Blackjack Probability and Odds: The Key Numbers
Basic strategy is derived from probability tables. Understanding the core numbers — dealer bust frequencies, player bust risks, blackjack likelihood — makes the strategy chart intuitive rather than arbitrary.
21simulator.com runs exact rule-set simulations so you can confirm theoretical odds against real distributions.
Dealer Bust Probability by Upcard
The dealer's upcard is the most important piece of information available to you. It determines when to stand on stiff hands, when to double aggressively, and when to split pairs. Dealer bust probabilities are why basic strategy says to stand on hard 12 vs a 4 — the dealer busts 40.3% of the time. Against a 7, they bust only 26.2%.
| Dealer Upcard | Dealer Busts | Reaches 17+ |
|---|---|---|
| 2 | 35.3% | 64.7% |
| 3 | 37.6% | 62.4% |
| 4 | 40.3% | 59.7% |
| 5 | 42.9% | 57.1% |
| 6 | 42.1% | 57.9% |
| 7 | 26.2% | 73.8% |
| 8 | 24.4% | 75.6% |
| 9 | 23.0% | 77.0% |
| 10 / face | 21.4% | 78.6% |
| Ace (S17) | 11.7% | 88.3% |
| Ace (H17) | 20.2% | 79.8% |
The dealer's "bust zone" — upcards 2 through 6 — is where basic strategy becomes most aggressive. You stand on stiff totals because the dealer will bust more than a third of the time. Against 7–Ace, the dealer completes their hand most of the time, making standing on stiff totals a losing play.
Note the Ace: in S17 games, the dealer stands on soft 17 and busts only 11.7% of the time — the lowest bust rate of any upcard. In H17 games, the dealer hits soft 17 and busts 20.2% of the time, making the Ace upcard significantly stronger for the player when the game uses H17.
Player Bust Probability When Hitting
The player's bust risk when taking a card increases dramatically as the hand total rises. This is the data behind the intuition to "not risk busting" — the question is whether that risk is outweighed by the dealer's position.
| Player Total (Hard) | Bust Probability on Next Card |
|---|---|
| 11 or less | 0% |
| 12 | 31% |
| 13 | 38% |
| 14 | 46% |
| 15 | 54% |
| 16 | 62% |
| 17 | 69% |
| 18 | 77% |
| 19 | 85% |
| 20 | 92% |
Hard 16 busts 62% of the time when hit. This is why the "don't bust" instinct kicks in — but the comparison to dealer bust probability matters. Against a dealer 10, the dealer reaches 17+ about 78.6% of the time. Standing on hard 16 vs a 10 costs −0.54 EV; hitting costs roughly the same or marginally better. The bust rate on the hit is high, but standing is not safe.
Hard 12 — the lowest "stiff" total — busts only 31% of the time on a hit. Against a dealer 2 or 3 (bust probability 35–37%), hitting hard 12 is correct: the dealer busts about as often as the player will, but the player also has the chance to improve their hand by hitting.
Probability of Being Dealt a Blackjack
A blackjack (natural) requires an Ace and a ten-value card as the first two cards. In a 6-deck game:
- There are 24 Aces and 96 ten-value cards in 312 total cards.
- P(Ace first, then ten) = (24/312) × (96/311) ≈ 2.37%
- P(ten first, then Ace) = (96/312) × (24/311) ≈ 2.37%
- Total P(blackjack) ≈ 4.75% — roughly once every 21 hands.
Both player and dealer receive blackjacks at the same frequency. When both have blackjack, the hand pushes. The net effect of blackjacks on EV: the player receives 1.5× on their naturals, while the dealer wins only even money from the player's perspective — a net advantage to the player that contributes about +2.3% to player EV.
Expected Value of Common Decisions
EV is expressed as units won or lost per unit bet. A positive EV means the player expects to gain; negative means they expect to lose.
- Hard 11 vs dealer 6 (double): EV ≈ +0.55 — one of the highest-value plays in the game.
- Hard 20 vs dealer 6 (stand): EV ≈ +0.70 — nearly certain to win.
- Hard 16 vs dealer 10 (hit): EV ≈ −0.54 — best of bad options.
- Hard 16 vs dealer 10 (stand): EV ≈ −0.54 — roughly the same.
- Hard 16 vs dealer 10 (surrender): EV = −0.50 — correct when available.
- Insurance vs dealer Ace: EV ≈ −0.074 per unit wagered — always incorrect in basic strategy.
How Deck Count Affects Probabilities
More decks make individual card composition more stable — the removal of one card has less impact on the remaining composition. This affects:
- Blackjack frequency: Barely changes — in single-deck vs 6-deck, blackjack probability differs by ~0.05%.
- Natural advantage from composition: Single-deck is more volatile in short run; a removed Ace meaningfully changes the remaining distribution. In 6-deck, removing one Ace barely shifts probabilities.
- Counting effectiveness: Lower deck counts make counting more powerful — each card removed has more impact on true count.
The simulation engine at 21simulator.com lets you run exact hand distributions under any deck count and rule set, so you can verify how the probabilities in this guide apply to your specific game.