-----BEGIN PGP SIGNED MESSAGE----- In article <EMgky8m9Lkmb085yn@netcom.com>, Alan Bostick <abostick@netcom.com> wrote:
Note: I haven't read Diaconis's work; just some reports of it in the news section of SCIENCE more than ten years ago, so people should take what I say with more than a grain of salt.
Here is a (surely oversimplified) model of a less-than-perfect riffle shuffle: the deck is divided into two equal stacks, and the shuffler typically introduces some number k of "errors" that result in a pair of adjacent cards in the shuffled deck being exchanged (compared to a perfectly-shuffled deck). In a fifty-two-card deck there are fifty-one possible pairs to exchange. log2(51) = 5.67, so we get 5.67 bits of entropy for each exchange, if the exchanges are distributed uniformly through the deck.
I studied the "imperfect shuffle" thing in my Randomized Algorithms class last year. If I remember correctly, an "imperfect shuffle" is something like this: Cut the deck into two piles, left and right. The number of cards in (say) the left pile is distributed binomially. Drop one card at a time to form the new deck. A card is dropped from the left or right pile, with probability proportional to the number of cards remaining in that pile. - Ian "someone else can figure out the entropy of this..." -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMpJ0CkZRiTErSPb1AQHeJQP/c+LDI5dP1FWBb8TrArZYJ/LGTMsCnSIr TWXEV1ZC7U30aKcXwYcoRh0COg3iSPpwwNCr8qveZz/F4t2nR9J1feu27NE2AqE/ M4CozehsGoX9jW4/zzZu+2M6YK2EhBlRu5JpsKUax7It0VBQCz34BccT+e/8CXMj Ym+nS0zF7CM= =s9HO -----END PGP SIGNATURE-----