Blackjack Odds Calculator
Calculate exact conditional probabilities of player busting on the next card, dealer outcome distributions (17–21 & bust), and card draw frequencies based on dealer upcard, rules, deck count, and shoe composition.
Last updated: October 8, 2026
Method: Finite-Shoe Recursive Dynamic Programming
Game & Shoe Configuration
Click to add card to player hand:
Specify additional cards removed from the shoe (exposed in other players' hands or previous rounds).
Hand Total: 16 (Hard)
Odds: ~1 in 1.61 draws
Cards 2 through 5 will not bust.
Dealer Outcome Distribution (Showing 6)
| Outcome | Probability | Fraction / Odds |
|---|
Next Card Value Probabilities (Current Shoe) 309 Cards Left
| Upcard | S17 Bust % | H17 Bust % | Bust Diff | S17 21 % | H17 21 % |
|---|
Critical Mathematical Distinction: Probability vs Strategy
This calculator measures conditional probabilities based on current shoe composition and game rules. It does not claim to predict individual game outcomes or provide guaranteed winning predictions.
The chance that drawing exactly one additional card causes the player total to exceed 21. For example, a player holding 16 has a 62.08% chance of busting on the next hit in a fresh 6-deck shoe.
The probability of winning, losing, or pushing the entire hand after player decisions (standing, hitting, doubling, splitting) and dealer draw procedures are completed.
How the Blackjack Odds Calculator Works
Blackjack is a game of dependent trials when played from a finite shoe. Unlike roulette or craps—where every spin or die roll is completely independent—every card dealt in blackjack alters the remaining shoe composition and adjusts the conditional probabilities of all subsequent draws.
Constructs the exact frequency vector of all remaining cards ($A, 2, 3, \dots, 10, J, Q, K$) after subtracting selected player cards, dealer upcard, and known removed cards.
Evaluates the exact count of remaining cards in the remaining shoe that would cause the hard player total to exceed 21: $P(\text{Bust}) = \frac{\text{Busting Cards Remaining}}{\text{Total Cards Remaining}}$.
Uses recursive dynamic programming across dealer hand states (accounting for Soft 17 and finite shoe removal) to calculate exact probabilities for dealer 17, 18, 19, 20, 21, and bust.
Player Bust Probability by Hand Total
The table below provides reference next-card bust probabilities for common hard player totals in a standard fresh six-deck shoe ($312$ cards total).
| Player Hard Total | Cards That Cause Bust | Bust Probability (6 Decks) | Safe Cards Remaining |
|---|---|---|---|
| 11 or lower | None | 0.00% | 100.00% (All cards safe) |
| 12 | 10, J, Q, K (10-value cards) | 31.10% | 68.90% (Cards A, 2–9) |
| 13 | 9, 10, J, Q, K | 38.80% | 61.20% (Cards A, 2–8) |
| 14 | 8, 9, 10, J, Q, K | 46.50% | 53.50% (Cards A, 2–7) |
| 15 | 7, 8, 9, 10, J, Q, K | 54.20% | 45.80% (Cards A, 2–6) |
| 16 | 6, 7, 8, 9, 10, J, Q, K | 61.90% | 38.10% (Cards A, 2–5) |
| 17 | 5, 6, 7, 8, 9, 10, J, Q, K | 69.60% | 30.40% (Cards A, 2–4) |
| 18 | 4, 5, 6, 7, 8, 9, 10, J, Q, K | 77.30% | 22.70% (Cards A, 2, 3) |
*Assumes standard 6-deck shoe before card removal adjustments. Soft totals (containing a flexible Ace counting as 11) cannot bust on a single additional draw.
Blackjack Dealer Bust Odds by Upcard
The dealer's final hand distribution is strictly constrained by mandatory drawing rules. Unlike the player, the dealer has no free choice: they must draw until reaching at least 17 (and hit soft 17 under H17 rules).
Published Dealer Outcome Distribution Matrix (6-Deck S17)
| Dealer Upcard | 17 % | 18 % | 19 % | 20 % | 21 % | Bust % |
|---|---|---|---|---|---|---|
| 2 | 13.98% | 13.29% | 13.04% | 12.58% | 11.84% | 35.28% |
| 3 | 13.50% | 13.06% | 12.50% | 12.33% | 11.45% | 37.16% |
| 4 | 13.05% | 12.59% | 12.19% | 11.59% | 10.82% | 39.76% |
| 5 | 12.22% | 12.23% | 11.73% | 10.83% | 10.15% | 42.84% |
| 6 (Weakest Upcard) | 16.54% | 10.63% | 10.61% | 10.16% | 9.77% | 42.29% |
| 7 | 36.86% | 13.78% | 13.77% | 13.37% | 7.82% | 25.99% |
| 8 | 12.86% | 35.91% | 12.86% | 12.86% | 6.71% | 23.80% |
| 9 | 12.00% | 12.00% | 35.05% | 12.00% | 5.61% | 23.34% |
| 10 / Face | 11.31% | 11.31% | 11.31% | 34.36% | 3.43% | 21.28% |
| Ace | 13.08% | 13.08% | 13.08% | 13.08% | 36.14% | 11.54% |
H17 vs S17 Rule Impact
When the dealer is forced to hit Soft 17 (H17), their outcome distribution changes subtly. H17 gives the dealer an additional chance to improve hands that start as Soft 17, slightly increasing the house edge by roughly 0.20%.
- S17 (Stands Soft 17): Dealer stops immediately on $A+6$. Dealer bust rate showing 6 is ~42.29%.
- H17 (Hits Soft 17): Dealer draws on $A+6$. Increases dealer bust probability to ~43.84% on upcard 6, but increases the overall proportion of strong final totals (18–21).
How Deck Count Changes Odds
Single-deck games have different exact conditional draw odds than 6-deck or 8-deck shoes. In single-deck, drawing a 10-value card removes $1/16$ of all 10s from the shoe, creating a stronger immediate effect on future draws.
- Natural Blackjack Probability (Fresh Shoe): Single Deck = 4.83%, 6-Deck = 4.75%, 8-Deck = 4.74%.
- Finite vs Infinite Model: Infinite deck assumes card probability remains fixed at $30.77\%$ for 10s ($16/52$), regardless of cards dealt.
Understanding Probability vs House Edge & Strategy
Probability
The likelihood that a specific single event or hand total occurs (e.g., $62.08\%$ chance of busting on 16).
Expected Value (EV)
The probability-weighted average monetary return of a specific strategy decision (Hit, Stand, Double, Split).
House Edge
The theoretical casino advantage over repeated wagering under optimal basic strategy (~$0.50\%$ in standard 6-deck 3:2 games).
A player holding 16 against a dealer 10 has a high bust probability ($62.08\%$) when hitting. Standing results in 0% bust probability, but loses to the dealer $76.8\%$ of the time. Basic strategy compares expected values: hitting loses less money per dollar wagered than standing in the long run.
Frequently Asked Questions
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How Adzvelo Calculates & Validates Blackjack Odds
Transparent methodology, assumptions and reference standards for this engine.
Mathematical Engine & Validation
- Finite Shoe Combinatorics: Calculates card draw probabilities dynamically based on remaining cards ($4N$ for non-10s, $16N$ for 10-value cards).
- Recursive Dealer State DP: Computes dealer final hand distributions by traversing all valid drawing branches to depth $\ge 17$.
- Validation: Cross-checked against published probability distributions by Wizard of Odds and verified to sum to exactly $100.00\%$.
Reference Sources
Disclaimer: Blackjack probabilities are model-dependent mathematical calculations based on selected rules, deck configuration, known cards, and theoretical draw distributions. They describe mathematical probabilities, not guaranteed outcomes. Actual casino play may differ due to shuffle procedures, penetration, and table rules.
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