In Magic Magazine, September 2000, Bob Farmer has a great math scam in his book.

Four playing card dice are mixed under four cups.
The victim picks one
The magician picks another.

the magician wins 2/3 of the time.

He states that it uses transitive numbers and that

Cup A will be beat Cup B 2/3 of the time.
Cup B will be beat Cup C 2/3 of the time.
Cup C will be beat Cup D 2/3 of the time.
Cup D will be beat Cup A 2/3 of the time.

The playing card dice are specially made with certain face values.

I just don't see how this possible!

Help!



(please remember...I am an idiot!)

The dice are non-transitive.

If they were transitive then the fact that
i) A beats B and
ii) B beats C and
iii) C beats D

would necessarily mean that A beats all the others.

We're all familiar with transitive relations:
If Al is taller than Bob
and Bob is taller than Carl,
then Al must necessarily be taller than Carl.

But not all relations are transitive.

Google "non-transitive dice" and you'll get what you're looking for.

Thanks!


(I told you I was stoopid!)


Farmer had playing card dice which confused me further!

http://www.grand-illusions.com/toyshop/ntdice1/


Hey! It's just like Rock Paper Scissors.