Amarillo Slim
 

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

Re: Amarillo Slim
 

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

Re: Amarillo Slim
 

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.

Re: Amarillo Slim
 

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

[/ QUOTE ]

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, but it wouldn't be nearly as much fun [img]/images/graemlins/smile.gif[/img])

Re: Amarillo Slim
 

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?

Re: Amarillo Slim
 

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?

Answers
 

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.

Re: Answers
 

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:)

Re: Answers
 

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

Re: Answers
 

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/birthd...nds_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