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Topic: Card shuffling
Replies: 7   Last Post: Jul 31, 2012 10:33 AM

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Mok-Kong Shen

Posts: 518
Registered: 12/8/04
Re: Card shuffling
Posted: Jul 31, 2012 4:31 AM
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Am 31.07.2012 05:01, schrieb john:
> "Mok-Kong Shen" <mok-kong.shen@t-online.de> wrote in message
> news:jv6lhp$n6b$1@news.albasani.net...

>>
>> For playing cards there are riffle shuffling etc., see e.g.
>> http://mathworld.wolfram.com/RiffleShuffle.html With computers
>> one is not dependent on constraints resulting from manual working
>> and consequently could specify more complex operations that may be
>> rather inconvenient to be performed manually with cards. I like to
>> pose a general question:
>>
>> Given a list of n different elements, could one find a permutation
>> operation on them which can be characterized by the (variable)
>> numerical value of one single parameter (corresponding essentially
>> to the cutting point of a card deck into two parts in manual
>> shuffling) and which is likely to lead to the highest degree of
>> derangement (disorder) of the original list?


> sure, 1/2
>
> trivial.


Sorry that I have not properly clearly stated my problem. Firstly,
to be like shuffling in practice, the cutting point is not always
exactly at the middle but chance determined. Secondly, in the
'ideal' case of exactly at the middle, one knows that eight
out-shuffles return a card deck to the original constellation, thus
showing that at least the out-shuffle is problematic. What I guess
to be desirable is an operation which is likely to be a bit more complex
than the common riffle and is characterized by a single parameter value
such that a random value in a certain range for that parameter would
always lead to quite high degree of disorders. BTW I have done a little
experiments, but I doubt that I have yet found a very good solution.

M. K. Shen






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