanding EV requires an understanding of Pot Odds. As I stated previously: "...Pot Odds are indeed a portion of understanding EV, just as the Return (bet-to-pot-size ratio) is part of understanding Pot Odds."

The reviewer of Sklansky's book understood the concept as Sklansky laid it out, and and truly drives our discussion home in his final two sentences on the subject:

Thankfully, the majority of poker players don’t understand this concept, and of those that do, many have trouble applying it. This is one of the ways winners are separated from losers.1

I agree with you, such other factors as Implied Odds (Profit on future betting round/hands), Position (often referred too as position, Position, POSITION), and playability (e.g. Is risking my tournament life worth it on a really good draw?), not to mention the simple reads you may get off a player and his bets, make things all the more complicated.

Basically, though, I'm glad there are plenty of players out there with your misunderstanding, as it amuses me when I deal and pays when I play.

If Wikipedia has people running the definitions that also misunderstand them, then I suppose when folks look it up (without reading this discussion) my cause for amusement and profit will be thusly furthered!

In other words, my input on the matter is complete. :D.

Aces Up!

BarryD9545 (talk) 05:04, 29 October 2008 (UTC)

We're talking past each other here. I'm only talking here about the first-paragraph definition of the term "pot odds" here, and Sklansky's definition agrees completely with that. The quote you provide says exactly that--he refers to his earlier definition of the term to make his present point about profitability. It would certainly not be out of place to include in the definition a mention that the term is often used that way, and I'll add that. And I'll ignore your childish insults; that's not the way to accomplish things around here, especially when it's clear that you can't understand your own examples. --LDC (talk) 16:18, 30 October 2008 (UTC)

The thing I find most surprising about this exchange is that BarryD9545 seems to imply that LDC doesn't understand the follow-on concept that takes into account the probability of improving the hand. Isn't it obvious to anyone who's not seething that BarryD9545 is calling the "compare your call amount to the pot amount" number "Return", LDC is calling it "pot odds", and they BOTH know that in order to determine whether or not to bet, there is then the extra step of comparing that number to the odds of improving the hand? LDC never said there was no such follow-up step...it's just a disagreement on terms. BarryD9545 is clearly correct that many players never get past the first calculation (if that far), and that is always pleasant when it happens at your table, but I think LDC is also correct that Slansky et al refer to BarryD9545's "Return" as "Pot Odds" in preparation for then comparing to the odds of improving the hand as a SECOND calculation. Cbarlow3 (talk) —Preceding undated comment added 18:45, 2 March 2009 (UTC).

Implied pot odds

I think the second example has some problems:

• Implied pot = $20 + $50 = $70, not $50.
• Alice can lose no more than her opponent on the final betting round, so she can lose no more than $50, not $100.
• Alice needs to plan what she will do in the last betting round if she does not make her flush. Presumably, she will fold, so her loss on the last betting round will be $0, not $100 (or $50), in that case. Her gain will also be $0 in that case.
• Alice's probability of losing when she makes her flush depends on whether her opponent is drawing to a flush. It should be less when her opponent is not drawing to a flush. I assume that she has estimated that it is 20% when her opponent is drawing to a flush and 0%, not 20%, when her opponent is not drawing to a flush. If this assumption is incorrect, then the example needs to be clarified.
• Alice also needs to estimate her probability of losing when she does not make her flush. Presumably, she has estimated that it is 100%, regardless of whether her opponent makes her flush. This would explain why she plans to fold if she does not make her flush.
• When computing EV, the call amount should be added to the implied pot before multiplying by the probability of winning, so in the EV calculation, the correct amount to use is $70 + $5 = $75.
• EV cannot be computed without Alice estimating the probability that her opponent is drawing to a flush. Since Alice seems to be worried that her opponent is drawing to a flush, she might estimate this to be greater than 50%, say 60%.
• EV should be computed as the probability-weighted sum of the amounts she will win from all possible outcomes. There are 8 possible outcomes, based first on whether her opponent will draw to a flush or not, then on whether Alice will make her flush or not, and last on whether Alice will win or not. The number of non-zero terms in this sum can be reduced to 4 by noting that the amount Alice will win or lose if she does not make her flush is $0, because she will fold in that case.
• So given all of the above, EV = (60% * 15% * 80% * $75) - (60% * 15% * 20% * $50) + (40% * 19% * 100% * $75) - (40% * 19% * 0% * $50) = $5.40 - $0.90 + $5.70 - $0.00 = $10.20. Since the cost to call is only $5, Alice should call, not fold.

Comments?

--Ronald King 07:40, 12 April 2007 (UTC)

I removed the second example under "Implied pot odds" for the reasons Ronald cited. The EV of a probable winner is only the product of the implied odds and estimated probability of losing. Adhall 10:43, 9 May 2007 (UTC)

Implied pot odds example

Now, I'm a beginner, so I'm probably making a mistake somewhere, but... "Second to last betting round" would be turn, right? So 4 cards are on the table. And Alice has 2 in her hand. That's 6 cards. She has 4 outs. So, her pot odds are: total number of cards (52) - cards she sees (2 in her hand and 4 on the table) : 4 outs = (52 - 6) : 4 = 11.5 : 1. And the article says pot odds are 10.5 : 1. What am I missing? --78.0.86.212 20:39, 22 September 2007 (UTC)

You're confusing "odds" and "probability"; probability is the ratio of favorable outcomes to all outcomes: 4/46 in this case, or 1/11.5. Odds are the ratio of favorable outcomes to unfavorable outcomes, 42 : 4 in this case (subtracting the four winners), or 10.5 : 1. Remember, a "1 in 4" chance or "25%" or "1/4 probability" is 3 to 1 odds, not 4 to 1. --LDC 00:15, 23 September 2007 (UTC)

Aha! Thanks a lot! --78.0.69.133 12:17, 23 September 2007 (UTC)

This example is a steal from David Sklansky & Mason Malmuth: "Small Stakes Hold'em". 93.139.63.131 (talk) 15:54, 6 June 2009 (UTC)

weak

Perhaps someone could edit the use of the word "weak". In the section on reverse implied pot odds we have the expression "If the opponent is weak or bluffing" appearing twice. This is ambiguous. Does this mean that the person is a weak player, or that he has a weak hand? Eclecticology (talk) 00:01, 8 October 2009 (UTC)

I made the edit. Not sure why you didn't do it yourself... Hazir (talk) 05:32, 8 October 2009 (UTC)

• As it happened I really didn't know which was correct. I had gone to the article in the first place to inform myself about the concept. Anyway, I've now at least made the same change in the other place where it occurs. FWIW, articles of this kind (not just about poker) often read quite differently for a person already familiar with the subject than for one who is just going there to find out. It did make me wonder how could I make this more readable without changing the information. Eclecticology (talk) 00:32, 9 October 2009 (UTC)

Manipulating pot odds

A bet of $6.43, resulting in pot odds of 4.11-to-1, would make his opponent mathematically indifferent to calling.

While this may work out to be zero-EV for us in theory, in practice its terrible, since the villain will usually have implied odds to make the call (we might river a set/2pair and be reluctant to lay it down, or we might click the wrong button accidentally). Also, if we make him break even on his call, we aren't going to profit from our bet. We want him to pay too high a price, which will cause him to make a mistake and then we profit. 93.139.67.66 (talk) 16:41, 25 February 2010 (UTC)

In practice, when implied odds factor into the equation, it becomes more of a game based upon inutition and instinct, ie... trying to work out what his implied odds are most likely to be and making the appropriate bet size based upon that. With regards to aiming to make an opponent mathematically indifferent to calling, it's in order to allow us to capitalise on our opponent's mistakes. From a game theory standpoint, betting more than what Nash would tell us to do would cause our opponent to fold more often than necessary. Of course, Nash isn't the be-all and end-all of game theory but I hope I've helped with your understanding of the reason behind why we want our opponents to be mathematically indifferent to calling. JaeDyWolf ~ Baka-San (talk) 16:11, 7 May 2012 (UTC)

Card suit symbols rejected

I am trying to write an example for using pot odds with card suit symbols, but Wikipedia rejects them as inappropriate since I am a new user. What can be done? Editor794 (talk) 18:35, 17 September 2021 (UTC) Editor 794

Addition Law of Probability

The given application of the Addition Law of Probability is incomplete as it doesn't subtract the probability of both cards being the straight card.

The addition law of probability combines the chances of making the straight on the turn (4/47 = 8.5%) and on the river (4/46 = 8.7%) to give the player an equity of 17.2%, assuming no other cards will give them a winning hand.

I believe it should be 4/47 + 4/46 - (4/47 * 3/46) = 8.5% + 8.7% - 0.6% = 16.7%

I didn't want to edit because I'm not entirely sure I've done the math right. Cjgeist (talk) 17:18, 19 September 2022 (UTC)

I think your result is much closer to the correct one than the one in the article, unless there's something I'm not understanding about the situation described (I'm not a poker player). I would do 4/47 + 43/47 * 4/46, or alternatively, 4/47 + 4/47 - (4/47 * 3/46). W. P. Uzer (talk) 19:59, 19 September 2022 (UTC)