Do "odds" really mean anything?

[Iamme]

Sounds stupid, doesn't it. of COURSE they do...right?

Well, they don't seem to matter to the person to whom the odds-against thing happened to.

Also, consider that at any given moment, there are tons of people out there who are a 'victim' of some odds against bad luck, or are the recipients of good fortune.

I have syncronistic coincidences happen to me, practically daily. I could place 1 in 50-1000 odds on many of these. What do THESE odds then become when they happen almost daily?!

A poster at JREF had a signature quote that I have never forgotten. It said that one in a million odds happens 70% of the time. At first I laughed at the silliness of this. Then, upon thinking of it...thinking of that which has happened to me...and other people. Hmmmmm.

 

[arcticpenguin]

I have syncronistic coincidences happen to me, practically daily. I could place 1 in 50-1000 odds on many of these. What do THESE odds then become when they happen almost daily?!

On what basis would you assign a probability to these occurences? Those numbers can't just be made up, they actually mean something (or should)

 

[Paul C. Anagnostopoulos]

Before I get started, I must tell you of a most amazing
thing. While I walked into this lecture hall, I saw a car
with the license plate 147-R-SGH! There are billions
of cars on the planet, so imagine the odds against me
seeing that particular car!

---Richard Feynman

 

[Iconoclast]

Also, consider that at any given moment, there are tons of people out there who are a 'victim' of some odds against bad luck, or are the recipients of good fortune.

"odds" (probabilities) only make sense a priori.

- What is the probability of intelligent life appearing on Earth: Bugger all.
- What is the probability that intelligent life exists on Earth: 1.

 

[Iconoclast]

I have syncronistic coincidences happen to me, practically daily. I could place 1 in 50-1000 odds on many of these. What do THESE odds then become when they happen almost daily?

Sure, lots of 1000 to 1 things happen to EVERYONE, EVERYDAY. However, there is an almost unlimited number of 1000 to 1 things that COULD happen to you every day, so the fact that quite a few of these things actually happen to you in any one day could be seen to be in line with probability.

Now, if you specified in advance half a dozen of these 1000 to 1 things and they ALL happened in the one day, that would be something else.

 

[Iconoclast]

Before I get started, I must tell you of a most amazing
thing. While I walked into this lecture hall, I saw a car
with the license plate 147-R-SGH! There are billions
of cars on the planet, so imagine the odds against me
seeing that particular car!

---Richard Feynman

Even more amazing, every time I see this quote the guy who owns the car has put a different number plate on it. I guess he probably gets sick of people coming up to him on the street to tell him how Dick Feynman was talking about his car in the lecture he just gave.

 

[glee]

Re: Re: Do "odds" really mean anything?

"odds" (probabilities) only make sense a priori.

- What is the probability of intelligent life appearing on Earth: Bugger all.
- What is the probability that intelligent life exists on Earth: 1.

I don't agree.
What are the odds of rolling a 6 on a fair dice? 1 in 6.
What are the odds of rolling a total of 6 on two dice? 5 in 36.
What are the odds of winning at craps? Well, about 49.6%.

What are the odds of life on any planet (without knowing any characteristics)? = (Number of planets with life in Universe) / (Number of planets in Universe).
What are the odds of life on a planet where life already exists? 1

 

[Iamme]

Arctic--Guilty of pulling figures out of thin air as accused.

This is how I came up with the 'odds' figures: I KNOW they are not 1 in a million. They are not THAT odd. But, they are odd enough.

I'll make up and example. I could have posted a rhyme to someone on the internet in the morning that said, "Peter Piper picked a peck...". Then, I get home that night and read the paper. In the paper is a feature about the success of Peter Pipers Pickle Patch. A n article I have never seen before, nor knew such a business existed.

This is a reasonable facsimile of actual syncronistic occurances that happen with me. What would YOU say the odds of this is?

 

[Rolfe]

This sort of thing was well illustrated by that ghastly Sally Clark "murder" case recently. The prosecution expert (who is now under investigation by the GMC) came up with very high odds against one mother suffering cot deaths in two of her children. In fact the same argument has been used to convict several people with pretty much no corroborative evidence, and appeals are pending.

If they'd only looked around, they'd have discovered that in the UK it actually happens to somebody about once every 18 months.

They simply couldn't get their brains round the concept that this wasn't about the odds of this happening to one pre-identified individual, but the odds of it happening to anyone at all in the entire population.

By the same argument, nobody ever wins the lottery. Tell, me, sir, where did you get all that money? Won it on the lottery, officer. Nonsense, the odds of anyone winning the lottery are 75 million to 1. Thief and Liar! To the cells with you!

Rolfe.

 

[Rolfe]

And I suppose the original conundrum was, no matter what the odds, once the event has happened, the probability is 1. Takes a bit of contemplating, that one.

Rolfe.

 

[chulbert]

Re: Re: Re: Do "odds" really mean anything?

I don't agree.
What are the odds of rolling a 6 on a fair dice? 1 in 6.
What are the odds of rolling a total of 6 on two dice? 5 in 36.
What are the odds of winning at craps? Well, about 49.6%.

What are the odds of life on any planet (without knowing any characteristics)? = (Number of planets with life in Universe) / (Number of planets in Universe).
What are the odds of life on a planet where life already exists? 1

"Odds" is the ratio of the probability of one event to the probability of another event. Lots of people make this mistake but I'm going to correct you because your examples are the most straightforward.

The odds of rolling a 6 on a fair die is 1 to 5. The probability is 1 in 6.

One of the things to watch out for with odds is that they're easily manipulated. Consider two events, A and B, that occur with probabilities of 99% and 96%, respectively. The odds of A is 99/1, or 99, while the odds of B is 96/4, or 24. This allows you to make misleading claims like "the odds of event A happening are nearly four times greater than B" even though both are very likely.

 

[T'ai Chi]

I have syncronistic coincidences happen to me, practically daily. I could place 1 in 50-1000 odds on many of these. What do THESE odds then become when they happen almost daily?!

If odds didn't mean anything, then entire realms: statistics, probability, medicine, physics, insurance, and more would be out of business. Basically any physical or social science that uses the discipline of statistics to come to a conclusion.

If an event E has probability p(E) of occuring, then the odds of E occuring are

odds(E) = p(E)/[1-p(E)].

If you are given the odds(E) first, then p(E) is odds(E)/[1+odds(E)]

For example, if p(having a certain genotype) = .25, then the odds(having that genotype) = .25/(1-.25) = .25/.75 = .333, which can also be expressed as 1:3.

If p(having a certain genotype) = .5, then odds(having that genotype) = 1, which is sometimes called 'even odds'.

If p(E) > .5, then odds(E) > 1.

Odds are simply an alternative way to express the likelihood that an event will occur. (despite the fact that most people incorrectly use 'odds' as a term for 'probability')

Sometimes p(E) and odds(E) will be very close to each other. This happens when the event E is a rare event.

 

[Beausoleil]

Re: Re: Re: Re: Do "odds" really mean anything?

"Odds" is the ratio of the probability of one event to the probability of another event. Lots of people make this mistake but I'm going to correct you because your examples are the most straightforward.

The odds of rolling a 6 on a fair die is 1 to 5. The probability is 1 in 6.

One of the things to watch out for with odds is that they're easily manipulated. Consider two events, A and B, that occur with probabilities of 99% and 96%, respectively. The odds of A is 99/1, or 99, while the odds of B is 96/4, or 24. This allows you to make misleading claims like "the odds of event B happening are nearly four times greater than A" even though both are very likely.

The same's lightly true of probability, in a way. Consider airplane statistics - some airlines have a crash every 1 million flights, some every 10 million flights. Is the latter 10 times safer?

Or do you look at the probability of a safe arrival, 0.9999990 vs. 0.9999999, making one airline 1.0000001 times safer than the other.

It seems to me the problems with probability always arise when you try to convert the numbers into a sentence.

 

[Iamme]

Read all the posts above. iIsee we have some math whizzes amongst us. I'm glad, because this keeps our dialogue from digressing into just mindless theory.

 

[American]

Aw god they mean EVERYTHING.

Let's say you got a 50-50 shot at something. The chance that you're going to get what you want is only half. So you play that once, and you end up losing like you thought you might. Then the same chance comes around, but this time you got twice as good odds, because half times 2 is one (100%), but on the second try multiply that by 2 to get double the odds of the outcome you want.

You got the odds cornered in a statistical "Catch-22". I base my entire life centered around this fact.

And I got it going on daddy-o!

 

[pupdog]

And then there's the difference in behavior people show for an outcome of some given probability, depending on whether they perceive it in terms of the probability of "winning" or the probability of "losing".

 

[QuarkChild]

Re: Re: Do "odds" really mean anything?

Aw god they mean EVERYTHING.

Let's say you got a 50-50 shot at something. The chance that you're going to get what you want is only half. So you play that once, and you end up losing like you thought you might. Then the same chance comes around, but this time you got twice as good odds, because half times 2 is one (100%), but on the second try multiply that by 2 to get double the odds of the outcome you want.

I never know when you are joking. Can't you at least use a smiley or something? To keep the mathematically inclined among us from having a heart attack?

Thank you.

 

[fishbob]

Do "odds" really mean anything?

Ye Gads - you never heard of insurance companies? An entire industry built on statistics, very similar to gambling.

Insurance sales guy: I bet you $300,000 that you are not going to die in the next 10 years.

Me: I bet you $15 per month that I will too.

Insurance guy: Its a bet. Sign right here.

 

[American]

Re: Re: Re: Do "odds" really mean anything?

I never know when you are joking. Can't you at least use a smiley or something? To keep the mathematically inclined among us from having a heart attack?

When someone uses a word like "daddy-o", you need not probe too deeply into what they really mean.

 

[UKBoy1977]

Just to be picky, Chulbert you expressed your odds the wrong way round. The odds of rolling a 6 on a fair die is 5/1, not 1/5!

To go back to the original post, yes probability is a funny concept. Of course any event is either going to happen or not happen. If we give odds of Evens on something happening it doesn't mean it might half happen, it means we estimate it is equally likely to happen as to not happen. Let's take a football match, the bookmakers estimate the home team has a 50% chance of winning. What does this mean? It means if we let the match run it's course (it being subject to all manner of random processes occurring within the match), note the result and then turn back time and let the match run again, note the new result, and do this over and over and over we would find in the long run that the home team won 50% of the time.

Also what you mentioned about long odds things happening to you, Iconoclast is right. Let's take 1,000 to 1 shots. There are millions and billions of possible things that could happen, any one of which might be a 1000 to 1 shot. Looked at this way, long odds things are happening ALL THE TIME. I would be amazed if they didn't! Here's an example:

I could go and switch my radio on right now. I could switch it on to a random station that could be playing any song that has ever been recorded. You will agree this runs into hundreds of thousands if not more. So the probability of any particular song is around, let's say, 1 in a million (in reality of course some songs are played more than others, but assume it is a very fair station which could play anything!). Now assume that I switch it on and the song that comes on is Help by the Beatles. What was the chance of this song coming on? It was 1 in a million. So here we have an absolutely earth shattering miracle? Of course not, because had any song in the history of music come on we could have said the same about it.

Now had we said before hand "The song will be Help by the Beatles" and it came on, now we have a true million to 1 shot happening! Does this prove psychic powers though? Well no.

If we asked everybody in the world to guess a song and then switch the radio on, assuming each person has a 1 in a million chance of being right (and the world population is about 6 billion) we would expect on average 6,000 people to perform this 'miracle'!