More or Less Is every card shuffle unique?
45 snips
Sep 5, 2026 
Matt Parker, an Australian mathematician, comedian, author, and creator of Stand-up Maths, brings a deck of cards and some huge calculations. He and Tim Harford explore why shuffled decks are almost certainly unique, how factorials and combinatorics count possible arrangements, and why matching a historical shuffle is effectively impossible. Expect billions, mind-boggling numbers, and wildly improbable experiments.
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Why Random Card Shuffles Are Almost Always Unique
- A 52-card deck has so many possible arrangements that a genuinely random shuffle is effectively unique.
- The claim depends on comparing the shuffled order against every arrangement anyone could have produced.
Factorials Make Small Counting Problems Explode
- Factorials count arrangements by multiplying the choices available at each position.
- Their growth becomes enormous far faster than ordinary exponential-looking estimates suggest.
Thirteen Cards Already Create Six Billion Orders
- Arranging 13 cards requires 13 choices first, then 12, then 11, continuing down to one.
- Multiplying those shrinking options produces 13 factorial, which exceeds six billion.