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