Amarillo Slim

[Eldog605]

First time short time...
In Amarillo Slim's bio he claims that there is an even money chance that 2 out of 23 people will share the same birthday. He then says if you ask 30 people their birthdays, its 70% that two share a birthday. This seems like way too high a probability, despite the fact that Slim won two bets off of it!!
EB

[Kopefire]

That's why it's such a good bet -- it goes against expectations (largely because most people are woefully under-educated in basic mathematics).

[Eldog605]

I guess I should have asked the math whizzes out there more directly...I was wondering if Slim's calculations, of even money and 70%, are correct. I tried doing (364/365)(363/364)(362/363)...etc, and I got a figure in the 93% range -- AGAINST two people having the same birthday. Maybe I'm doing the math wrong, so I would like to ask that anyone who knows about probability figure out if Slim's figures are accurate or not. It just doesn't seem plausible. I think Slim just got lucky.

[topspin]

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It just doesn't seem plausible. I think Slim just got lucky.

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Yes, unfortunately that's the problem with small sample sizes. What you should do is look him up and challenge him to this bet a few more times -- I hear around these parts 10,000 samples is considered a good number.

(Or, you could check this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=974030&page=&view=&sb=5&o =&vc=1), but it wouldn't be nearly as much fun /images/graemlins/smile.gif)

[Kopefire]

And it's thanks to people who are fully ignorant of math, that proposition gamblers can make a good living.

Just because you can't figure it out or it doesn't make sense to you doesn't mean that someone else is wrong.

Given that you admit to not being good enough at basic math to figure the odds yourself, which do you think is more likely -- That the guy most widely considered to be one of the greatest propositional gamblers ever managed to screw up a simple odds calculation problem, or that you just don't have the math background to understand it?

[Eldog605]

Why are you jumping down my throat? Is it a scientific fact that if I ask 30 people their birthday that 2 of them will definitely have the same birthday? I don't think so, so why don't you calm down. So I can't figure out the equation, does that mean I have to believe hook line and sinker every statistic I hear? I'm not allowed to be skeptical?

Even if Slim did have a 70% chance, he still could have gotten unlucky and lost the bet. If you want to bet me that I can't find 30 people with 30 different birthdays, I'll gladly put up my house.

You seem to be missing the whole point of my thread. I'm not arguing that the stat is false, I just find the statistic a bit "unreal," for lack of a better word. And the funny thing is, you STILL can't seem to provide the math! You mock me because I don't know the formula to figure the problem out. Well, that's why I'm posting...To get the formula. So I ask again, can some one with a "proper background in math" please post the formula?

Are all people on this forum as condescending as you?

[well]

For n people (with 0<=n<=365), the probability of them not having all different birthdays is:

1 - 365!/ ((365-n)!*365^n)

For n=23 this is: .507297
For n=30 this is: .706316

Note: Feb 29 is ignored.

[david050173]

Lets image you don't have a calculator and can't do combination math in your head. You have ~24 people so for each month there are 2 people. The odds of them having the same birthday is ~1/30 and you have 12 chances which is close enough to even money for a back of the envelope calculation.
Now the big question is are birthday's evenly distributed throught the year? Maybe their is a big cluster 9 months after the Christmas and New Years eve parties:)

[citizenkn]

[ QUOTE ]
Now the big question is are birthday's evenly distributed throught the year? Maybe their is a big cluster 9 months after the Christmas and New Years eve parties:)

[/ QUOTE ]

Or maybe a lot of births in mid-November? I know my parents had a couple of very happy Valentines..... /images/graemlins/smile.gif

[Eldog605]

Thanks for your help, that made things clearer. After searching for a while I found a website that listed the most popular birthday months. (Still can't find the most popular dates).

http://pressroom.hallmark.com/birthday_trends_stats.html

These are the percentages of people born in each month.

1. August 9.07
2. July 8.80
3. September 8.62
4. October 8.60
5. March 8.51
6. May 8.30
7. January 8.25
8. June 8.15
9. April 8.12
10. December 8.07
11. November 7.96
12. February 7.55

[Kopefire]

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Why are you jumping down my throat?


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Because you are stating that you'd prefere to believe someone with proven capacity to do this sort of thing well is making a fundamental error instead of admitting that your lack of understanding comes from your own ignorance. There's nothing wrong with being ignorant of some things, we cant' know everything after all. But there is something wrong with assuming flaws in your interloquitors simply because you don't understand something. It's called hubris, and it is frown on in polite society.

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Is it a scientific fact that if I ask 30 people their birthday that 2 of them will definitely have the same birthday?


[/ QUOTE ]

No. But then, that's not what Slim claimed, is it? This is known as a 'straw man" argument, it's also frowned on in polite society.

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I don't think so, so why don't you calm down.


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I'm not upset. I'm amused.

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So I can't figure out the equation, does that mean I have to believe hook line and sinker every statistic I hear?


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Absolutely not. But do you insist that every equation you can't personally figure out must be wrong because you can't understand it? That's what you did. That's what I'm jumping down your throat over.

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I'm not allowed to be skeptical?


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Skepticism born of ignorance is generally of very little value. If one is ignorant of a subject the best course of action when investigating that subject is to politely ask questions of people who know more without assuming that anything you don't understand can't be true.

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Even if Slim did have a 70% chance, he still could have gotten unlucky and lost the bet.


[/ QUOTE ]

Well no doh. That's why it's called gambling. It wouldn't be much of a gamble if it wasn't? Wanna bet me $10 that 2+2=4?

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If you want to bet me that I can't find 30 people with 30 different birthdays, I'll gladly put up my house.


[/ QUOTE ]

Dude, you really know nothing about statistics do you. Oh, and this is another straw man. No one is saying 30 people can't have different birthdays. There's a big difference between a nearly random sample and a systematically selected sample.

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You seem to be missing the whole point of my thread.


[/ QUOTE ]

So far it seems the point is for you to brag about how you don't understand statistics so therefore Amarillo Slim and anyone else who believes his claims must be wrong because you don't understand the equations yourself.

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I'm not arguing that the stat is false, I just find the statistic a bit "unreal," for lack of a better word.


[/ QUOTE ]

Yes, it's counter-intuitive for people who don't understand statistics. That's what makes it a good bet. We've covered this before.

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And the funny thing is, you STILL can't seem to provide the math!


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1) someone else already provdied the math.
2) I can provide the math, but that's not the aspect of your post I'm responding to.

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You mock me because I don't know the formula to figure the problem out.


[/ QUOTE ]

I haven't mocked you because you are ignorant of the math. I have berrated you because instead of stopping with stating you didn't understand something, you presumed that because of that lack of ability on your part someone else must be stupid. That's a rather arrogant and uncivil thing to do.

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Well, that's why I'm posting...To get the formula. So I ask again, can some one with a "proper background in math" please post the formula?


[/ QUOTE ]

To figure out the a priori probability of an event happening, you subtract from 1 the probability of it not happening.

Since the opposite of none of them having the same birthday is all of them having different birthdays, the formula is:

365!/ ((365-number_of_peopl)!*365^number_of_people)

Subtract that from 1 and there you are.

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Are all people on this forum as condescending as you?

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I don't know. Are you always so insulting of people who know more than you?

To recap - I started off agreeing with you - it's counter intuitive and noted that that's what makes it a good bet. You're the one that decided the follow up should be; well, then I can't figure it out, so folks who believe it must be wrong!

*shrug*

Personally, I'd rather be considered condescending for not accepting uncivility towards others than be so uncivil without cause.

Have a good day.

[benedetti]

If someone needs a practical prove can go to this site (http://www.tifr.res.in/~vsrp/VSRP2004/VSRP%20Selected%20Students%20List.htm) and try it. I have found this webpage through a Google search: "list of students" "date of birth", and it is the first match. In the first 25 students, there are two with the same date of birth. And it happens again in the next 12 and the next 18.