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« I never drink water because of the disgusting things that fish do in it »
W. C. Fields
Faro

What's This Page All About?

You'll find here tools about the mathematics of the Faro shuffle. This page is dedicated to Alex Elmsley, Ed Marlo, Karl Fulves, Murray Bonfeld, Persi Diaconis, Paul Swinford and Brent Morris.

Tool 1: Recycling Table

This table sums up how many Faro shuffles of the same type are needed to recycle a deck, that is, to get it back to its original order. For instance, for a deck made of 32 cards, 5 Out-Faros shuffles are required, or 10 In-Faros.

Type of sort
 


Tool 2: Recycling Tables (Detail)

This tool breaks down the cycle of Faro shuffles of the same type needed to recycle a deck. The table shows the indexes of the cards positions.

Faro
Cards
 


Tool 3: Transformations (Indexes)

This tool allows to apply a series of transformations to a deck. Fill in the matrix with the transformations required (using the O, I or R buttons) and display the table.

- O will apply an Out-Faro.

- I will apply an In-Faro.

- R will reverse the deck.

Only 12 transformations are allowed!

Matrix
Cards
 


Tool 4: Transformations (Specific Decks)

Same tool than above, but using specific decks.

- USPCC1: Current US Playing Cards Company order. That is: Ace to King of , Ace to King of , King to Ace of , King to Ace of .

- USPCC2: Former US Playing Cards Company order. That is: Ace to King of , Ace to King of , Ace to King of , Ace to King of .

- STEBB1: As published by Si Stebbins in "Card Tricks And The Way They Are Performed" (around 1913).

Matrix
Deck
 


Tool 5: Transformations (Custom Deck)

< Work in progress... >

Tool 6: Rings/Chains

This tool breaks down the cycle of Faro shuffles of the same type into positionning rings and chains (also named endless belts).

Faro
Cards
 

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