[math-fun] Faro shuffling with jokers
It's fairly well-known that perfectly Faro shuffling a standard deck of playing cards 8 times will return them to their original order. For some reason I happened to compute Sloane A123320, which gives a table for different size decks cut at different places. I noticed that if you add two jokers to the deck and cut evenly the number is 52. If however you cut the regular deck evenly and place the jokers on top of the pile whose top card winds up on top it's still 8. On the other hand, if you do the same but put them under the pile whose bottom card winds up on the bottom it's 380. I can't think of any use for this factoid--other than maybe one magician hacking another (it'd require marks that can Faro shuffle!)--but perhaps it's still fun enough to share here...
participants (1)
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Marc LeBrun