Exact model
A natural blackjack from a six-deck shoe
- Probability:
- 4.75%
- Odds:
- 1 to 20
- dBan
- −13 dBan
About one in 21.06 initial two-card deals from a full six-deck casino shoe is a natural blackjack: an ace and a ten, jack, queen, or king, in either order.
Calculation
p = 2 × (24 aces / 312 cards) × (96 ten-valued cards / 311 remaining cards) ≈ 0.047489488
Assumptions
The 312-card shoe contains 24 aces and 96 ten-valued cards and is uniformly shuffled. A natural is the initial two-card hand, so a 21 made after a split is excluded. Receiving a natural does not mean winning against the dealer. Unknown burned or intervening cards do not change this unconditional chance. Known shoe depletion can change it.
Sources
- French casino rules: blackjack Article 55-4, current text checked 26 October 2026