Shuffling the evidence

Randomness theory: Who shuffled these then?

A professor of maths at the University of Oxford has worked out how much shuffling is needed to make a pack of playing cards random.

Nick Trefethen, Professor of Numerical Analysis, has calculated that almost complete randomness can be achieved within five or six shuffles.

This might seem trival but it is applied to ...

Military camouflage

Biological camouflage

Cryptography

Conductivity and superconductors

Analysing stock market movements

The carrying capacity of pipelines

But this quickest path to randomness requires that the "riffle" shuffle is used, which involves cutting the pack in half, placing the cards face down and then rapidly inter-leaving them, says the Balliol College academic.

And it depends upon the efficiency of the shuffler - although if the division of the pack is too accurate, such as being exactly half and half, this will take away from the required randomness.

If this is performed five or six times, the "bits" of information that carried the original sequence will have been so disrupted as to be almost random.

Using the "overhand shuffle", which involves holding both halves of a cut deck and inserting a few from one half into the other, is much less effective, says the professor.

Professor Trefethen recommends the "riffle" method for shuffling

But if this all seems a little trivial, there are some very serious applications to understanding this "randomising" process - which is in effect analysing the point at which a pattern is no longer discernible.

Professor Trefethen works on studying randomness with his father, an academic in the United States, who uses concepts of disrupting patterns as part of his research into camouflage.

In these studies, instead of cards being shuffled to destroy a sequence, images are broken up by camouflage until they no longer have a recognisable shape.

There is also research into the point at which the blurring and distortion of an image makes it unrecognisable to the human eye.

Stock market

Apart from military and biological applications for this research, Professor Trefethen says that his work on the identifying and breakdown of patterns is used in the stock market.

"A substantial proportion of our students end up in the City, where they work on elaborate mathematical models of the stock markets."

Randomness and destroying evidence of sequences is also being applied to the expanding business of cryptography, an application that has been boosted by interest in secure online transactions.

"The mathematics of this is also closely related to practical questions such as why water becomes turbulent in pipes," says Professor Trefethen.

And it is also applied to examining conductivity and the development of superconductors.