Questions for you:
- When I accomplish something, do I appreciate its uniqueness even if it seems mundane or unremarkable?
- How often do I dismiss experiences as “ordinary” when they’re actually statistically singular?
- Do I conflate “unique” with “valuable” – can I recognise that something unprecedented might still be unremarkable?
Organisational applications:
- Project post-mortems: Stop trying to extract “repeatable lessons” from one-off projects. The specific team, market conditions, and timing that produced your success are 52-factorial-level unlikely to recur. Document what happened, but don’t pretend it’s a playbook.
- Hiring: Each team configuration is unique. Stop searching for “culture fit” based on past successful hires – those specific combinations won’t repeat. Focus on current gaps rather than historical patterns.
- Innovation theatre: Firms that try to recreate Bell Labs or Pixar’s “creative environment” are missing the point. Those outcomes emerged from unrepeatable combinations of people, problems, and timing. Build for your actual circumstances.
Further reading
On factorials and combinatorics:
Enumerative Combinatorics, Volume 1 by Richard P. Stanley (Cambridge University Press, 1997). Academic but foundational text on counting permutations and combinations. Explains the mathematics behind factorial growth and why these numbers become so large.
The Art of Mathematics: Coffee Time in Memphis by Béla Bollobás (Cambridge University Press, 2006). More accessible treatment of combinatorial problems, including card arrangements and permutations, aimed at general mathematical audiences.
On card shuffling specifically:
The Mathematics of Shuffling Cards by Persi Diaconis, R.L. Graham and William Kantor (Advances in Applied Mathematics, 1983). The seminal academic paper on riffle shuffles, showing that seven shuffles are needed to properly randomise a deck.
Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks by Persi Diaconis and Ron Graham (Princeton University Press, 2011). Stanford mathematician and professional magician explores the mathematics of card tricks, including detailed analysis of shuffling and permutations.
Persi Diaconis. One of the leading experts in the mathematics of card shuffling, Persi Diaconis has a fascinating backstory: a professional magician, a gambler, and then a Harvard Math Graduate who consulted for casinos to identify problems with their card-shuffling machines.
https://statistics.stanford.edu/people/persi-diaconis
How many times must you shuffle a deck of cards? Brad Mann’s paper gets deep into the mathematical detail of how much shuffling is enough (spoiler alert: seven riffle shuffles).
There are a surprisingly large number of ways of shuffling a deck of cards.
https://en.wikipedia.org/wiki/Shuffling
On understanding enormous numbers:
The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck by David Spiegelhalter (Profile Books, 2024). It’s from this book that we learned the facts about card deck shuffling. Explores how to think about randomness, probability and enormous numbers in everyday life. Particularly strong on making incomprehensible scales comprehensible.
The Art of Statistics: Learning from Data by David Spiegelhalter (Pelican, 2019). Cambridge statistician makes probability and large numbers comprehensible for general readers. Particularly strong on helping readers grasp what astronomical odds actually mean in practice.
The Art of the Infinite: The Pleasures of Mathematics by Robert Kaplan and Ellen Kaplan (Oxford University Press, 2003). Makes very large numbers comprehensible through clear explanations and engaging examples. Includes factorial growth.
How Much Is a Million? by Seth Fishman (Greenwillow Books, 2019). Although aimed at younger readers, provides excellent visual comparisons for understanding scale – useful for grasping how incomprehensibly large 52! actually is.
On probability and uniqueness:
The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day by David J. Hand (Macmillian, 2025). Explains why truly unique events are simultaneously inevitable and invisible – relevant to understanding why every shuffle creates uniqueness yet feels mundane.
Struck by Lightning: The Curious World of Probabilities by Jeffrey S. Rosenthal (HarperCollins, 2005). Accessible explanations of probability including discussion of rare events and what “astronomical odds” actually means in practice.
Broader context:
The Universe in a Nutshell by Stephen Hawking (Bantam, 2001). For context on comparisons like “more arrangements than atoms on Earth” – provides scale of the observable universe.
Interactive exhibit
Permutations are pretty mind-boggling. Play around with them here.
About the image
The original version was a fairly dull stock image of a hand holding a fan of cards in front of a satellite view of the Earth. This reworking was a “five in the morning” moment of inspiration: I laid out some cards from a pack on my dining table and took a photo. I then used a world map to cut out the image in Photoshop.
Photo montage and photo by Matt Ballantine, 2026
Random the Book 