Exact model
Reproduce one specified deck order
- Probability:
- 1.24 × 10⁻⁶⁶%
- Odds:
- 1 to (8.07 × 10⁶⁷)
- dBan
- −679.1 dBan
Shuffle a 52-card deck well: the order in your hands has very probably never occurred anywhere in human history. On human timescales, seeing that same order recur is similarly remote.
Calculation
p = 1 / 52! ≈ 1.24 × 10⁻⁶⁸
Assumptions
The deck contains 52 distinct cards and no jokers. The earlier order is specified before an independent shuffle, and every permutation is equally likely. The number of distinct deck orders produced across human history is unknown. Conditional on any finite set of N distinct comparison orders fixed as targets, whether earlier or later, the chance of matching one is N / 52!.
Sources
- John Baez: well-shuffled deck permutations published 5 February 2013; checked 27 October 2026