Blackjack Odds Calculator
The Bust Risk Curve Is Steeper Than It Feels
A hand totaling 12 busts on roughly 3 cards in 10; a hand totaling 16 busts on more than 6 in 10. That jump from a 30% risk to a 62% risk across just four points of hand total is why the decision to hit or stand at 16 is one of the most-discussed lines in basic strategy. This calculator computes the exact bust probability for any hand total against a full, freshly shuffled deck's rank composition.
The Formula
The deck composition used is a standard 52-card set: ranks 2 through 9 at 4 cards each, 16 ten-value cards (10, J, Q, K), and 4 aces counted as 1 (since an ace never causes a bust when counted low).
Bust Probability by Hand Total
| Hand total | Bust probability |
|---|---|
| 12 | 30.77% |
| 13 | 38.46% |
| 14 | 46.15% |
| 15 | 53.85% |
| 16 | 61.54% |
| 17 | 69.23% |
| 18 | 76.92% |
| 19 | 84.62% |
| 20 | 92.31% |
| 21 | 100.00% |
This figure assumes a single freshly-shuffled deck composition and does not account for cards already seen in play — card counting adjusts this estimate based on which cards have already been dealt.
Where This Applies
- Understanding basic strategy charts — the hit/stand thresholds in published basic strategy tables are built directly from bust probabilities like these, combined with the dealer's up-card.
- Comparing hand totals objectively — seeing the exact probability rather than a rough intuition of "16 is risky."
- Studying probability and combinatorics — a concrete, real-world application of counting favorable outcomes over a fixed sample space.
How to Use This Calculator
- Enter Current Hand Total (2–21).
- Select Calculate to see the probability of busting on the next card drawn.
Related Calculations
Work out the house edge behind any wager with the House Edge Calculator, or track a Hi-Lo count with the Blackjack Card Counting Calculator.