Talk:Odds

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The book "An Introduction to Medical Statistics" by Martin Bland says "Note that 'odds' is a singular word, not the plural of 'odd'." (p. 200), and uses this word in the singular form (e.g. "The odds of that event is p/(1-p)."). This sounds odd to me (pardon the pun), could any native speaker confirm that (Bland himself is American afaik, so he should know, I guess).

"Odds" is a plural noun (i.e., it has no singular form), like "scissors." As such, it is normally used with a plural verb. —Jt512 (talk) 06:31, 10 February 2022 (UTC)[reply]

p/(1-p) = p/q

"/" = ":"

You are a bit stuck with just p and q. If you make p p1, q p2, then extend this?

p1 : p2 : p3 ... ?

Ratios of a financial balance are also written out.

Sometimes you don't want to simplify fractions. 2A02:A03F:E03F:6300:C42D:E935:4E14:4284 (talk) 13:20, 7 February 2023 (UTC)[reply]

How can it be that the chance of you picking a Sunday is 1/6 instead of 1/7? I don't get it - someone explain. —Preceding unsigned comment added by 68.199.229.122 (talk • contribs)

It's one Sunday versus six non-Sundays. The probability that you pick a Sunday is 1/7. That's the same as saying the odds in favor of picking a Sunday is 1/6. More long-windedly, we have

1 / 7 1 − 1 / 7 = 1 6 . {\displaystyle {1/7 \over 1-1/7}={1 \over 6}.}

Nobody said the "chance" that you pick a Sunday is 1/6. It said "odds", not "chance". "Odds" is a precisely definted concept, not the same as "chance" and not the same as "probability", and you have to read its definition.

Michael Hardy 23:41, 18 March 2007 (UTC)[reply]

But people also use the word "odds" to mean probability. Like for example on this PowerBall page when they say the odds of winning the biggest jackpot are 1 in 175,223,510 they mean the probability of winning is 1/175,233,510 (five white balls from 1 to 59, and one red ball from 35 -- match in any order C(59,5)*35 = 175,233,510). This is also the way that Wired magazine used the word "odds" (article about planets). And it also seems to be the way that the web site The Book of Odds used the term (they would have odds like the probability that an adult MLB fan roots for the Yankees is 1 in 9.77). The Book of Odds web site seems to be defunct now, but it is still available on the waybackmachine. On the other hand it seems that Wolfram|Alpha, MathWorld, and various dictionaries [1] [2] have the same definition.

Perhaps the solution is that the article should be updated to reflect the fact that people might use the term to mean the raw probability. If somebody says the odds of success are "5 in 7" then that means the probability of success is 5/7. This is different from saying "5 to 7" Jjjjjjjjjj (talk) . —Preceding undated comment added 00:07, 16 May 2012 (UTC).[reply]

Could someone explain why these are used in probability theory? I mean, I can see that they're used in betting because of hysterical raisins, but why elsewhere? They seem very counterintuitive to me and I always have to convert them to probabilities by doing a:b ==> a/(a+b) except when they are in form 1:x or x:1 where x is large, meaning that I can conveniently convert them to "very (im)probable". I like the naming, though, odd as they are. 82.103.198.180 10:52, 23 July 2006 (UTC)[reply]

Odds and probabilities convey the same amount of information, but sometimes one is easier to use than another. Try odds ratio, logit and logistic regression as examples. --Henrygb 20:55, 23 July 2006 (UTC)[reply]

They certainly don't seem unintuitive to me. Michael Hardy 23:41, 23 July 2006 (UTC)[reply]

Odds are sometimes easier to compute with. For example, it's easier to write a Bayesian filter with odds than with probabilities. The product of two independent sets of odds appropriately combines them as evidence for or against a proposition, while the product of probabilities means something else.

In common usage, bigger odds' seems to mean less likely (a bigger 'against' odd). It also seems to mean the same in betting. [3]. Can somebody confirm this and move it to the article? Andy Rosa 18:22, 28 December 2006 (UTC)[reply]

in bookies how come the odds are like 7/2 i never understand what they mean. if it said odds are: win 1/2 that would mean 50% chance right? but more often than not it will be top heavy. someone explain please

What does it mean when I see a website posting odds for certain candidates, like Guiliani has 9-2 odds, or Hillary Clinton has 7-2 odds? DRosenbach ^{(Talk | Contribs)} 13:55, 27 June 2007 (UTC)[reply]

The very second line of this article is wrong. You go on to say that the probability of picking Sunday is 1/7, which is correct. That would also be expressed as 6:1 odds If the formula m/(m+n) gives probablity of an event with m to n odds, then the probablity in this scenario would be 6/7, which is wrong.

It should say n/(m+n)

In gambling, representation of probabilities differs by location - (EU: 1.25, UK: 1/4, US: -400). Juz saying --90.185.76.189 (talk) 20:28, 2 April 2009 (UTC)[reply]

This is a good question. Most of the comments on this discussion page need to be deleted. The most common question - "I don't understand the meaning of 7 to 1 odds or why this is different to P=1/7" - is answered with UNNECESSARY REPETITION (roughly the second half of the article needs to be deleted). However I'm surprised that not all the notations are well explained. "1.25 odds" means a win returns a total (including stake) of bet x 1.25, but "-400" ("moneyline odds") is currently explained as "the stake required to return 100" ... this mystifies me, since I don't know how to bet negative money! All I know is that likely results are negative numbers while unlikely ones are positive. — Preceding unsigned comment added by 110.175.57.184 (talk) 09:41, 28 May 2011 (UTC)[reply]

Starting an article with a mathematical equation is not the best way to inform people. Can we have some "plain speak" for those of us who are math challenged? —Preceding unsigned comment added by 65.23.116.46 (talk) 06:54, 2 May 2009 (UTC)[reply]

I believe that the explanation in the article is plainly wrong, and there is no reference. The odds for getting six when throwing a die, (a dice), is 1 to 5, not 1/5. Odds are unnormalized probabilities. The normalizing divisor is the sum of the odds, so the probability for getting six when throwing a die is 1/(1+5), and the probability for not getting six when throwing a die is 5/(1+5). While probabilities are almost never integers, odds are very often integers, and so odds are more easily accepted by nonmathematicians. Bo Jacoby (talk) 19:22, 21 July 2009 (UTC).[reply]

I have never come across this way of speaking. On this account if an event were given odds of 1000, it would be considered very likely. However in the UK, "a thousand to one" would refer to a very UNlikely event. This page gives no references as to where exactly this information is coming from. Please supply that information. Incompetnce (talk) 13:36, 3 August 2009 (UTC) This is where metaphor maybe encountered, such as the Australian colloquialism "What are the odds?...London to a brick" if someone were giving opinion of the millions-to-one certainty of a horse winning. How about infinity-to-one? See article on infinity and certainty.SignedJohnsonL623 (talk) 04:51, 17 July 2011 (UTC)[reply]

This passage uses a single example to touch on two different issues, which I think would be better addressed in separate sections:

1) The distinctions among the terms "odds","probability", and "chances".
2) The distinction between the odds a bookie posts and (his beliefs about) the true odds of each outcome

Btw, does "chances" have an agreed-upon definition, either in math or in common parlance? Or do people sometimes use it to mean odds and sometimes use it to mean probability?

Kathryn Tzvia (talk) 11:20, 28 January 2010 (UTC)[reply]

There is an agreed-on definition but some writers are sloppy or careless. 2 IN 5, and 2 TO 3 are both sometimes call chances, sometimes odds, obviously they both define the same probability, hence people don't need to be careful.

Also one can say "a chance" meaning an opportunity and "chance" meaning probability.

2 chances for and 3 chances against is odds 2:3. It's 2 chances in favour out of 5 altogether so a chance of 2/5. Richard Gill (talk) 05:59, 23 April 2013 (UTC)[reply]

"In a 3-horse race, for example, the true chances of each of the horses winning based on their relative abilities may be 50%, 40% and 10%. These are the relative probabilities of the horses winning and are simply the bookmaker's 'odds' multiplied by 100 for convenience."

1) I think 50%, 40%, 10% can(must?) be called probabilities of the horses winning (not "relative probabilities"), since they represent the probability of that horse winning out of all possible outcomes, as opposed to the ratio between the probabilities of any two of the horses winning.

Agree. 50% is a chance, not an odds. 50%= 50/100.Richard Gill (talk) 05:51, 23 April 2013 (UTC)[reply]

2) A more vital point: the percentages given are the probabilities [put in decimal form and] multiplied by 100, not the odds multiplied by 100.

Probability of horse #1 winning is 1/2, i.e, .5, i.e., 50%.

Probability of horse #2 winning is 2/5, i.e. .4, i.e., 40% etc.

Odds of horse #2 winning are 2:3, b/c if they have a 40% chance of losing, they have a 60% chance of winning, so the ratio is 40/60 or 2/3 or 66.67%, although I'm not sure it would really mean anything coherent to say "the odds of horse 2 winning are 66.67%".

The odds are 2:3 (2 in favour, 3 against) and the probability is 40% = 2/(2+3). Richard Gill (talk) 05:54, 23 April 2013 (UTC)[reply]

3) In the rest of the passage, I believe the odds of each horse winning are all stated backwards, meaning they actually give the odds of each horse losing. Saying the probability of a horse winning is 60% represents odds of 6:4, not 4:6.

I'm a new editor and only a dabbler in probability, so worry that I'm making errors and/or am unable to explain my points clearly, so wanted to get some second opinions before I put anything into the article. Thanks! Kathryn Tzvia (talk) 11:20, 28 January 2010 (UTC)[reply]

You're absolutely right. Some more references would help. Richard Gill (talk) 05:54, 23 April 2013 (UTC)[reply]

I propose merging most of Fixed-odds betting into Odds, with any material that doesn't fit there being moved into Bookmaker or Gambling. As it stands, the Fixed-odds betting article does not seem to make much sense as a stand-alone article. It covers much of the same ground as the Odds article, including different ways of displaying odds (fractional, decimal etc). It seems to have been created purely as a means of distinguishing between fixed-odds betting, Parimutuel betting and Spread betting. If this is the case, then the article should be rewritten to reflect this, and the explanation of different types of odds etc. redirected here. Any thoughts? Peaky76 (talk) 00:20, 26 April 2013 (UTC)[reply]

There seems to be a lot of overlap between articles on these topics. It would seem sensible to have fewer, better articles, but I'm not an expert in this field: I just link here a lot when writing about horse racing. As several articles would be affected I would raise the issue at WikiProject Gambling and then go ahead if no-one objects. Tigerboy1966  08:38, 11 May 2013 (UTC)[reply]

If the gamble was paying 4-1 and the event occurred, one would make 40 units, or a profit of 30 units.

I think it should be

...make 50 units, or a profit of 40 units.

Jmichael ll (talk) 01:33, 23 September 2013 (UTC)[reply]

An editor has identified a potential problem with the redirect Betting odds and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 18#Betting odds until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Bonoahx (talk) 22:52, 18 May 2022 (UTC)[reply]

يوجد خطء ما الصفحه لا تعمل اطلاقا ولا أعلم السبب 41.68.66.202 (talk) 23:25, 3 June 2023 (UTC)[reply]

The redirect Shoo-in has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 April 25 § Shoo-in until a consensus is reached. Utopes _{(talk / cont)} 04:36, 25 April 2024 (UTC)[reply]

Instead please see the discussion the section Talk:Odds § Equations for odds and probability are currently wrong —Quantling (talk | contribs) 16:59, 8 July 2024 (UTC)[reply]

Hello @Quantling, you reverted edits I recently made to https://en.wikipedia.org/wiki/Odds so that the first two equations on the page are wrong again. You said my changes were not consistent with following paragraphs. Let's try to fix the following paragraphs to be consistent with the corrected equations instead of using wrong equations. Please point out which parts of the paragraphs following the equations are inconsistent with the corrected equations? Stanmanish (talk) 20:02, 5 July 2024 (UTC)[reply]

My experience is that when people say "odds", it's not always clear whether they mean "odds in favor" or "odds against". For example, gambling odds (payoffs) are usually based upon "odds against"; it pays 10 to 1 because the odds against it are high. But saying your odds of winning are "10 to 1" is giving "odds in favor". I think we should change the lede to address this up front, giving formulas for both in terms of a probability p that an event happens. Thoughts? —Quantling (talk | contribs) 02:20, 7 July 2024 (UTC)[reply]

@Stanmanish: I have edited the article lede to include both the original formula and the one in your recent edit. If you think the article needs more work, feel free to edit boldly if you think that appropriate, or to discuss it further here. Thank you —Quantling (talk | contribs) 22:37, 7 July 2024 (UTC)[reply]

@Stanmanish: I have further edited the lede. Although my previous edits might have included your formula "in spirit", now my edits include your formula close to verbatim. —Quantling (talk | contribs) 16:55, 8 July 2024 (UTC)[reply]

@Quantling, thanks for your edits. Unfortunately I'm not receiving notification of when you make changes, so I'm a bit late responding.

You write "p=s/t", but you've not defined s or t at that point. Assuming s is the stake and t are the odds, then the correct equations can be deduced from the definition at the start of the section entitled "Statistical usage" and the accompanying figure. Using p and q from that figure, we can write the odds as

t = p/q

For a stake of s, with fair odds of t, the winnings are

w = s/t

so t can also be written as

t = s/w

As an illustrative example, consider betting s on throwing a 6 with a six sided die. The probability of a 6 is

p = 1/6

The probability of "not 6" is

q = 5/6

so the fair odds are

t = p/q = 1/5.

Since the odds are fair, on average the total payout, defined as w+s, would equal the sum of the stakes. If we bet 6 times we would expect a payout of w+s from the 6 stakes of s, so that

w+s = 6*s = s/p

therefore

p = s/(s+w) = t/(1+t)

and, therefore,

t = p/(1-p) = p/q

which takes us full circle and agrees with the figure at the start of the "Statistical usage" section. Stanmanish (talk) 18:01, 9 July 2024 (UTC)[reply]

@Stanmanish: Sometimes a probability can be written as a fraction. s/t is meant to be that fraction. For example, 40% can be written as 2/5. I'll re-write that part to try to make that clearer. —Quantling (talk | contribs) 18:05, 9 July 2024 (UTC)[reply]

In your most-recent message you are not distinguishing "odds in favor" from "odds against" that I can tell. I believe you are assuming "odds in favor" when you write that throwing a six on a die as odds of "1/5". Sometimes people instead think in terms of "odds against": the odds against throwing a six on a die is 5/1; and fair gambling odds are "5 to 1" or "6 for 1". The goal of my re-write is to explicitly indicate whether we mean "odds in favor" vs. "odds against". —Quantling (talk | contribs) 18:14, 9 July 2024 (UTC)[reply]

@Quantling, I was using "odds in favour" as I was building on what was already written in the section entitled "Statistical Usage".

I still think what you've written is wrong as the probability (of the event) can not be written as s/t. The probability can be written in terms of s and t as

p = s/(s+s/t) Stanmanish (talk) 12:22, 10 July 2024 (UTC)[reply]

@Stanmanish: You have assumed some definitions for s and t that I did not intend. I believe that that is the current source of confusion. If one starts with p = 0.25 then that can be written as a fraction in any number of ways, such as 1/4, 2/8, and 7/28. If one chooses the last one, one is writing p = 7/28; that is, in this case, s = 7 and t = 28 can be chosen so that p = s / t. With these choices for s and t it becomes clear that that p = 0.25 is the same as "7 to 21 in favor", "21 to 7 against", and "7 in 28". Additionally, a fair bet would "pay 21 to 7" or "pay 28 for 7".

The part where you instead write that s is "stake" and t is "odds" is not at all what I am trying to convey. Would it help if I change s and t to different letters, such as N and D? —Quantling (talk | contribs) 12:46, 10 July 2024 (UTC)[reply]

I've gone ahead and changed some variable names. Hopefully that clears up some things. —Quantling (talk | contribs) 12:55, 10 July 2024 (UTC)[reply]

@Quantling, I carried on using the definitions of s and t that were used on the first version of the page that I edited that you reverted, and I used above in my comments. What were your definitions of s and t when you wrote p = s/t?

I think the Odds page should start with a definition of odds using symbols like s, w, t, and p (for stake, winnings, odds and probability), similar to what is done in the "Mathematical relations" section, but I'm not sure that the definition of "odds for", o_f, in that section is correct as it says

o_f = W/L

using the W and L notation in that section. I think

o_f = L/W

since, when betting on a very low probability event, the possible winnings (W) will be larger than the possible loss (L, which I previously called s = stake).

This page https://www.alloprof.qc.ca/en/students/vl/mathematics/the-odds-for-and-the-odds-against-m1350 defines the "odds for" as

o_f = "number of favourable events" / "number of unfavourable events".

This is the same as

o_f = p/(1-p)

where p is the probability of the "favourable event". It is exactly what I wrote above, but in different notation as

t = p/(1-p) = p/q

On this page https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1130_Mathematical_Ideas_Mirtova_Jones_(PGCC%3A_Fall_2022)/03%3A_Probability/3.02%3A__Odds#:~:text=For%20example%2C%20suppose%20we%20roll,number%20six%20is%201%3A5.

it says that the "odds in favor of rolling a six on a die is 1:5", so the loss is 1 and the winnings is 5, which agrees with what I wrote above, ie, o_f = L/W, and disagrees with what it currently written on the wiki page, which is o_f = W/L.

The whole odds page is so confusing (with errors, and different notations and definitions), presumably because of piecemeal editing of the page (which I admit I am guilty of), that it would take a major overhaul to fix.

Another possibility is that some people define "odd for" as the reciprocal of what other people define it as, ie, there really is ambiguity in the definition. Stanmanish (talk) 17:42, 12 July 2024 (UTC)[reply]

The s and t that I originally used were not meant to mean anything other than two numbers such that if you divide s by t then you get p. All the confusion that s might be "stake" and that t might be "odds" is why I changed s and t to N and D. I have only ever meant them to be two arbitrary numbers whose ratio happens to be p.

We have to be careful what we mean by W and L. If you win when a six is thrown on a die then, one possibility is that W = 5 is the amount you win if you are right and L = 1 is the amount that you lose if you are wrong. The two values switch if one instead is saying that only W = 1 outcome makes you a winner and L = 5 outcomes make you lose. —Quantling (talk | contribs) 21:46, 12 July 2024 (UTC)[reply]

Hi @Quantling, I don't really understand what you are saying in your last comment. If there is confusion about winnings (W) and loss (L) they should be defined. I'm going to stop contributing to this page now. I only contributed initially to correct the two equations that found to be wrong. I now feel that I understand odds and their relationship with probability, winnings, stake and payout, but the page needs a lot of work and I don't have time to do it. 81.111.15.147 (talk) 23:15, 12 July 2024 (UTC)[reply]

Yes, I think there was confusion in the article about some of the definitions. Stanmanish's comments helped me to make changes to the article to clarify the definitions. I am hopeful that the page's equations are now correctly supported by those definitions. But this is Wikipedia, there's always room for improvement, and your work is appreciated at any level of participation. Thank you —Quantling (talk | contribs) 15:02, 13 July 2024 (UTC)[reply]

Shoo in, as well as other redirects that point to this article, are at RfD. Please see Wikipedia:Redirects for discussion/Log/2025 February 6 § Shoo in. Thanks, Sdrqaz (talk) 04:14, 6 February 2025 (UTC)[reply]