Casino
Blackjack Probability Calculator
Calculate natural blackjack probability and one-hit bust probability from a supplied remaining shoe, with soft and hard hand handling.
Your result
4.7489488%
Natural probability for a new two-card draw
- Cards remaining
- 312
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Rank counts are user supplied. For hit probabilities remove all visible cards from the shoe first.
Probability of a natural blackjack
If N cards remain, A are aces and T are ten-value cards, a newly drawn two-card natural has probability 2AT / [N(N−1)]. For an untouched six-deck shoe this is 4608/97032, about 4.74895%. Known removed cards change the result.
Enter the remaining rank counts exactly. The natural calculation applies to a new two-card draw from that shoe. For a current hand’s one-hit bust chance, enter its ranks and use counts after removing all visible cards, including that hand and the dealer upcard.
Hard and soft hands on one additional card
Aces count as 11 when the hand can stay at 21 or below, otherwise as 1. A hard 16 busts on ten-valued cards or 6 through 9. A soft hand can convert an ace to 1, so a single hit on an ordinary soft total at or below 21 does not bust.
The calculator weighs each rank by its remaining count. It does not choose a move, simulate a full round, include splits or forecast the next dealt card. Use blackjack payout arithmetic to settle a natural or ordinary win.