Blackjack Odds Calculator
How to use: Blackjack next-hit bust odds
This blackjack tool estimates your chance of busting on the next hit from your current hand total, whether the total is soft because an Ace counts as 11, and the dealer’s exposed card. It also supplies a deliberately simplified hit/stand prompt.
Limitations and assumptions: Blackjack deck model
- Infinite-deck model: every blackjack draw uses standard single-deck proportions (52-card ratios), even after cards have been seen.
- Card values: 2–9 retain face value; 10/J/Q/K count as 10; an Ace may count as 1 or 11.
- Scope: the player result is next-hit bust risk only; it does not evaluate splits, doubles, surrender, or card removal.
Formula for blackjack next-hit bust probability
For each possible next blackjack card value v, the calculator adds it to your hand total, initially valuing a new Ace at 11, then lowers the total by 10 for each usable soft Ace needed to avoid a bust. The next-hit bust probability is:
where is the number of next cards that would bust you and is the number of cards in the ratio model (52).
Worked example: hard 16 next-hit bust odds
With a hard 16, a next card valued 6 through 10 takes the hand over 21. The 6, 7, 8, and 9 contribute four cards each, while the ten-valued cards contribute sixteen, for 32 busting cards out of 52, or about 61.5 %.
An Ace does not bust hard 16: it can count as 1, producing 17 rather than 27. Treating the four Aces as busts would incorrectly produce 36 of 52, or 69.2 %; that is the correct next-hit bust percentage for hard 17.
How the blackjack suggestion is chosen
The blackjack prompt follows a narrow rule: when your bust chance exceeds 50% and the dealer shows a weak 2–6, it leans toward Stand. It also leans toward Stand on a hard 17 or higher; otherwise it leans toward Hit. It is not a replacement for a complete basic-strategy chart.
Introduction: Reading blackjack bust probabilities
This blackjack odds calculator focuses on the immediate consequence of taking one more card: whether that card makes the player total exceed 21. That question is useful whenever a hand feels stiff, but it is only one part of a blackjack decision. Enter the current total, mark a hand as soft when an Ace is presently worth 11, and select the dealer upcard to see the player’s next-hit risk alongside the dealer’s modeled bust chance. The result is an explanation of card risk, not a promise that a particular hand will win.
Blackjack bust math begins with the values available in a standard deck. Cards 2 through 9 have their printed values, while 10, jack, queen, and king all have value 10. The Ace is the exception: it can be 1 or 11. A hand is soft when one Ace is currently being counted as 11. If a later draw would push a soft hand above 21, that Ace can become 1, reducing the total by 10. This calculator applies that adjustment for the player and also while tracing dealer hands.
For quick blackjack estimates, the calculator uses an infinite-deck assumption. Each draw therefore has the same proportions as a fresh deck: four cards each for values 1 through 9 and sixteen cards worth 10. A hard 16 illustrates the count: values 6, 7, 8, 9, and 10 bust it, while an Ace remains safe because it may be valued at 1.
The blackjack table below lists next-hit bust probabilities for common hard totals under those fixed card proportions. The dealer upcard does not alter these player percentages; it affects the dealer comparison and the simple prompt only.
| Player Total | Bust Probability on Hit |
|---|---|
| 11 or less | 0 % (no single card can bust you) |
| 12 | 30.8 % (16 of 52) |
| 13 | 38.5 % (20 of 52) |
| 14 | 46.2 % (24 of 52) |
| 15 | 53.8 % (28 of 52) |
| 16 | 61.5 % (32 of 52) |
| 17 | 69.2 % (36 of 52) |
| 18 | 76.9 % (40 of 52) |
| 19 | 84.6 % (44 of 52) |
| 20 | 92.3 % (48 of 52) |
These blackjack percentages show how rapidly a hit becomes riskier as a hard total rises. At 12, most card values remain safe on one draw. At 18, only cards valued at 3 or less avoid a bust, so the safe portion of the deck is much smaller. Soft totals work differently because a usable Ace can absorb ten points of a draw before the hand actually busts.
The dealer’s upcard adds context to the player’s next-hit percentage. Dealers must follow a fixed drawing rule in this model: draw below 17 and stand at 17 or above. A dealer 2 through 6 can be vulnerable because repeated required draws may create a hard total that must still take another card. Higher upcards, particularly 10 and Ace, more readily lead to a made dealer total. The displayed hit-or-stand prompt distills this contrast, rather than calculating the full expected value of every blackjack action.
This blackjack calculator remains an educational infinite-deck model. Real tables may use several decks, different shuffle timing, and rules affecting dealer soft 17, doubling, splitting, and surrender. Cards already dealt also change the remaining composition of a real shoe. Those details matter for exact strategy and card-counting analysis, but they are intentionally outside this next-card calculation.
When you are ready to examine related casino math, compare rule changes with the blackjack EV ruleset composition calculator, study long-run bankroll swings through the gambler's ruin probability tool, and cross-check house edges with the roulette odds calculator to keep casino games in perspective.
What a blackjack dealer upcard reveals
This blackjack page calculates dealer bust probability from the selected upcard as well as player next-hit risk. The dealer follows a fixed policy—draw below 17, then stand—so the infinite-deck outcome can be found recursively from the same card proportions. The model produces dealer bust rates of about 35 % for a 2, roughly 42 % for a 6, about 26 % for a 7, and about 21 % for a 10.
An Ace is the dealer’s strongest upcard in this model, with a bust probability near 11.5 %. Sixteen of 52 cards are ten-valued, so the dealer immediately makes 21 whenever one follows the Ace. Other first draws make a soft total, and the Ace can switch to 1 before the dealer busts. A hard dealer total must develop before busting can occur, which explains the much lower Ace bar.
Correct soft-Ace handling is essential to these blackjack dealer figures. The recursion counts usable Aces instead of storing only a yes-or-no soft status, so a hand with more than one Ace can demote them one at a time when needed. This is also why the dealer calculation differs from a simplistic rule that treats every Ace as permanently worth 11.
Blackjack bust odds are only half of a decision
A blackjack next-hit bust percentage alone does not decide whether to hit. Standing cannot bust immediately, yet a player who stands on a stiff total against a strong dealer upcard may still lose frequently when the dealer completes a standing hand. For example, basic strategy can call for hitting 16 against dealer 10 despite its 61.5 % next-card bust chance, because the alternative can be worse overall.
The blackjack chart displays this distinction directly. Your next-hit bust chance appears as a dashed horizontal line because it depends on your hand rather than the dealer’s exposed card. Dealer bust chances appear as bars for all upcards, with the chosen one highlighted. Comparing the line and bars can show why a weak dealer card and a risky player hit often point in different directions than a strong dealer card and the same player total.
Sources. The blackjack percentages displayed here are computed from the stated infinite-deck model, allowing the card-ratio calculations to be reproduced from the explanation above.
- Rules of play, the dealer's fixed drawing policy and hand values: Bicycle Cards, How to Play Blackjack.
- Probability of a compound event and the recursive expectation used for the dealer outcome: OpenStax, Introductory Statistics 2e, Probability Topics.
- If gambling has stopped being entertainment, free confidential help is available: National Council on Problem Gambling, help and treatment.
Questions about blackjack bust probabilities
Does an Ace ever bust my hand?
Never on its own. An Ace can count as 1 or 11, so it can be treated as 1; adding 1 to a total of 20 or less cannot exceed 21. For a hard 16, counting the four Aces as busting cards would incorrectly raise the count from 32 to 36 cards. Thirty-six of 52 is instead the next-hit bust figure for a hard 17.
Why is the dealer bust probability lowest against an Ace?
An Ace upcard frequently becomes an immediate 21 when the dealer draws one of the sixteen ten-valued cards. Any other first draw leaves a soft dealer total, which can reduce an Ace from 11 to 1 rather than busting. The dealer must first reach a hard total before a bust is possible, so the infinite-deck model gives an Ace a much lower bust rate than a 5 or 6.
Why do dealer 5 and 6 upcards get called bust cards?
With a 5 or 6, the dealer must draw and cannot make 17 with one card. Subsequent low cards commonly leave a hard total in the teens that still requires another draw. Under this calculator's infinite-deck, stand-on-17 model, those upcards have bust rates above 41 %, compared with about 21 % for a 10.
What is the infinite-deck assumption and how much does it matter?
It treats each draw as if the standard card proportions are restored: four cards of every non-ten rank and sixteen ten-valued cards out of 52. Actual decks and shoes lose cards as they are dealt, so this calculator does not model card removal, running counts, or deck penetration.
Is the hit or stand hint the same as basic strategy?
No. The displayed hint is a deliberately simple rule using your next-hit bust chance, a weak dealer upcard, and hard totals of 17 or more. Full basic strategy compares expected values for every player hand and dealer upcard and depends on options such as doubling, splitting, surrender, and table rules.
Does a lower bust probability mean I should hit?
Not by itself. Standing has no immediate bust risk, but a stiff hand against a strong dealer upcard can still lose often when the dealer makes a standing total. The calculator's bust percentage describes only the next card; choosing the best action overall requires comparing complete player and dealer outcomes.
| Your bust probability on the next card | — |
|---|---|
| Cards that would bust you | — |
| Safe cards that would not | — |
| Dealer bust probability with this upcard | — |
| Chance the dealer makes a standing hand | — |
| Suggestion | — |
Arcade Mini-Game: Blackjack Odds Calculator Calibration Run
Use this quick arcade run to practice separating useful scenario inputs from common planning mistakes before you rely on the calculator output.
Start the game, then use your pointer or arrow keys to catch useful inputs and avoid bad assumptions.