Mathematical Stacks
by Bill Hallahan

Bracelet sequences and algorithmic stacks.

Mathematical Stacks contains a collection of various stacks made with 52 standard playing cards. Although some routines and presentations are mentioned, the 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.

The book contains stacks with bracelet sequences and built-in routines. The book includes stacks with binary bracelet sequences, e.g. a red-black suit bracelet sequence, where six consecutive cards identify the cards. Some stacks contain a base-4 bracelet sequence, where the suits of three consecutive cards identify the cards.

There's an old trick where knowing the suits of six consecutive cards allows identifying the first card, and since the cards are in a known order, all the cards are then known. The Cherry Stack provides a new full-deck 52-card method for this that does not require memorizing bracelet codes and has relatively simple calculations to determine the first card.

Some stacks with bracelet sequences can be Faro-shuffled and still have a valid bracelet sequence.

Some of the stacks contain a valid binary bracelet sequence for any two suits that are selected. The "Ultimate Bracelet Stacks" are three stacks that each contain a valid bracelet sequence for any two suits that are selected, and each stack has a bracelet sequence for the even and odd cards. Each of the three stacks has multiple other value sequences.

If the card values from Ace to King are put in a circle, any six or any seven consecutive cards going around the circle can be chosen, and that card group from a value bracelet sequence in at least one of the three Ultimate Bracelet Stacks.

The book also has a comprehensive explanation of how to calculate card-to-position and position-to-card for any Si Stebbins-like stack.

The Bart Harding stack is explained with some Poker deals. And more ...

• Introduction 1
• About Mathematical Stacks
• Bracelet Sequences
  • Binary Bracelet Sequences
  • Base Four Bracelet Sequences
  • Memorized Decks
  • The Cherry Stack and the Red Stack
  • Stacks Created by Other People
• Stack Features
  • Spelling
  • Ten Card Poker Deal
  • Any Hand Called For
• Introduction References
• Introduction References
• 1 Suitcase Stack
  • 1.1 Introduction to the Suitcase Stack
  • 1.2 Suitcase Routines
    • 1.2.1 Suitcase Suitability
    • 1.2.2 Spelling
    • 1.2.3 Ten Card Poker Deal
    • 1.2.4 Any Hand Called For
  • 1.3 History
  • Suitcase Stack References
• 2 Suitcase Faro Stack
  • 2.1 Introduction to the Suitcase Faro Stack
  • 2.2 Suitcase Faro Routines
    • 2.2.1 Suitcase Faro Suitability
    • 2.2.2 Spelling
    • 2.2.3 Ten Card Poker Deal
    • 2.2.4 Any Hand Called For
    • 2.2.5 Creating the Suitcase Faro Stack
  • 2.3 History
  • Suitcase Faro Stack References
• 3 Suit Shuffle Stack
  • 3.1 Introduction to the Suit Shuffle Stack
  • 3.2 Suit Shuffle Routines
    • 3.2.1 Suit Shuffle Suitability
    • 3.2.2 Spelling
    • 3.2.3 A Ten Card Poker Deal
    • 3.2.4 Suit Shuffle Dealing the Aces
  • 3.3 History
  • Suit Shuffle Stack References
• 4 Suit Bracelet Stack
  • 4.1 Suit Bracelet Stack Introduction
  • 4.2 Suit Bracelet Routines
    • 4.2.1 Suit Bracelet Stack Suitability
    • 4.2.2 Spelling
    • 4.2.3 Ten Card Poker Deal
    • 4.2.4 Suit Bracelet Poker Deal
  • 4.3 History
  • Suit Bracelet Stack References
• 5 Bracelet Faro Stack
  • 5.1 Introduction to the Bracelet Faro Stack
  • 5.2 Bracelet Faro Routines
    • 5.2.1 Bracelet Faro Know-The-Cards
    • 5.2.2 Spelling
    • 5.2.3 Ten Card Poker Deal
    • 5.2.4 Any Hand Called For
  • 5.3 History
  • Bracelet Faro Stack References
• 6 Two Suits Suitability Stack
  • 6.1 Introduction to the Two Suits Suitability Stack
  • 6.2 Two Suits Suitability Routines
    • 6.2.1 Two Suits Suitability Stack Suitability
    • 6.2.2 Two Suits Suitability Binary Bracelet Codes
    • 6.2.3 Spelling
    • 6.2.4 Ten Card Poker Deal
    • 6.2.5 The Two Suits Suitability Stack Poker Deal
  • 6.3 History
  • Two Suits Suitability Stack References
• 7 Ultimate Bracelet Stacks
  • 7.1 Introduction to the Ultimate Bracelet Stacks
  • 7.2 Ultimate Bracelet Stacks
    • 7.2.1 Ultimate Bracelet Mind Reading Routine
  • 7.3 History
    • 7.3.1 New Ideas
    • 7.3.2 Finding the Stacks
  • 7.4 Multiple Choice Stacks and Deck Tables
    • 7.4.1 Extra Nine Major Sequence Stack
  • Ultimate Bracelet Stacks References
• 8 Cherry Stack
  • 8.1 Introduction to the Cherry Stack
  • 8.2 Cherry Stack
    • 8.2.1 The Mind Reading Routine
    • 8.2.2 The Mind Reading Method
    • 8.2.3 Variations on the Cherry Stack
  • 8.3 Other Presentation Ideas
  • 8.4 History
  • 8.4.1 How I created this stack
  • Cherry Stack References
• 9 Red Stack
  • 9.1 Introduction to the Red Stack
  • 9.2 Red Stack
    • 9.2.1 The Mind Reading Routine
  • 9.3 History
  • Red Stack References
• 10 Maroon Stack
  • 10.1 Maroon Stack Introduction
  • 10.2 Maroon Stack and Bracelet Sequence Codes
    • 10.2.1 Shuffling the Stack to Create Other Bracelet Sequences
  • 10.3 History
  • Maroon Stack References
• 11 Red-Black Stack Hack
  • 11.1 Red-Black Stack Hack Introduction
  • 11.2 Red-Black Stacks
    • 11.2.1 The Si Stebbins Stack
    • 11.2.2 The Nikola Stack
    • 11.2.3 The McCaffrey Stack
    • 11.2.4 The Joyal Stack
    • 11.2.5 The Bart Harding Stack
    • 11.2.6 The Marlo Stack
    • 11.2.7 The Aronson Stack
    • 11.2.8 The Osterlind Breakthrough Card System
    • 11.2.9 The Mnemonica Stack
    • 11.2.10 QuickerStack
    • 11.2.11 The Redford Stack
    • 11.2.12 Easy Stack
    • 11.2.13New Deck Order
  • 11.3 History
  • Red-Black Stack Hack References
• 12 The Si Stebbins Stack
  • 12.1 Introduction to The Si Stebbins Stack
    • 12.1.1 Terms
    • 12.1.2 Si Stebbins Stack Parameters
  • 12.2 The Si Stebbins Stack
    • 12.2.1 Stack Calculations Tips
    • 12.2.2 Si Stebbins Position-To-Card
    • 12.2.3 Si Stebbins Card-To-Position
    • 12.2.4 Si Stebbins Example Calculations
  • 12.3 History
  • The Si Stebbins Stack References
• 13 The Bart Harding Stack
  • 13.1 Introduction to the Bart Harding Stack
  • 13.2 The Bart Harding Stack
    • 13.2.1 Bart Harding Base Stack Card-To-Position
    • 13.2.2 Bart Harding Base Stack Position-To-Card
    • 13.2.3 Bart Harding Stack Card-To-Position
    • 13.2.4 Bart Harding Stack Position-To-Card
    • 13.2.5 Spelling
    • 13.2.6 Bart Harding Poker Deals
  • 13.3 History
  • The Bart Harding Stack References
• 14 Easy Stack
  • 14.1 Introduction to the Easy Stack
    • 14.1.1 Terms
  • 14.2 Easy Stack
    • 14.2.1 Easy Stack Calculations
    • 14.2.2 Easy Stack Position-To-Card
    • 14.2.3 Easy Stack Card-To-Position
    • 14.2.4 Easy Stack Position-To-Card Examples
    • 14.2.5 Easy Stack Card-To-Position Examples
    • 14.2.6 Finding the Aces
    • 14.2.7 Easy Stack Poker Deals
  • 14.3 History
  • Easy Stack References
• 15 Creating Stacks With Bracelet Sequences
  • 15.1 Introduction to Creating Stacks With Bracelet Sequences
  • 15.2 Creating the Ultimate Bracelet Stacks
    • 15.2.1 High-Level Description for the Ultimate Bracelet Stacks
    • 15.2.2 Generating Bracelet Sequences
    • 15.2.3 The Sequence Generators
    • 15.2.4 Suit Sequences
    • 15.2.5 Value Sequences
    • 15.2.6 Displaying the Sequences
  • 15.3 Card Stack Generation
    • 15.3.1 More Ways to Generate Card Stacks
    • 15.3.2 Other Possible Initial Value Sequences
    • 15.3.3 Mistakes and Possible Mistakes I Made
    • 15.3.4 Summary for Creating the Ultimate Bracelet Stacks
    • 15.3.5 Additional Stacks
• Index

1st edition 2024, PDF 173 pages.
word count: 39146 which is equivalent to 156 standard pages of text