This document provides an overview of randomization techniques for shuffling cards and discusses proper vs improper shuffling. It defines relative and absolute randomization and discusses how different shuffling techniques like riffling and piling affect the randomness of a deck. It also outlines signs that may indicate a player is not shuffling properly like orientation of the deck or eyes of the shuffler. Guidelines are provided for when and how to investigate potential improper shuffling or cheating during shuffling.

1. Shuffling
THE SUBTLETIES OF RANDOMIZATION

2. Small group session outline
• Quick overview of randomization techniques, and what it means for the state of the deck.
• Defining terms ‘Relative vs Absolute’ randomization.
• Effects of GSR (Riffle, Weave) shuffle on an ordered deck.
• Uncommon ‘Red Flag’ shuffling techniques.
• Investigations and Remedies.
• Demonstration of deceptive shuffling techniques.
• Discussion encouraged!

3. Discussion Goals
Equip judges with knowledge of shuffling techniques for:
• Teaching players new shuffling techniques who may be putting themselves at a disadvantage.
• Spotting and handling potential dishonest play.
• Curiosity
Additionally, group discussion about experiences with the subject, or subject content.
Shared learning is best learning.

4. Randomization techniques
RIFFLE, GSR
Pros:
Pseudo-Random fashion keeps relative order of cards difficult to keep track of
Fast technique, easy to repeat.
Cons:
Relative sequences of cards are kept intact, with each shuffle only providing one
break.
Bottom and Top cards in the deck typically experience very little variance, which
players can utilize to stack their presented decks.
PILE, WEAVE
Pros:
Allows a player to count their deck before presenting to opponent
Relative sequences are kept intact with an ordered pile shuffle, but introduces (n)
breaks per pile shuffle, where (n) is the number of piles.
Unordered pile shuffles potentially introduce greater variance.
Cons:
Slow technique, may be abused to run out the clock.
Player retains direct manipulation over each card, which players can utilize to stack
their presented decks.

5. Relative vs. Absolute
A standard singleton deck has 60! combinations. (Approximately the number of
atoms in the observable universe.) Even accounting for repetition, most standard
decks have at least 1049 permutations.
A random deck as most players define it is a deck where the order and positioning of
cards within the deck is not known. This is defined as ‘Relative’ randomization.
Standard shuffling by honest players will achieve this.
(Note: This level of randomization is sufficient for tournament play per the IPG
guidelines)
A truly random deck is a deck where each of the 1049 permutations is equally likely to
occur. Standard shuffling by players is likely insufficient to be close to this, although
with repeated shuffles, you can get sufficiently close.
It is possible for a player to achieve relative randomization, but put themselves at a
disadvantage by having a deck that maintains overall sequences.

6. Rule of 7 Cliffnotes
Persi Diaconis and Dave Bayer published “Trailing the Dovetail Shuffle to its Lair” in 1992, where he explores the variation distance between a known and random deck after (n)
riffle shuffles.
For a casino deck of 52 cards, Diaconis observes, using the Gilbert-Shannon-Reeds model of riffle shuffling, a sharp approach to total variation after the 7th shuffle.
Furthermore, he remarks that 3/2log2n shuffles are needed to mix (n) cards. For a 52 card deck, this equates to 8.55 shuffles. A 60 card deck would result in a value of 8.86.
Empirical Excel shuffling results suggest similar opening hands of land to non-land ratio between absolute-randomized decks, and sorted decks after 7 GSR riffle shuffles.
In 2004, Anke van Zuylen and Frans Schalekamp published “The Achilles Heel of the GSR-Shuffle”, where they evaluate the degree of randomness after (n) shuffles.
A game of ‘New Age Solitaire’, a perfectly played game using an absolute randomized deck has a 50% chance of winning. However, a sorted deck given 7 GSR riffle shuffles will
win 81% of the time. This is due to the nature of a GSR-riffle shuffle in such that it preserves relative sequences of cards, which is essential to winning that version of solitaire.
http://statweb.stanford.edu/~cgates/PERSI/papers/bayer92.pdf
http://arvanzuijlen.people.wm.edu/NewAgeS.pdf

7. Normal Riffle
Deck is cradled in one hand.
Shuffling hand obscures bottom card.
Deck is positioned perpendicularly to eyes.

8. Dishonest Riffle (The Humphries shuffle)
Hands are positioned in a fashion to obscure
the deck from the opponents eyes.
Thumb is resting on bottom card of the deck.
Bottom of the deck is not held.
Deck is positioned such that bottom card is
easily revealed.
Topmost cards are kept constant.

9. Improper Shuffling vs. Cheating
As per the IPG (9/26/2014), section 3.4 –
Improper Shuffling
A deck is not shuffled if the judge believes a
player could know the position or distribution
of one or more cards in his or her deck.
Infraction – Warning
Remedy – Shuffle the deck thoroughly, taking
into account any parts of the deck ordered
through gameplay.
Examples when to use Improper Shuffling:
A player forgets to shuffle his library after
searching for a card.
A player searches for a card, then gives the
deck a single riffle-shuffle before presenting
the deck to her opponent.
A player fails to shuffle the portion of his deck
revealed during the resolution of a cascade
ability.

10. When to investigate?
When shuffling the deck of an opponent, there are unfortunately many methods of sleight of
hand. However, they all share one thing in common: The dishonest shuffler must know the
location of certain cards since the deck is foreign to them, and so they must look.
The two best indications that further investigation needs to take place are:
• The orientation of the deck
• The shuffler’s eyes

11. How to investigate?
For Cheating to be applicable, three criteria must be met:
• A player must break a rule
• A player must be attempting to gain an advantage by breaking the rule
• A player must be aware that what they are doing is illegal
Don’t alert the table until the shuffle is complete, and the decks are presented back to their
owners, much like a deck check, then interrupt. You can even interrupt the match under the
pretext of a deck check.
Gather the deck and investigate the stacked cards.
If, based on your observations, you believe a player has committed a cheating infraction, get the
head judge involved!