Name: Stephanie
Who is asking:
Student
Level: Middle
Question:
Last year, I did a science project in which I asked, "Which shuffles
better, an automatic card shuffler or shuffling by hand?" To measure
this I decided the "best" shuffler was the one to become random
first. Last year, to measure randomness, I numbered cards 1-52 and had
the subjects shuffle them until they broke up the rising sequences or
reached 10 shuffles. (Usually 10 shuffles came first...) Anyway, I did
the same
thing with the automatic card shuffler, and, as hypothesized, the automatic
card shuffler randomized the deck first.
This year, I have decided to continue the project. The problem is, I need a new way to measure randomness without the use of fancy computers or something. I have searched the Internet, I have posted my query on websites based on math, and I have searched the local library.
I have found many useful things on the Internet, but none of them can tell me a new way to measure randomness. I cannot do a perfect shuffle, and I am not terribly gifted in the art of using computers. If you have any information (anything will help) or advice, I would be greatly obliged.
Thank you for your time!
Hi Stephanie,
What you ask a very difficult, "I need a new way to measure randomness." There is a mathematical concept called Kolmogrov complexity that addresses your question. Information on this concept can be found at http://homepages.cwi.nl/~paulv/kolmogorov.html. To quote from this page
Kolmogorov complexity is a modern notion of randomness dealing with the quantity of information in individual objects; that is, pointwise randomness rather than average randomness as produced by a random source.
In your situation Kolmogorov complexity measures the randomness in a particular shuffle rather than the average randomness produced by an automatic card shuffler or the average randomness produced by shuffling by hand.
Andrei