# Innumeracy by John Allen Paulos

5 replies [Last post]
Jpwoo
Offline
Joined: 03/26/2009

I just finished reading this short book about the bad effects of Innumeracy. (The math equivilent of illiteracy.)

I enjoyed it quite a bit for the afternoon it took me to read it. Of particular interest to people here, is the author spends a good chunk of one chapter going over probability and posing some interesting questions. But it is all in a pretty accessable way. I would recommend this book for any of the designers here who like to get 'under the hood' of a game and explore its numbers. I would also recommend it for the more casual designer as it may encourage them to look a bit closer at the mathmatics behind their own designs.

And he mentions a set of 4, 6 sided dice labled in a such a way that, A beats B, B beasts C, C beasts D, and D beasts A, all 2/3rds of the time. And that is just cool.

Brykovian
Offline
Joined: 07/21/2008
Re: Innumeracy by John Allen Paulos

Jpwoo wrote:
And he mentions a set of 4, 6 sided dice labled in a such a way that, A beats B, B beasts C, C beasts D, and D beasts A, all 2/3rds of the time.

That sentence doesn't make any sense to me ... does that make me innumerate? ;-)

-Bryk

Epigone
Offline
Joined: 12/31/1969
Re: Innumeracy by John Allen Paulos

Brykovian wrote:
That sentence doesn't make any sense to me ... does that make me innumerate? ;-)

There exists a set of four dice {A,B,C,D}. Each die has 6 sides. Each side is labeled with some integer. To "roll a die" is to choose one of the 6 sides of a die, each equally likely. Suppose one rolls dice A and B. Then with probability 2/3, the integer on the chosen side of A will be larger than the integer on the chosen side of B. An identical result holds for die pairs (B,C), (C,D), and (D,A).

Also, here is a site with some interesting nontransitive dice thoughts. The first presented is a set of three dice where A>B, B>C, and C>A, but if you roll each die twice and sum the results, then A

Jpwoo
Offline
Joined: 03/26/2009
Innumeracy by John Allen Paulos

No it makes me a poor writer :)

Apparently this was discovered by a guy named Bradley Efron.

You have four dics. A, B, C, and D.

Die A has the following faces: 4,4,4,4,0,0
Die B is: 3,3,3,3,3,3
Die C is: 2,2,2,2,6,6
Die D is: 1,1,1,5,5,5

If you roll die A against die B, A will win 2/3 of the time. B beats C 2/3 of the time, C beats D, and D beats A! All at a rate of 2/3.

In the book this leads to a discussion of voting paradoxes which is pretty interesting.

Jpwoo
Offline
Joined: 03/26/2009
Innumeracy by John Allen Paulos

Thanks for the link Epigone!