109 entries in Cards / Sleights / Shuffles (non-riffle) / Faro Shuffle / Mathematical Facts & Curiosities
  
Creators Title Comments & References Source Page Categories
Unknown The Eighteenth Card using 18-35-faro-principle with honest shuffle, risky Expert Card Technique 150
Fred Black The Shuffle faro tablesRelated to Expert Card Technique 145
Fred Black The Endless Belts Related to Expert Card Technique 147
Fred Black Chart of Seventeen Related to Expert Card Technique 147
Edward Marlo Half and Half Shuffle basically the stay stack principle applied to two cards The Faro Shuffle 29
Edward Marlo "Half Plus One" bringing a key card next to a certain card with faro shuffle The Faro Shuffle 30
Edward Marlo Observations faro as a false shuffle and other comments The Faro Shuffle 34
Edward Marlo A Correction commentary on ECT tables, see also new hardcover edition for further commentaryInspired by Faro Notes 8
Edward Marlo The Chain Calculator how to calculate position of any card after faro shuffles, memorized deck Faro Notes 12
Russell "Rusduck" Duck Faro Favorites Elmsley's Restacking PackRelated to The Cardiste (Issue 10) 14
Russell "Rusduck" Duck Perma-Stack based on Elmsley's Restacking Pack ideaRelated to The Cardiste (Issue 10) 15
Alex Elmsley In and Out Definition The Faro Shuffle 1
Alex Elmsley In and Out Shuffle Definition Faro Notes 1
Unknown 18-35 Principle Faro Controlled Miracles 19
Edward Marlo On the Re-Stacking Pack two spectators decide for numbers and remember the cards at their number four times with faros in between, each has a four of a kindInspired by Faro Controlled Miracles 18
Karl Fulves Faro-Shuffling Machines examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y, discussed with a 6-card deck Epilogue (Issue 1) 7
Roy Walton A Faro Tree examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position yAlso published here Epilogue (Issue 1) 8
Karl Fulves Q & A a deck is given a known sequence of faro shuffles (e.g. IOIIOOOIOIIOOIO), problem: how to recycle to get original order with faro shuffling Epilogue (Issue 2) 15
Edward Marlo Marlo Re-Stacking Pack two spectators decide for numbers and remember the cards at their number four times with faros in between, each has a four of a kindInspired by Expert Card Mysteries 175
Karl Fulves Faro Transforms discussing properties of the faro to exchange two cards within the deck and to recycle the order Faro & Riffle Technique (Issue Faro Techniques) 2
Karl Fulves Faro Rings notation to illustrate behavior of cards during faro shuffles, see also Addenda on page 60 Faro & Riffle Technique (Issue Faro Techniques) 2
Karl Fulves Position Determination following a card's position during in and out faros Faro & Riffle Technique (Issue Faro Techniques) 3
Karl Fulves The Triple Faro Ring Faro & Riffle Technique (Issue Faro Techniques) 4
Karl Fulves Three Way Transposition note Faro & Riffle Technique (Issue Faro Techniques) 15
Karl Fulves The 3n Deck properties related to the Triple Faro Faro & Riffle Technique (Issue The Triple Faro) 46
Karl Fulves Recycling The 3n Deck with the Triple Faro Faro & Riffle Technique (Issue The Triple Faro) 47
Karl Fulves Inverse Shuffles properties of the Triple Faro Faro & Riffle Technique (Issue The Triple Faro) 47
Karl Fulves General Transform Characteristics discussing how the order is affected through faro shuffling in a 2n deck
1. Reversibility
2. The Recycling Corollary
3. Commutative Property
4. Additive Property
5. Position Equivalency
6. Substitutions
7. Non-Symmetric Transforms
Faro & Riffle Technique (Issue Faro Techniques) 7
Karl Fulves The Fourth-Order Deck discussing transpositions of two cards within the deck Faro & Riffle Technique (Issue Faro Techniques) 12
Karl Fulves Fractional Transforms note Faro & Riffle Technique (Issue Faro Techniques) 15
Karl Fulves The Recycling Problem "The general solution is somewhat more involved and will not be discussed here.", see references for more on thatRelated to Faro & Riffle Technique (Issue Faro Techniques) 16
Karl Fulves Adjacencies problem of bringing two cards at random position together with faro shuffles Faro & Riffle Technique (Issue First Supplement) 53
Edward Marlo 1835 Prediction card at chosen number is predicted, using 18-35 faro principle, three methods (duplicate card, equivoque, ..) Hierophant (Issue 7 Resurrection Issue) 55
Murray Bonfeld Faro Functions further notations and properties Faro Concepts 8
Murray Bonfeld Even Number Of Cards relationships for decks with 2n cards Faro Concepts 8
Murray Bonfeld Faro Shuffle Recycling Table required number of in and out shuffles listed for a deck with 2-52 cards Faro Concepts 10
Murray Bonfeld Up And Down Faro System turning one half over before faro shuffling them together and how it affects the recycling properties Faro Concepts 11
Murray Bonfeld Novel Faro Relationships introducing mathematical language and some properties
- Basic Terminology and Operations
- For A 52 Card Deck Only
- For A 51 Card Deck Only
Faro Concepts 2
Murray Bonfeld Unit Shuffles Related to Faro Concepts 11
Murray Bonfeld Multiples Of Four relationships for decks with 4n cards Faro Concepts 12
Murray Bonfeld Odd Numbers Of Cards relationships for decks with 2n-1 cards Faro Concepts 13
Murray Bonfeld Unit Restorations Related to Faro Concepts 16
Murray Bonfeld The 32-Card Deck: An Analysis twenty properties and relationships for a deck with 32 cards, some things also hold for a deck with 2n cards Faro Concepts 18
Murray Bonfeld The Principle of Internal Shuffling following groups and belts within a 52-card deck and how they behave under variations of in- and out-shuffles
- Controlling 16 Cards Among 52
- Controlling 10 Cards Among 52
- Controlling 8 Cards Among 52
- Inshuffle Groups
- Odd Deck Technique
Related to Faro Concepts 27
Murray Bonfeld More Theorems relationships when faros are combined with cuts in even deck
- Cuts And Faros Combined
- Shuffle Theorems
Faro Concepts 52
Murray Bonfeld Any Card, Any Number - The First System shuffling card from position x to the top in odd deck, modified in-faro for even deck that ignored bottom card, reverse method for Alex Elmsley's Binary Translocation No. 1Inspired byRelated to Faro Concepts 41
Murray Bonfeld Any Card, Any Number - The Second System bringing a card from position x to y with faro shuffling, odd deck, with even deck modified in-faro is required that ignores top card, generalization of Alex Elmsley's Binary TranslocationsRelated to Faro Concepts 42
Murray Bonfeld, Alex Elmsley Principles and Routines applicationsInspired by Faro Concepts 48
Edward Marlo The 49 Control five cards Marlo's Magazine Volume 3 363
Karl Fulves Utter Chaos some properties for decks with and odd number of cards Faro Possibilities 8
Karl Fulves Solution to a Problem how to return to original order if a known sequence of in and out faros was performed Faro Possibilities 19
Karl Fulves (3) The Half Faro faro applied to long-short deck, double faro Faro Possibilities 27
Karl Fulves The Null Anti-Faro Restacking pack concept Faro Possibilities 4
Karl Fulves The Theoretical Faro definition of IO and OI as an entity and properties of IO- and OI-sequences
- The Conjugate Pair Faro
- The Inverted Conjugate Pair Faro
Related to Faro Possibilities 6
Karl Fulves The Null Faro an idea similar to Alex Elmsley's Restacking conceptRelated to Faro Possibilities 8
Karl Fulves, Steve Shimm Faro Shuffle Machines examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y, discussed with a 6-card deckRelated to Faro Possibilities 9
Roy Walton A Faro Tree examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position yAlso published here Faro Possibilities 13
Karl Fulves The Tracking Faro stay stack type principle with two separate odd decks Faro Possibilities 17
Karl Fulves The General Recycling Problem how to return to original order if an unknown sequence of in and out faros was performedRelated to Faro Possibilities 20
Karl Fulves The Missing Link relation of Milk Build Shuffle to faro Faro Possibilities 25
Karl Fulves (2) Primitive Cycles maintaining sequences that are repeatedRelated to Faro Possibilities 27
Karl Fulves (4) Faro/Stebbins bringing a thirteen-cards deck into Si Stebbins order with faros Faro Possibilities 28
Karl Fulves Interrogating the Deck bringing a card to top with faro shufflesRelated to Faro Possibilities 29
Murray Bonfeld Morray Bonfeld's Faro Program program for programmable calculator to find how many faros are required for recycling the orderRelated to Interlocutor (Issue 29) 112
Karl Fulves Fake Shuffles fake faro shuffle and fake false shuffle with gaffed red/blue decks Octet 38
Steve Beam False Faro diagonal pressure and swivel cutRelated to The Trapdoor - Volume One (Issue 4) 59
T. Nelson Downs No Shuffle eight perfect shuffle recycle a deck The Fred Braue Notebooks (Issue 2) 14
Karl Fulves Least Totals six-card deck solution for problem in introduction The Return Trip 2
Karl Fulves Flotation Device another solution for problem in introduction The Return Trip 4
Karl Fulves A Catalog of Shuffles another solution for problem in introduction The Return Trip 6
Karl Fulves The Uniqueness Theory on the uniqueness of the order after a random in/out faro shuffle sequence The Return Trip 9
Karl Fulves Time Bent Back what one knows about the last shuffle of an in/out faro shuffle sequence The Return Trip 13
Karl Fulves Ring Diagrams Related to The Return Trip 5
Karl Fulves Transpoker two poker hands, each Ace through Five in red and black, spectator names one of the values, performer shuffles the hands together and deals, named value is only odd-backed card in both hands, "transposition shuffle"Related toVariations The Return Trip 11
Karl Fulves Separation Shuffles faro shuffle sequences that mix each half within itself, keeping them separatedRelated to The Return Trip 14
Karl Fulves Singleton Shuffles "separation shuffles" that allow one card from both halves to transpose The Return Trip 16
Karl Fulves If Known another solution for problem in introduction if total number of shuffles is known The Return Trip 22
Karl Fulves Shuffle Diagrams Related to The Return Trip 23
Karl Fulves Ring Subset The Return Trip 26
Karl Fulves How Many States? The Return Trip 27
Karl Fulves The Stay Stak Constraint as stay stack features applies to problem in introduction The Return Trip 25
Karl Fulves Basic Shuffle Equations how many shuffles it takes to get a deck back to original order The Return Trip 29
Karl Fulves Position Equations notation for faro shuffling The Return Trip 30
Karl Fulves Mix Relativity faro type from the point of view of the card The Return Trip 31
Karl Fulves Expanded Decks notation for faro shuffling The Return Trip 31
Karl Fulves Not in Descartes futile method of Cartesian notation The Return Trip 32
Karl Fulves Faro Trees "The faro tree gives a clear, unambiguous picture of what happens to the deck as it is shuffled." The Return Trip 33
Juan Tamariz Notes on the Faro and other Shuffles 1. On the supposed difficulty of the Faro
2. On the effects that can be performed with the Faro
3. On other uses
4. On subtleties, variations and new ideas
Sonata 82
Juan Tamariz 1. To correct small errors Sonata 83
Alex Elmsley The Mathematics of the Weave Shuffle long article for "mathematicians" with the following subchapters The Collected Works of Alex Elmsley - Volume 2 302
Alex Elmsley The Odd Pack and Weave The Collected Works of Alex Elmsley - Volume 2 304
Alex Elmsley Equivalent Odd Pack The Collected Works of Alex Elmsley - Volume 2 304
Alex Elmsley Returning a Pack to the Same Order mathematical discussion The Collected Works of Alex Elmsley - Volume 2 305
Alex Elmsley Solving the Shuffle Equation how to find out number of shuffles required to return pack to same order The Collected Works of Alex Elmsley - Volume 2 306
Alex Elmsley Stack Transformations how faro shuffles affect a stack The Collected Works of Alex Elmsley - Volume 2 307
Alex Elmsley The Restacking Pack stack whose value distribution is not affected by faro shufflesRelated toVariations The Collected Works of Alex Elmsley - Volume 2 309
Alex Elmsley Binary Translocations 1) to bring top card to any position with faros
2) to bring card to top with 2^x cards
3) variation of 2)
Related toVariations The Collected Works of Alex Elmsley - Volume 2 311
Alex Elmsley Penelope's Principle bringing center card to position corresponding with number of cards in cut-off pileRelated to The Collected Works of Alex Elmsley - Volume 2 313
Alex Elmsley The Obedient Faro shuffling a card to any position up to twenty with two shuffles, for magicians The Collected Works of Alex Elmsley - Volume 2 346
T. Nelson Downs A Real Dovetail Shuffle observation that 8 perfect (faro) shuffles restore order More Greater Magic 1084
T. Nelson Downs Four Perfect Riffle Shuffles to Restore Full-Deck Order no perfect faros, but blocks are released (riffle shuffle stacking type) More Greater Magic 1085
Unknown The Mathematical Basis of the Perfect Faro Shuffle - Mathematical Principles Card College - Volume 3 692
Pit Hartling Elimination - Faro Ordering removing cards so they can be ordered later with faro shuffles Card Fictions 22
Denis Behr Faro and Anti-Faro Combination Handcrafted Card Magic 50
Unknown 18/35 Principle Related to Dexterity Manual 48
Unknown Calculating Positions after One Faro memorized deck Lessons in Card Mastery 32
Gary Plants, Richard Vollmer, Roberto Giobbi Seven position of selection in small packet is predicted, anti faro principle Confidences 177
Mahdi Gilbert Dueling Pianos Handling for the Piano Card Trick, bringing in a subtlety from Thieves & SheepInspired by
  • "Piano Card Trick" (Uncredited, Stanyon's Magic, Aug. 1902) Add a reference
Related to
Semi-Automatic Card Tricks - Volume 9 194
Pepe Lirrojo A.C.A.A.N. Teórico Inspired by Panpharos 47