The three audiences I had in mind when creating this math magic presentation:
1. Dog lovers who want to be entertained AND blown away at the same time!
2. Math card magic enthusiasts who want to add a few more shuffling & mixing procedures to their repertoires.
3. Mathematicallyminded who would enjoy a glimpse into an exciting new area of studyrooted in Group theory, Combinatorics, Probability, and Information theory.

Technical Notes:

Although I independently developed the sequence at the heart of my presentation (The Luckiest Dog Alive) while studying relationships between Cyclic & Mirrored structures, I have since discovered that it is related to the ThueMorse sequence.

For an entertaining introduction to the ThueMorse sequence and some of its applications, I recommend that you watch the following video by Matt Parker (of StandUp Maths) who shows that the ThueMorse sequence is the fairest way to share things between two people. And that it does "all sorts of other crazy stuff."

"The Fairest Sharing Sequence Ever"
   • The Fairest Sharing Sequence Ever  

Little did anyone know that the ThueMorse sequence would have an intimate connection to packet structures of cards that are invariant under virtually every (systematic) mixing procedure commonly used today!

More significant, mathematically, my research proves that NO combination in ANY quantity (finite or infinite) of the 20 shuffles featured in this presentation can be used to truly randomize a packet of 8 distinct cards: There will ALWAYS be surviving structure that can be tapped or exploited.

Question: Do these results apply to any packet sizes larger than 8?
Answer: Yes.

Dr. Kent A. Bessey
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The 20 Shuffles from the Presentation:

1. LR (alternately deal into a left and a right pile, then randomly stack)
2. R x C (deal R piles of C cards, built one level at a time, then stack from first to last)
3. R x C (deal R piles of C cards, built one level at a time, then stack from last to first)
4. J R x C (judicious R x C, set pile 1 on 3 , pile 2 on 4, then randomly stack)
5. J R x C (judicious R x C, set pile 4 on 2 , pile 3 on 1, then randomly stack)
6. UPJ Even (upjog & stripout evenposition cards, then randomly stack)
7. Monge (overunder)
8. Monge (underover)
9. Faro (in)
10. Faro (out)
11. Klondike
12. Australian (downunder)
13. 50% COAT (deal top half, then drop rest on top)
14. Charlier 1 (Charlier shuffle that moves one card at each stage)
15. Bessey 11 (repeat drawing one card from top, then one from bottom)
16. Bessey 22 (repeat drawing two cardsone at a timefrom top, then two from bottom)
17. Pairwise Transpose (deal transposed pairs, then stack from first to last)
18. Pairwise Transpose (deal transposed pairs, then stack from last to first) = Packet Reversal
19. JTranspose (judicious Pairwise Transpose; set pile 1 on 3 , pile 2 on 4, then randomly stack)
20. JTranspose (judicious Pairwise Transpose; set pile 4 on 2 , pile 3 on 1, then randomly stack)
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Hidden Structures (Channel)
   / @absolutemathmagic  

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MISMAG822