perfect riffle shuffle\nwithout details, four shuffles for sixteen cards to recycle, "mr. downs, however, can handle a full pack of 52 cards withthe degree of dexterity necessary to restore its original order."\ncharles t. jordan
1919/1920
thirty card mysteries Charles T. Jordan

Perfect Riffle Shuffle

without details, four shuffles for sixteen cards to recycle, "Mr. Downs, however, can handle a full pack of 52 cards withthe degree of dexterity necessary to restore its original order."

a correction\ncommentary on ect tables, see also new hardcover edition for further commentary\nedward marlo\nthe shuffle\nfred black
1958
faro notes Edward Marlo

A Correction

commentary on ECT tables, see also new hardcover edition for further commentary

on the re-stacking pack\ntwo spectators decide for numbers and remember the cards at their number four times with faros in between, each has a four of a kind\nedward marlo\nthe restacking pack\nalex elmsley
1964
faro controlled miracles 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 kind

faro-shuffling machines\nexamining 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\nkarl fulves
1967
epilogue 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

a faro tree\nexamining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y\nroy walton\na faro tree\nroy walton
1967
epilogue Roy Walton

A Faro Tree

examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y

q & a\na deck is given a known sequence of faro shuffles (e.g. ioiioooioiiooio), problem: how to recycle to get original order with faro shuffling\nkarl fulves
1968
epilogue 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

marlo re-stacking pack\ntwo spectators decide for numbers and remember the cards at their number four times with faros in between, each has a four of a kind\nedward marlo\nthe restacking pack\nalex elmsley
1969
expert card mysteries 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 kind

faro transforms\ndiscussing properties of the faro to exchange two cards within the deck and to recycle the order\nkarl fulves
1969
faro & riffle technique Karl Fulves

Faro Transforms

discussing properties of the faro to exchange two cards within the deck and to recycle the order

faro rings\nnotation to illustrate behavior of cards during faro shuffles, see also addenda on page 60\nkarl fulves
1969
faro & riffle technique Karl Fulves

Faro Rings

notation to illustrate behavior of cards during faro shuffles, see also Addenda on page 60

general transform characteristics\ndiscussing how the order is affected through faro shuffling in a 2<sup>n</sup> deck
1. reversibility
2. the recycling corollary
3. commutative property
4. additive property
5. position equivalency
6. substitutions
7. non-symmetric transforms\nkarl fulves
1969
faro & riffle technique Karl Fulves

General Transform Characteristics

discussing how the order is affected through faro shuffling in a 2^{n} deck
1. Reversibility
2. The Recycling Corollary
3. Commutative Property
4. Additive Property
5. Position Equivalency
6. Substitutions
7. Non-Symmetric Transforms

the recycling problem\n"the general solution is somewhat more involved and will not be discussed here.", see references for more on that\nkarl fulves\nthe general recycling problem\nkarl fulves\nintroduction\nkarl fulves
1969
faro & riffle technique Karl Fulves

The Recycling Problem

"The general solution is somewhat more involved and will not be discussed here.", see references for more on that

1835 prediction\ncard at chosen number is predicted, using 18-35 faro principle, three methods (duplicate card, equivoque, ..)\nedward marlo
1975
hierophant Edward Marlo

1835 Prediction

card at chosen number is predicted, using 18-35 faro principle, three methods (duplicate card, equivoque, ..)

faro shuffle recycling table\nrequired number of in and out shuffles listed for a deck with two to 52 cards\nmurray bonfeld
1977
faro concepts Murray Bonfeld

Faro Shuffle Recycling Table

required number of in and out shuffles listed for a deck with two to 52 cards

up and down faro system\nturning one half over before faro shuffling them together and how it affects the recycling properties\nmurray bonfeld
1977
faro concepts Murray Bonfeld

Up And Down Faro System

turning one half over before faro shuffling them together and how it affects the recycling properties

novel faro relationships\nintroducing mathematical language and some properties
- basic terminology and operations
- for a 52 card deck only
- for a 51 card deck only\nmurray bonfeld
1977
faro concepts Murray Bonfeld

Novel Faro Relationships

introducing mathematical language and some properties

the 32-card deck: an analysis\ntwenty properties and relationships for a deck with 32 cards, some things also hold for a deck with 2<sup>n</sup> cards\nmurray bonfeld
1977
faro concepts 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 2^{n} cards

the principle of internal shuffling\nfollowing 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\nmurray bonfeld\nother forms of the transposition\nkarl fulves\n(2) primitive cycles\nkarl fulves
1977
faro concepts 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

more theorems\nrelationships when faros are combined with cuts in even deck
- cuts and faros combined
- shuffle theorems\nmurray bonfeld
1977
faro concepts Murray Bonfeld

More Theorems

relationships when faros are combined with cuts in even deck

any card, any number - the first system\nshuffling 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. 1\nmurray bonfeld\nbeginning again\nwilliam zavis\nbinary translocations\nalex elmsley
1977
faro concepts 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. 1

any card, any number - the second system\nbringing 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 translocations\nmurray bonfeld\nbinary translocations\nalex elmsley
1977
faro concepts 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 Translocations

solution to a problem\nhow to return to original order if a known sequence of in and out faros was performed\nkarl fulves
1979
faro possibilities Karl Fulves

Solution to a Problem

how to return to original order if a known sequence of in and out faros was performed

the theoretical faro\ndefinition of io and oi as an entity and properties of io- and oi-sequences
- the conjugate pair faro
- the inverted conjugate pair faro\nkarl fulves\nunit shuffles\nmurray bonfeld\nunit restorations\nmurray bonfeld
1979
faro possibilities Karl Fulves

The Theoretical Faro

definition of IO and OI as an entity and properties of IO- and OI-sequences

the null faro\nan idea similar to alex elmsley's restacking concept\nkarl fulves\nthe restacking pack\nalex elmsley
1979
faro possibilities Karl Fulves

The Null Faro

an idea similar to Alex Elmsley's Restacking concept

faro shuffle machines\nexamining 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\nkarl fulves\nsteve shimm\nmorray bonfeld's faro program\nmurray bonfeld
1979
faro possibilities 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 deck

a faro tree\nexamining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y\nroy walton\na faro tree\nroy walton
1979
faro possibilities Roy Walton

A Faro Tree

examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y

the general recycling problem\nhow to return to original order if an unknown sequence of in and out faros was performed\nkarl fulves\nthe recycling problem\nkarl fulves\nintroduction\nkarl fulves
1979
faro possibilities Karl Fulves

The General Recycling Problem

how to return to original order if an unknown sequence of in and out faros was performed

(2) primitive cycles\nmaintaining sequences that are repeated\nkarl fulves\nother forms of the transposition\nkarl fulves\nthe principle of internal shuffling\nmurray bonfeld
1979
faro possibilities Karl Fulves

interrogating the deck\nbringing a card to top with faro shuffles\nkarl fulves\nthe interrogation technique\nkarl fulves
1979
faro possibilities Karl Fulves

morray bonfeld's faro program\nprogram for programmable calculator to find how many faros are required for recycling the order\nmurray bonfeld\nfaro shuffle machines\nkarl fulves\nsteve shimm
1979
interlocutor Murray Bonfeld

Morray Bonfeld's Faro Program

program for programmable calculator to find how many faros are required for recycling the order

transpoker\ntwo 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"\nkarl fulves\nunit transpo\nkarl fulves\nshuttle shuffle\nkarl fulves\ntranspoker ii\nkarl fulves\ntranspoker iii\nkarl fulves
1986
the return trip 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"

separation shuffles\nfaro shuffle sequences that mix each half within itself, keeping them separated\nkarl fulves\ncarbon copy\nkarl fulves
1986
the return trip Karl Fulves

Separation Shuffles

faro shuffle sequences that mix each half within itself, keeping them separated

faro trees\n"the faro tree gives a clear, unambiguous picture of what happens to the deck as it is shuffled."\nkarl fulves
1986
the return trip Karl Fulves

Faro Trees

"The faro tree gives a clear, unambiguous picture of what happens to the deck as it is shuffled."

notes on the faro and other shuffles\n1. 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\njuan tamariz
1989/91
sonata 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

a far out faro chart for faro fantasizers\ntable in which can be seen which cards transpose in a single faro shuffle with packets from eight to fifty-two cards (like 18 <-> 35 in a full deck)\npeter duffie\n"countdown to purgatory" (rod ethtie, al smith's abacus, vol. 1 no. 11)
1993
card selection Peter Duffie

A Far Out Faro Chart For Faro Fantasizers

table in which can be seen which cards transpose in a single faro shuffle with packets from eight to fifty-two cards (like 18 <-> 35 in a full deck)

Inspired by

"Countdown to Purgatory" (Rod Ethtie, Al Smith's Abacus, Vol. 1 No. 11)

the mathematics of the weave shuffle\nlong article for "mathematicians" with the following subchapters\nalex elmsley
1994
the collected works of alex elmsley — volume 2 Alex Elmsley

The Mathematics of the Weave Shuffle

long article for "mathematicians" with the following subchapters

solving the shuffle equation\nhow to find out number of shuffles required to return pack to same order\nalex elmsley
1994
the collected works of alex elmsley — volume 2 Alex Elmsley

Solving the Shuffle Equation

how to find out number of shuffles required to return pack to same order

the restacking pack\nstack whose value distribution is not affected by faro shuffles\nalex elmsley\nfaro favorites\nrussell "rusduck" duck\nperma-stack\nrussell "rusduck" duck\non the re-stacking pack\nedward marlo\nmarlo re-stacking pack\nedward marlo\nthe null faro\nkarl fulves\nprimitive cycles\nkarl fulves\nsimon-eyes\nsimon aronson\nunicycle stack\niain girdwood\nthe permanent deck principle\nwoody aragon
1994
the collected works of alex elmsley — volume 2 Alex Elmsley

The Restacking Pack

stack whose value distribution is not affected by faro shuffles

binary translocations\n1) to bring top card to any position with faros
2) to bring card to top with 2^x cards
3) variation of 2)\nalex elmsley\nfaro as a control\nedward marlo\noil always floats\npaul swinford\nany card, any number - the first system\nmurray bonfeld\nthe core\npit hartling\na.c.a.a.n. teórico\npepe lirrojo
1994
the collected works of alex elmsley — volume 2 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)

penelope's principle\nbringing center card to position corresponding with number of cards in cut-off pile\nalex elmsley\nprinciples and routines\nmurray bonfeld\nalex elmsley\nreverse penelope\nalex elmsley\njohn born
1994
the collected works of alex elmsley — volume 2 Alex Elmsley

Penelope's Principle

bringing center card to position corresponding with number of cards in cut-off pile

the obedient faro\nshuffling a card to any position up to twenty with two shuffles, for magicians\nalex elmsley
1994
the collected works of alex elmsley — volume 2 Alex Elmsley

The Obedient Faro

shuffling a card to any position up to twenty with two shuffles, for magicians

four perfect riffle shuffles to restore full-deck order\nno perfect faros, but blocks are released (riffle shuffle stacking type)\nt. nelson downs
1994
more greater magic T. Nelson Downs

Four Perfect Riffle Shuffles to Restore Full-Deck Order

no perfect faros, but blocks are released (riffle shuffle stacking type)

lightning divination\nthought card, number corresponding to value is removed from deck and card divined\ncésar fernández \nthe faro knows\nbob king
2004
semi-automatic card tricks — volume 5 César Fernández

Lightning Divination

thought card, number corresponding to value is removed from deck and card divined

seven\nposition of selection in small packet is predicted, anti faro principle\ngary plants\nrichard vollmer\nroberto giobbi
2012
confidences Gary Plants, Richard Vollmer, Roberto Giobbi

Seven

position of selection in small packet is predicted, anti faro principle

a look inside perfect shuffles\ndescribes the mathematics of perfect faro shuffles, how to stack the deck using in and out shuffles\npersi diaconis\nron graham
2012
magical mathematics Persi Diaconis, Ron Graham

A Look Inside Perfect Shuffles

Describes the mathematics of perfect faro shuffles, how to stack the deck using in and out shuffles

all the shuffles are related\nexplains how perfect faro shuffles, reverse faro shuffles, monge shuffles, milk shuffles and down-under shuffles are related\npersi diaconis\nron graham
2012
magical mathematics Persi Diaconis, Ron Graham

All the Shuffles Are Related

Explains how perfect faro shuffles, reverse faro shuffles, Monge shuffles, milk shuffles and down-under shuffles are related

dueling pianos\nhandling for the piano card trick, bringing in a subtlety from thieves & sheep\nmahdi gilbert\n"piano card trick" (uncredited, stanyon's magic, aug. 1902) add a reference\nthieves and sheep\nlillian bobo
2015
semi-automatic card tricks — volume 9 Mahdi Gilbert

Dueling Pianos

Handling for the Piano Card Trick, bringing in a subtlety from Thieves & Sheep

Inspired by

"Piano Card Trick" (Uncredited, Stanyon's Magic, Aug. 1902) Add a reference