Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
5 hours ago
- #cutoff phenomenon
- #mathematical proof
- #card shuffling
- Mathematicians proved that seven perfect riffle shuffles can randomize a deck of cards, revealing a cutoff phenomenon where order suddenly breaks down after the seventh shuffle.
- The original proof required strict constraints, such as cutting the deck evenly and interleaving cards one by one, limiting its applicability to realistic shuffling.
- Three mathematicians, Mark Sellke, Jialu Shi, and Jiamin Wang, extended the result to sloppy shuffles where cuts are uneven, proving a cutoff phenomenon still exists.
- They introduced a barcode system to track cards through shuffles, using cold spots (regions resisting mixing) to simplify proving that order disappears exponentially.
- For a 52-card deck with random cuts each shuffle, about 14 shuffles are needed for full randomization, though the model still assumes single-card interleaving, not clumps.