I always play in Casino, in theory i wonder how can i tell if a deck
of card is shuffled randomly to be "as reasonable as possible"? Any
Maths/Estimation prob behind? I wish to know the details behind the
scene please.

Thanks

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Request for Question Clarification by mathtalk-ga on 15 Oct 2004 17:40 PDT

Hi, rndgroup-ga:

It would help to prepare a cogent explanation if you described your
math background.

thanks,
mathtalk-ga

One aspect of such a question is the observability of the shuffled
decks.  In some games one is not able to see all the cards dealt, or
to be able to reconstruct the order in which specific cards are dealt.

If one is dealing with a game (perhaps blackjack?) where it is
possible to reconstruct all or a substantial part of the initial
ordering of a shuffled deck, then it's possible to apply any of a
variety of tests of randomness to the observed order.  One test that
comes to mind is a "runs" test, e.g. how long is the maximum run of
increasing or decreasing card values in the order dealt.

Knuth (Art of Computer Science, vol. 2:  Semi-numerical algorithms)
discusses the problem of testing for randomness (and its importance in
judging routines designed to produce random sequences), and the runs
test is included in this discussion.

The subject of this question (Likelihood of card) suggests another
sort of test, a frequency test (how often will a particular card
appear).  For games in which the observation of dealt cards is
"censored", one can easily imagine ways that such a limitation affects
the observed frequency of cards.  Example:  A poker game in which
"folding" a hand results in the cards held remaining concealed is apt
to decrease the frequency of low-value cards appearing.

regards, mathtalk-ga

For a standard 52-card deck, seven shuffles are generally reckoned to be enough.

http://www.bridgeguys.com/SGlossary/ShuffleofCards.html

Or maybe six or five, depending on how you measure randomness.

http://flatrock.org.nz/topics/art_of_playing_cards/how_to_win_at_poker.htm

Thanks for quick answers both of you :)

In http://flatrock.org.nz/topics/art_of_playing_cards/how_to_win_at_poker.htm
(1)The researchers simulated it on a computer--> Any shuffle emulator on Internet?
(2)They found that, according to their definition of the "information"
remaining about the order of the cards, the randomness accumulates
steadily right from the first shuffle, and is virtually complete by
the 6th.  Even four shuffles does a fair job of reducing the
"information content" of the pack.-->So they only track the position
of cards? For example i got 4 cards, 12345, if i mixed them up and
then i get 54321, it's defined as most randomized? but it's still
straight! I wanna now the details or maths of it, i.e. why 7 times in
most of the websites referred

Thanks!

Mathtalk,

"then it's possible to apply any of a variety of tests of randomness
to the observed order."-->What is it?
"runs" test-->May I know more how it works?
Than
ks

Hi rndgroup,
Yes, there is a card shuffling simulator online at:
http://www.math.washington.edu/~chartier/Shuffle/simulation.html

based on the paper "Trailing the Dovetail Shuffle to Its Lair"

hope that helps.

-googleexpert

Thanks googleexpert.

If got more please feel free to tell me.