Exact model

Reproduce one specified 32-card belote order

Probability:
3.8 × 10⁻³⁴%
Odds:
1 to (2.63 × 10³⁵)
dBan
−354.2 dBan

Lay a belote pack in one particular order, gather it, and shuffle well. Landing back on that exact arrangement is still staggeringly unlikely, even with only 32 cards.

Calculation

p = 1 / 32! ≈ 3.80 × 10⁻³⁶

Assumptions

The pack contains 32 distinct cards: ranks 7 through ace in each of four suits. The target order is specified before an independent uniform shuffle. For any finite set of N distinct orders fixed in advance, the chance of matching one is N / 32!.

Sources

  1. French Belote Federation: belote rules 32-card pack composition checked 27 October 2026
  2. John Baez: well-shuffled deck permutations published 5 February 2013; checked 27 October 2026