

Bill Hallahan Inner circle New Hampshire 3230 Posts 
In 2018, I started doing research to try to create a mathematical card stacks. That lead to my post in Red Phish DeBruijn 52.
The result was the over 150 page book, Mathematical Stacks. My favorite items in my book are The Bart Harding Stack, created by the late Arthur Bridgman, Cherry Stack, and the chapter on the Si Stebbins Stack. The Introduction to the book states: Quote:
This book contains a collection of various stacks made with standard playing cards, excluding the Jokers. Although some routines and presentations are mentioned, this book is not predominately about either routines or presentations. The very few presentations listed in this book are generally the bare minimum to demonstrate an effect. Although the author has performed some items in this book, this is not a book of audiencetested routines. The focus is on stacks, some that might be useful, and some that definitely are useful. The book contains the following chapters and stacks:
My primary impetus to write this book was a book by Persi Diaconis and Ron Graham titled, Magical Mathematics. However, posts by glowball, TomasB, and Scott Cram, also made me want to write this book. If glowball, TomasB, or Scott Cram want a copy of the book for free, as long as they promise not to share with anyone else, I'll send it to them. They can contact me in a private message here in the Magic Cafe.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
 The character of â€˜Deathâ€™ in the movie "Hogswatch" 
ddyment Inner circle Gibsons, BC, Canada 2523 Posts 
The Harding stack, while unquestionably important in its day (1962), is no longer seen as a particularly good solution to the algorithmic deck challenge. Not because of its rule exceptions, but because (1) it requires a level of mental arithmetic [adding and subtracting multiples of thirteen, for example] that is difficult for many to accomplish "under fire", and (B) it has detectable sequences [e.g., aces, twos, & threes are always followed by Jacks, Queens, & Kings, respectively).
Its core idea, though (starting with an easily calculated stack and then applying simple conversion rules to create a second stack), is an excellent one. New deck order is, unfortunately, not easily calculated by most people (quickly, what is the 37th card?). Considerably better solutions for algorithmic fulldeck stacks have been developed in the 60+ years since Mr. Bridgman's proposal.
The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More :: (order "Calculated Thoughts" from Vanishing Inc.)

Bill Hallahan Inner circle New Hampshire 3230 Posts 
I like and use your Quickerstack too. It's a brilliant creation. It has even easier cardtoposition and positiontocard calculations than the Bart Harding stack.
What I like about the Bart Harding stack isn't just related to the calculations. I do find those calculations relatively easy though. Adding or subtracting 0, 13, 26, and 39 is easy. That's required for most algorithmic stack position calculations. The calculations where 5 is added or subtracted can be treated as single digit calculations that never have any carries or borrows. So those also aren't difficult. Also, because the suits fall in ranges of numbers in the base stack, after the calculations, I find the determining the suit of a card for Bart Harding stack really easy. There's no need to consider any remainders to determine the suit of a card. The Bart Harding stack has the patterns you mentioned, although it is more examinable than many other algorithmic stacks I've seen. That's rarely an issue in performing though. There are other reasons I like the Bart Harding stack. By moving one or two cards, the Bart Harding stack supports a specific routine. It also can be easily shuffled to support two other routines.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
 The character of â€˜Deathâ€™ in the movie "Hogswatch" 
ddyment Inner circle Gibsons, BC, Canada 2523 Posts 
"QuickerStack" and its successor, "QuickStack 3.0", are designed to be tetradistic, thus are not carefully examinable, due to the "banks of thirteen" issue (although they offer shortcut ways around the associated arithmetic). But they enable a whole host of published effects, which is why tetradistic stacks are so popular ("the strongest of all stacks", to quote cardman Alan Ackerman).
On the other hand, an algorithmic stack such as my "Q Stack" (for example) is thoroughly and extensively examinable, has no exceptions to the algorithm, has no "thirteen" issue, no repeated anything, and requires only trivial arithmetic (no multiplication, division, remainders; no addition or subtraction of values greater than three).
The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More :: (order "Calculated Thoughts" from Vanishing Inc.)

Bill Hallahan Inner circle New Hampshire 3230 Posts 
The book Mathematical Stacks has been updated. People who already purchased the book can download the Second Edition.
The only significant change is a rewrite of Chapter 8, which is about the Cherry Stack. The Cherry Stack has not changed. It's the same stack order as before. I noticed something the stack supports, and added that to the book. This is the new description of the stack. Quote:
The Cherry stack is a fulldeck stack with two binary bracelet sequences where itâ€™s very easy to calculate the suit and value of one of six consecutive cards merely by knowing which of the six cards have a suit that is a Heart or a Diamond (HD), or alternatively, knowing which cards are a Club or a Diamond (CD).  Initially, I was surprised by this. After updating the book, I figured out why the second sequence works, although I didn't explain that in the book.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
 The character of â€˜Deathâ€™ in the movie "Hogswatch" 
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