Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

Mathematicians have extended a decades-old proof about card shuffling to show that a "cutoff phenomenon" occurs even with imprecise riffle shuffles, not just the perfectly executed ones required by the original 1992 proof. The new work by Mark Sellke and colleagues demonstrates that a deck of cards transitions suddenly from ordered to randomized states regardless of how evenly you cut the deck, updating a finding that previously only worked with magician-level precision. This breakthrough is significant because cutoff phenomena appear across many complex systems in physics and other fields, making the insight broadly relevant beyond card games.