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
