Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Card shuffling
Posted:
Jul 31, 2012 4:31 AM


Am 31.07.2012 05:01, schrieb john: > "MokKong Shen" <mokkong.shen@tonline.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 outshuffles return a card deck to the original constellation, thus showing that at least the outshuffle 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



