**Shuffle the cards**

How many times do you have to shuffle a deck of cards to be sure it's real,

But really, mixed? This issue of sleep measurement is not only from the eyes of

Quick-fingered dealers, but also from the eyes of statisticians

and mathematicians. A new study, published last month in the company's journal

Royal London, claims that the task is easier than they were inclined to believe

Today around the blackjack tables.

At the beginning of the nineties it seemed that this question had found its solution

the final Three mathematicians (Aldaeus, Bair and Diakonis) tried in 1992

Calculate how many times you need to devour a standard pack of 52 cards to

Be sure that the order it had before has been lost. According to the calculation they proposed,

Somewhere between the seventh and eighth mix the package gets so mixed up

that the cards are now placed in random order. And not only that, the researchers added

and spread their calculations in an article that has since become a classic, but four

The first mixes hardly bring the package closer to the coincidences

the desired The calculations showed a sudden turning point in the mixing level of

The package, which takes place immediately after the fifth mixing.

But the new study, it seems, is back and devouring the cards. Lloyd N. Turfton

from the University of Oxford and Lloyd M. Turfthan from Tufts University,

Massachusetts, argue that the problem can be attacked from a completely different angle, then

to discover that after the fifth mixing it is impossible to distinguish between the piles

the original and another random pile. According to the new calculation, the pair adds

Turpentine, there is no sudden breaking point in mixing as suggested by the previous study,

But with each mixing the level of disorder rises to the same extent, until it reaches

To the total disorder, after the fifth mixing.

Beyond the anecdotal piquancy, the new study actually reveals a poignant debate,

which has far-reaching consequences. The question at the heart of this debate is how

Measure order, or in other words how can you tell when the mess is big

So much so that it can be called random. This question has

Implications for almost all areas of life. This is a key question not only for

Physicists, computer scientists, linguists or biologists. when and how

Can, for example, stock market analysts report a certain pattern of fluctuations

in the value of a stock, and when should investors be told that market fluctuations are accidental?

The two studies offer two different ways of examining such questions.

The number of ways to arrange a deck of 52 cards is about 8 with 67 zeros

after him If, for example, at the beginning the cards are arranged in ascending order, unlikely

that after one shuffle they will suddenly be arranged in descending order. Although an

You can know exactly what the new order is, but you can point to a small group

A relative number of arrangements, out of the trillions of trillions of arrangements

The possible ones, which are likely to be obtained after one mixing. The old study, look for another

The random order, calculate the number of shuffles needed to move away from the order

The first, until it is no longer possible to say about a certain order of the cards if it is

More likely or less likely. The researchers' conclusion was that after seven o

Eight mixes, it is no longer possible to guess which arrangements are considered.

The second study, however, defines the coincidences in a different way. the researchers

Use a mathematical theory called information theory. a certain order of

Cards is basically information. Any mixing confuses the information

this. How can you measure the amount of information that was lost in everything

Mixing? Let's say the dealer holds the mixed pack and offers us to ask

same questions to discover the new order. Information theory calculates the

The minimum number of questions needed to discover the new order. If the dealer

Shuffle the pile only once, this number of questions is small because we

We know that the cards were arranged in ascending order, and we know how to evaluate

the number of cards that can change their place in one shuffle. But if

The dealer shuffled the pile five times, information theory reveals, says

The questions we will have to ask him before we discover the new order will be the same

For the number of questions we will have to ask him about a pile we don't know

Nothing on her. Therefore, according to information theory, the new study states,

After five sweeps the pile is already completely messy.

The difference between the results of the two calculations confuses you too

the mathematicians. Even the authors of the second study seem to be having trouble determining

Which of the two definitions correctly describes the pursuit of perfect mixing.

The really difficult question, on which the researchers now have to wrestle,

It is in which cases the difference in the definition of randomness will have practical consequences.

In the casinos, meanwhile, there is no excitement.

{Appeared in Haaretz newspaper, 17/10/2000{

The knowledge website was until 2002 part of the IOL portal from the Haaretz group

**By Yanai Ofran**