Exact model

Reproduce one specified 78-card tarot order

Probability:
8.83 × 10⁻¹¹⁴%
Odds:
1 to (1.13 × 10¹¹⁵)
dBan
−1150.5 dBan

Shuffle a full French tarot pack well and its 78-card order enters a space vastly larger than the 52-card deck’s. Returning to one order chosen in advance is an almost inconceivably rare coincidence.

Calculation

p = 1 / 78! ≈ 8.83 × 10⁻¹¹⁶

Assumptions

The pack contains 78 distinct cards: 56 suited cards, 21 trumps, and the Excuse. 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 / 78!.

Sources

  1. French Tarot Federation: official tarot rules 78-card pack composition checked 27 October 2026
  2. John Baez: well-shuffled deck permutations published 5 February 2013; checked 27 October 2026