From: Rick Brown <rbrown@...>

Date: Mon, 04 Oct 1999 19:49:53 -0500

Date: Mon, 04 Oct 1999 19:49:53 -0500

Jay Reeve wrote: > >Yours is a brilliantly > >fast and simple recipe for "random" > >shuffling a deck of cards. > > > >However I cannot quite convince myself that you > >have produced a perfectly shuffled deck. > >Have you an argument to prove that it is? > > > >The order 1,...,320 does play a definite r^ole > >in the shuffling so why not some r^ole in the result? > > Hi Larry, > > I couldn't get this to go through privately, so I'm sending it to the > list. Perhaps it will interest someone else, too. I guess a rigorous proof would show that the probability of a given "card" ending up in a given position is equal for all cards and for all positions. I'm not sure I'm up to such a proof; however, I have a hunch it's true. Some "cards" will almost certainly be swapped multiple times. The ordering of the swaps _does_ mean that card #1 is the most likely card to be swapped multiple times, and card #320 is the least likely. However, I don't think that should affect the probability of the final outcome. If a given card gets move 4 times, is its final position any more "random" than if it had been moved only once? My intuition tells me no. - Rick