The Blackjack Probability Calculator computes the statistical probability of busting from any hand total and the dealer's bust probability from each upcard. Transforms blackjack from intuition-based play into quantitative risk assessment with exact percentages for every hand situation.
53.85
%
46.15
%
24
cards
47.5
%
-1.3
pp
53.85
%
46.15
%
24
cards
47.5
%
-1.3
pp
Every blackjack decision is a probability problem: if I hit, what is my chance of busting? If the dealer shows a 6, how likely are they to bust? If I stand on 15, what is the probability the dealer makes 16, 17, 18, 19, 20, 21, or busts? The blackjack probability calculator answers all these questions quantitatively for any specific hand situation, transforming the gut-feel decisions most players make into precise expected value calculations.
The probability of busting if you take one more card, from an infinite deck approximation:
Note: these are exact only for an infinite deck. In a 6-deck shoe, the probabilities vary slightly based on cards already dealt. Use this online calculator to compute exact probabilities for your specific situation. The blackjack odds calculator converts these probabilities into optimal strategic decisions.
The dealer's probability of busting (reaching 22+) based on visible upcard (6-deck, S17 rules):
This is why basic strategy says to stand on 12–16 vs. dealer 2–6 (let the dealer bust) but hit vs. dealer 7+ (dealer is unlikely to bust, so you must improve your hand). The probability simulators provide broader statistical analysis tools.
The probability of being dealt a natural blackjack (ace + 10-value card) from a freshly shuffled 6-deck shoe:
P(blackjack) = 2 × P(ace) × P(10-value | ace) = 2 × (24/312) × (96/311) ≈ 4.75%
The factor of 2 accounts for the ace or 10-value card being either the first or second card dealt. With a fresh shoe, you can expect a blackjack approximately once every 21 hands — which is why "21" is the game's name. In a continuous shuffle machine (CSM), the probability is constant; in a dealt shoe, it varies based on remaining composition.
When the dealer shows an ace, the player is offered insurance (a side bet paying 2:1 that the dealer has blackjack). The breakeven probability of dealer blackjack: 1/(1+2) = 1/3 = 33.3%. Actual probability: in a 6-deck shoe with no knowledge of other cards, P(dealer 10 in hole) = 96/311 ≈ 30.9% — below the 33.3% breakeven. Insurance has a house edge of approximately 7.5% and is never the correct play for a basic strategy player. Exception: card counters with a true count above approximately +3 (deck very rich in tens) may take insurance profitably. For everyone else: always decline insurance — it is one of the worst bets in the casino.
Bust Probability shows your chance of going over 21 if you hit. Safe Hit Probability is the complement (chance of staying at 21 or below). Cards That Bust shows the minimum card value that would bust you (e.g., 7 means any card valued 7-10/A would bust). Approx Win % (if Stand) estimates your winning chance if you keep your current total. Dealer Bust Probability shows how likely the dealer is to bust based on their upcard.
Basic strategy recommends hitting when bust probability is acceptably low and the dealer has a strong upcard (7-A), and standing when the dealer has a weak upcard (2-6) and is likely to bust.
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Results
With a hand of 15 against dealer's 7, hitting has a 58.5% bust chance. However, standing gives only ~30% win probability since dealer 7 has a low bust rate. Basic strategy says hit here despite the high bust risk.
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Results
With hand 12 against dealer's 5, only 10-value cards bust you (30.8%). The dealer showing 5 has a 42.9% bust probability. Basic strategy says stand here because the dealer is likely to bust.
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