Welcome to the Monastery  
PerlMonks 
Comment on 
( #3333=superdoc: print w/replies, xml )  Need Help?? 
"But the real problem with this subroutine is that it does not sample the space of permutations uniformly."
It is certainly true that the method described initially does not sample the space of permutations uniformly because the permutations utilized are all a product of $n transpositions, so in particular they all have the same parity (even if $n is even, etc). Zaxo's comment that there may be some difference between a "fair shuffle" and a uniformly distributed selection over permutations" is perceptive. A shuffle might be considered "fair" if it tends to remove specific orderings that exist (e.g. in playing cards, one wants to nullify the effect of various groupings that have occurred in previous hands.) On the other hand, if one wants to model what actually occurs in a sequence of "random" shuffles, then restricting to permutations of fixed parity seems objectionable. It's a bit hard to define what "randomizing" shuffle means; Perci Diaconis (a highly respected mathematician) has studied this and written some good articles on the subject which should be found easily by web search. chas In reply to Re: A bad shuffle
by chas

Log In^{?}
Chatterbox^{?}
Other Users^{?}
Others lurking in the Monastery: (8)
As of 20170124 20:18 GMT
Sections^{?}
Information^{?}
Find Nodes^{?}
Leftovers^{?}
Voting Booth^{?}
Do you watch meteor showers?
Results (211 votes). Check out past polls. 