Frank Morgan

Revised to “Five or Six” from “Eight” November 7, 2010.

In response to frequent questions, I now recommend shuffling the bridge deck just five or better six times and then preferably dealing the cards back and forth instead of cyclically. The recent article by Conger and Howald** supersedes the revolutionary 1992 paper of Bayer and Diaconis* in showing how the randomness of a shuffled deck is enhanced by dealing out the cards, even more so if the cards are dealt back and forth (West North East South South East North West) instead of the usual repeated cycle (West North East South West North East South). Their following table shows the remaining order after n shuffles for the undealt deck, for the bridge hands dealt cyclically as usual, and for the bridge hands dealt back and forth

n                 5      6      7       8       9      10

undealt       92%  61%  33%  17%   8.5%  4.3%

cyclic deal   23%   7%   3%     2%     1%

back&forth  31%   3%   1%

Dealing back and forth has the added advantage of being a bit faster than dealing cyclically as usual. Some questions about the accuracy of the mathematical model remain. Continue reading ‘Five or Six (not Eight) Shuffles’ »