perfect riffle shuffle \n 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." \n charles 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 \n commentary on ect tables, see also new hardcover edition for further commentary \n edward marlo \n the shuffle \n fred black
1958
faro notes Edward Marlo

A Correction

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

perma-stack \n based on elmsley's restacking pack idea \n russell "rusduck" duck \n the restacking pack \n alex elmsley
1958
the cardiste Russell "Rusduck" Duck

on the re-stacking pack \n 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 \n edward marlo \n the restacking pack \n alex 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 \n 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 \n karl 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 \n examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y \n roy walton \n a faro tree \n roy 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 \n a deck is given a known sequence of faro shuffles (e.g. ioiioooioiiooio), problem: how to recycle to get original order with faro shuffling \n karl 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 \n 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 \n edward marlo \n the restacking pack \n alex 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 \n discussing properties of the faro to exchange two cards within the deck and to recycle the order \n karl 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 \n notation to illustrate behavior of cards during faro shuffles, see also addenda on page 60 \n karl 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 \n discussing 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 \n karl 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 \n karl fulves \n the general recycling problem \n karl fulves \n introduction \n karl 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 \n card at chosen number is predicted, using 18-35 faro principle, three methods (duplicate card, equivoque, ..) \n edward marlo
1975
hierophant Edward Marlo

1835 Prediction

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

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

Novel Faro Relationships

introducing mathematical language and some properties

faro shuffle recycling table \n required number of in and out shuffles listed for a deck with two to 52 cards \n murray 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 \n turning one half over before faro shuffling them together and how it affects the recycling properties \n murray 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

the 32-card deck: an analysis \n twenty properties and relationships for a deck with 32 cards, some things also hold for a deck with 2<sup>n</sup> cards \n murray 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 \n 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 \n murray bonfeld \n other forms of the transposition \n karl fulves \n (2) primitive cycles \n karl 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

any card, any number - the first system \n 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 \n murray bonfeld \n beginning again \n william zavis \n binary translocations \n alex 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 \n 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 \n murray bonfeld \n binary translocations \n alex 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

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

More Theorems

relationships when faros are combined with cuts in even deck

the theoretical faro \n definition of io and oi as an entity and properties of io- and oi-sequences
- the conjugate pair faro
- the inverted conjugate pair faro \n karl fulves \n unit shuffles \n murray bonfeld \n unit restorations \n murray 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 \n an idea similar to alex elmsley's restacking concept \n karl fulves \n the restacking pack \n alex elmsley
1979
faro possibilities Karl Fulves

The Null Faro

an idea similar to Alex Elmsley's Restacking concept

faro shuffle machines \n 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 \n karl fulves \n steve shimm \n morray bonfeld's faro program \n murray 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 \n examining the problem of finding an algorithm to find a faro combination to shuffle from position x to position y \n roy walton \n a faro tree \n roy 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

solution to a problem \n how to return to original order if a known sequence of in and out faros was performed \n karl 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 general recycling problem \n how to return to original order if an unknown sequence of in and out faros was performed \n karl fulves \n the recycling problem \n karl fulves \n introduction \n karl 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 \n maintaining sequences that are repeated \n karl fulves \n other forms of the transposition \n karl fulves \n the principle of internal shuffling \n murray bonfeld
1979
faro possibilities Karl Fulves

interrogating the deck \n bringing a card to top with faro shuffles \n karl fulves \n the interrogation technique \n karl fulves
1979
faro possibilities Karl Fulves

morray bonfeld's faro program \n program for programmable calculator to find how many faros are required for recycling the order \n murray bonfeld \n faro shuffle machines \n karl fulves \n steve 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 \n 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" \n karl fulves \n unit transpo \n karl fulves \n shuttle shuffle \n karl fulves \n transpoker ii \n karl fulves \n transpoker iii \n karl 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 \n faro shuffle sequences that mix each half within itself, keeping them separated \n karl fulves \n carbon copy \n karl 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." \n karl 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 \n 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 \n juan 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 \n 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) \n peter 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 \n long article for "mathematicians" with the following subchapters \n alex 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 \n how to find out number of shuffles required to return pack to same order \n alex 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 \n stack whose value distribution is not affected by faro shuffles \n alex elmsley \n faro favorites \n russell "rusduck" duck \n perma-stack \n russell "rusduck" duck \n on the re-stacking pack \n edward marlo \n marlo re-stacking pack \n edward marlo \n the null faro \n karl fulves \n primitive cycles \n karl fulves \n simon-eyes \n simon aronson \n unicycle stack \n iain girdwood \n the permanent deck principle \n woody 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 \n 1) to bring top card to any position with faros
2) to bring card to top with 2^x cards
3) variation of 2) \n alex elmsley \n faro as a control \n edward marlo \n oil always floats \n paul swinford \n any card, any number - the first system \n murray bonfeld \n the core \n pit hartling \n a.c.a.a.n. teórico \n pepe 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 \n bringing center card to position corresponding with number of cards in cut-off pile \n alex elmsley \n principles and routines \n murray bonfeld \n alex elmsley \n reverse penelope \n alex elmsley \n john 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 \n shuffling a card to any position up to twenty with two shuffles, for magicians \n alex 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 \n no perfect faros, but blocks are released (riffle shuffle stacking type) \n t. 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 \n thought card, number corresponding to value is removed from deck and card divined \n césar fernández \n the faro knows \n bob 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 \n position of selection in small packet is predicted, anti faro principle \n gary plants \n richard vollmer \n roberto giobbi \n "a four-tunate choice" (gary plants, genii, sep. 1997)
2012
confidences Gary Plants, Richard Vollmer, Roberto Giobbi

Seven

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

Inspired by

"A Four-tunate Choice" (Gary Plants, Genii, Sep. 1997)

a look inside perfect shuffles \n describes the mathematics of perfect faro shuffles, how to stack the deck using in and out shuffles \n persi diaconis \n ron 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 \n explains how perfect faro shuffles, reverse faro shuffles, monge shuffles, milk shuffles and down-under shuffles are related \n persi diaconis \n ron 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