The dealer busts 28.19% of rounds at a six-deck table where the dealer stands on soft 17, and you are dealt a natural blackjack 4.75% of the time, once in about 21 hands. Those two figures are the backbone of blackjack odds. This page lays out all of them, from the dealer’s final total by upcard to how long a losing streak lasts, each computed exactly or simulated from our own engine.
Everything below assumes six decks, double allowed on any two cards, doubling after a split, late surrender and a dealer who peeks for blackjack. Where the dealer hitting soft 17 changes the answer, both versions are shown.
- Rounds in which the dealer busts (6 decks, dealer stands on soft 17)
- 28.19%
- Hands that start with a blackjack (6 decks)
- 1 in 21.06
- Rounds a basic-strategy player loses, against 42.43% won
- 49.08%
- Hands, on average, until the first run of 7 straight losses
- 284
Source: Our study S5, src/data/studies/s5-blackjack-odds.json
The dealer’s bust chance, card by card
The dealer has no choices. The rules force a draw on 16 or less and a stand on 17 or more, so the card showing decides almost everything. A 6 is the weakest card in the game: the dealer busts 42.28% of the time, and a 5 is nearly as bad at 41.84%. A 7 changes the picture completely, because a dealer holding a 7 already has 17 once the hole card is a ten, and busts only 26.19%.
The ace is the strongest upcard by a wide margin. It can count as 11, so the dealer rarely busts (11.55%) and often makes 20 or 21. A ten is next at 21.25%.
Source: Our study S5 (dealer.6d-s17.byUpcard[].bustProbability)
See the numbers as a table
| Dealer busts | |
|---|---|
| 2 | 35.35% |
| 3 | 37.42% |
| 4 | 39.58% |
| 5 | 41.84% |
| 6 | 42.28% |
| 7 | 26.19% |
| 8 | 24.37% |
| 9 | 22.92% |
| 10 | 21.25% |
| Ace | 11.55% |
Averaged over every upcard (a ten shows four times as often as any other value), the dealer busts 28.19% of rounds. If the dealer also hits soft 17 the figure rises slightly to 28.58%. Most of the extra busts come from the ace, which jumps from 11.55% to 13.91%, and the 6, which rises from 42.28% to 43.93%.
| Dealer shows | Stands on soft 17 | Hits soft 17 | After a no-blackjack peek (stands) | Dealer has a natural |
|---|---|---|---|---|
| 2 | 35.67% | 35.35% | 0.00% | |
| 3 | 37.70% | 37.42% | 0.00% | |
| 4 | 39.85% | 39.58% | 0.00% | |
| 5 | 41.96% | 41.84% | 0.00% | |
| 6 | 43.93% | 42.28% | 0.00% | |
| 7 | 26.19% | 26.19% | 0.00% | |
| 8 | 24.37% | 24.37% | 0.00% | |
| 9 | 22.92% | 22.92% | 0.00% | |
| 10 | 21.25% | 23.02% | 7.72% | |
| Ace | 13.91% | 16.70% | 30.87% |
The two rule sets are identical for upcards 7 to 10 and differ only slightly for 2 to 5; the 6 and the ace move most. The after-peek column is what you face when you make a decision, because a dealer natural has already ended the round.
Source: Our study S5 (dealer[*].byUpcard[])
Notice that the 10 and the ace rows change once the dealer has peeked. With a ten showing, the dealer has a natural 7.72% of the time, and when no natural is there the bust chance is 23.02%. With an ace showing, the natural turns up 30.87% of the time, and the surviving hands bust 16.70% of the time. When you are choosing between hitting and standing, those are the numbers that apply. The full strategy chart is built on these after-peek numbers.
What the dealer ends up with
A bust is only one outcome. The other five are the final totals 17 through 21. The chart shows the full spread for each upcard, after a peek has ruled out a natural, so every bar adds up to 100%.
Source: Our study S5 (dealer.6d-s17.byUpcard[].givenNoBlackjack)
See the numbers as a table
| 17 | 18 | 19 | 20 | 21 | Bust | Total | |
|---|---|---|---|---|---|---|---|
| 2 | 14.0% | 13.4% | 13.0% | 12.4% | 11.8% | 35.4% | 100.0% |
| 3 | 13.4% | 13.1% | 12.5% | 12.1% | 11.5% | 37.4% | 100.0% |
| 4 | 13.1% | 12.4% | 12.1% | 11.6% | 11.2% | 39.6% | 100.0% |
| 5 | 12.2% | 12.2% | 11.8% | 11.2% | 10.8% | 41.8% | 100.0% |
| 6 | 16.6% | 10.6% | 10.6% | 10.2% | 9.7% | 42.3% | 100.0% |
| 7 | 36.9% | 13.8% | 7.8% | 7.9% | 7.4% | 26.2% | 100.0% |
| 8 | 12.9% | 36.0% | 12.9% | 6.9% | 7.0% | 24.4% | 100.0% |
| 9 | 12.0% | 11.7% | 35.2% | 12.0% | 6.1% | 22.9% | 100.0% |
| 10 | 12.1% | 12.1% | 12.1% | 36.8% | 3.8% | 23.0% | 100.0% |
| Ace | 18.8% | 18.9% | 18.9% | 18.9% | 7.7% | 16.7% | 100.0% |
Three patterns stand out. A 7, 8 and 9 each produce a spike at the matching total: the dealer finishes on 17 in 36.92% of 7s, on 18 in 36.00% of 8s and on 19 in 35.19% of 9s. A ten finishes on 20 in 34.00% of hands. And a 6 makes 17 in 16.57% of rounds, more than any other low card.
| Dealer shows | 17 | 18 | 19 | 20 | 21 | Bust |
|---|---|---|---|---|---|---|
| 2 | 14.0% | 13.4% | 13.0% | 12.4% | 11.8% | |
| 3 | 13.4% | 13.1% | 12.5% | 12.1% | 11.5% | |
| 4 | 13.1% | 12.4% | 12.1% | 11.6% | 11.2% | |
| 5 | 12.2% | 12.2% | 11.8% | 11.2% | 10.8% | |
| 6 | 16.6% | 10.6% | 10.6% | 10.2% | 9.7% | |
| 7 | 36.9% | 13.8% | 7.8% | 7.9% | 7.4% | |
| 8 | 12.9% | 36.0% | 12.9% | 6.9% | 6.9% | |
| 9 | 12.0% | 11.7% | 35.2% | 12.0% | 6.1% | |
| 10 | 12.1% | 12.1% | 12.1% | 36.8% | 3.8% | |
| Ace | 18.8% | 18.9% | 18.9% | 18.9% | 7.7% |
Source: Our study S5 (dealer.6d-s17.byUpcard[].givenNoBlackjack)
The same hand against different cards
Take a hard 14, a hand that cannot be improved much. If the dealer shows a 6, the dealer busts 42.28% of the time. If the dealer shows a 10, the figure is 21.25% before the peek and 23.02% after it. The cards in your hand are identical, but the dealer is about half as likely to fail, so a sensible player treats the two situations differently. Much of the strategy chart is a response to this one column of the table.
The soft-17 rule changes that column only a little, but it changes it where it hurts. A dealer who hits soft 17 busts more often (13.91% against an ace, not 11.55%), yet also finishes with a better hand more often, which is why the rule costs the player. Under the hit rule the dealer ends on 17 only 5.73% of the time when showing an ace, against 13.00% under the stand rule, so the hand is pushed toward 18, 19 and 20 instead.
Why standing on 12 to 16 wins against a 2 to 6
Those five upcards bust between 35.35% and 42.28% of the time. A hand that cannot beat 17 still wins whenever the dealer busts, so there you let the dealer take the risk. Against a 7 to ace the dealer busts at most 26.19%, and the same stiff hand has much worse prospects.
How often you are dealt a blackjack
A natural needs an ace and a ten-value card in your first two cards. The exact chance is 2 x (4d) x (16d) divided by (52d) x (52d − 1), where d is the number of decks. It is a ratio of counted card pairs, not a simulation.
| Decks | Chance per hand | About once in (hands) |
|---|---|---|
| 1 deck | 4.83% | 20.72 |
| 2 decks | 4.78% | 20.92 |
| 6 decks | 4.75% | 21.06 |
| 8 decks | 4.75% | 21.07 |
Exact combinatorics. The chance falls only slightly as decks are added, by a few hundredths of a point for each extra deck.
Source: Our study S5 (blackjackOdds[])
A single deck gives 4.83% and a six-deck shoe 4.75%, a difference of less than one-tenth of a percentage point. Deck count therefore hardly matters for how often you get a natural. What matters is what the natural pays. For the money impact of 6:5 against 3:2, see where the table edge comes from.
In 100 hands you can expect about 4.75 naturals, but any given hundred varies widely, so a 30-minute stretch with none is ordinary.
What happens in a normal round
Under basic strategy, a round has three outcomes: win, lose, push. We measured them by playing the engine’s own chart for 20,000,000 rounds. A round counts as a win or loss on its net result, so surrendering (−0.5), a lost double, or a split that loses overall count as losses.
| Dealer rule | Win | Loss | Push | Loss, pushes ignored | Longest losing run in 1,000 hands (avg) |
|---|---|---|---|---|---|
| Dealer stands on soft 17 | 42.43% | 8.50% | 53.63% | 9.07 | |
| Dealer hits soft 17 | 42.18% | 8.37% | 53.96% | 9.16 |
Source: Our study S5 (streaks[*].perRound, lossGivenDecided, expectedLongestLosingStreak)
Wizard of Odds publishes a similar split for a six-deck, stand-on-17 game: 42.43% wins, 8.48% pushes and 49.09% losses. Our numbers (42.43%, 8.50%, 49.08%) agree within a hundredth of a point, even though their rules are slightly more liberal (aces may be resplit).
The surprise is that you lose far more rounds than you win. That is normal. A basic-strategy player still gives up only about 0.33% of money wagered at these rules, because a 3:2 blackjack pays more than a normal win, and the hands where you double or split are the ones where you win the most. The question of why the edge is that small, and how rules move it, belongs to the house edge guide. When the dealer hits soft 17, the player wins 42.18% of rounds instead of 42.43% and loses 49.45% instead of 49.08%, and a few plays change, as covered in the chart for tables where the dealer hits soft 17.
Losing streaks: how long, how often
Because 49.08% of rounds are losses, runs of losses are common. We computed the exact chance that the next N hands are all losses, the average wait until the first such run, and the chance of at least one in a session. Pushes break a streak in these figures, which is the strict reading of “N losses in a row”.
| Streak length N | Next N hands all lost | About 1 in | Average hands until the first one | At least one in 100 hands | At least one in 1,000 hands |
|---|---|---|---|---|---|
| 3 | 11.821% | 8.46 | 100.0% | 100.0% | |
| 4 | 5.801% | 17.24 | 96.6% | 100.0% | |
| 5 | 2.847% | 35.12 | 78.3% | 100.0% | |
| 6 | 1.397% | 71.57 | 51.1% | 99.9% | |
| 7 | 0.686% | 145.80 | 28.8% | 97.2% | |
| 8 | 0.337% | 297.10 | 15.1% | 82.2% | |
| 9 | 0.165% | 605.40 | 7.6% | 56.9% | |
| 10 | 0.081% | 1,234.00 | 3.7% | 33.7% | |
| 11 | 0.040% | 2,514.00 | 1.8% | 18.2% | |
| 12 | 0.020% | 5,122.00 | 0.9% | 9.4% |
Exact run-length recurrence on per-round win, loss and push frequencies from 20,000,000 simulated rounds. The 8-hand and 10-hand 1,000-hand figures match 10,000 simulated 1,000-hand sessions.
Source: Our study S5 (streaks.6d-s17.byN[])
Three losses in a row happen once in 8.46 hands. Five happen once in 35.12 hands, and in 100 hands there is a 78.3% chance of at least one such run. A run of 7 losses has a 0.69% chance of starting at any given hand (1 in 145.8), yet the average wait for the first one is 284 hands, about twice 1 in 145.8, because losing runs cluster and one long run contains several overlapping starting points.
Source: Our study S5 (streaks.6d-s17.byN[].probabilityAtLeastOneStreakIn100Hands / In1000Hands)
See the numbers as a table
| Streak length N (hands lost in a row) | In 100 hands | In 1,000 hands |
|---|---|---|
| 3 | 100.0% | 100.0% |
| 4 | 96.6% | 100.0% |
| 5 | 78.3% | 100.0% |
| 6 | 51.1% | 99.9% |
| 7 | 28.8% | 97.2% |
| 8 | 15.1% | 82.2% |
| 9 | 7.6% | 56.9% |
| 10 | 3.7% | 33.7% |
| 11 | 1.8% | 18.2% |
| 12 | 0.9% | 9.4% |
Read down the wait column and you see a pattern: each extra hand in the run roughly doubles the wait. A run of 7 takes 284.41 hands on average, 8 takes 581.54 (2.04 times as long), 9 takes 1,187 and 10 takes 2,420.7. That doubling is the signature of a repeated event with a roughly even-money chance of each loss: the next hand is lost about half the time, so every extra loss halves the odds of the run.
The dealer rule moves these numbers slightly. With the dealer hitting soft 17 the loss rate is a little higher (49.45%), so the first run of 7 arrives sooner, after 271.76 hands. In 1,000 hands the chance of an 8-hand run is 83.9% instead of 82.2%, and the expected longest run is 9.16 instead of 9.07. These are small shifts, but they all point the same way.
Over a 1,000-hand session, which is roughly 14 hours at a typical table pace, the expected longest losing run is 9.07 hands. A run of 8 shows up in 82.2% of such sessions, 10 in 33.7% and 12 in 9.4%. A 100-hand evening has an expected longest run of 5.85. With a 10-hand streak, you need an average of 2,421 hands before the first one appears, so it is rare in any single evening but certain across a long enough series of nights.
Two things are worth keeping in mind:
- Long runs do not mean the next hand is more likely to win. Each round is dealt from a freshly shuffled shoe in this model. The chance of losing the next hand is still 49.08%.
- Pushes matter. If you ignore them, losing 3 decided hands in a row is 15.43% likely instead of 11.82%, and a run of 12 decided losses has a 0.057% chance per start instead of 0.020%.
Seven losses means the table is rigged
Seven straight losses has a 0.69% chance of starting at any hand, and one of them is expected within 284 hands. In a 1,000-hand session the chance of at least one is 97.2%. It is part of ordinary variance, not a sign of anything wrong. If you are tempted to raise stakes to win it back, our test of the doubling system shows why the table limit usually ends that plan.
A typical 100 hands
Put the rates together for one 100-hand stretch, about an hour and a half at 70 hands an hour. You can expect around 42 wins, 49 losses and 8 or 9 pushes. You will be dealt about 4.75 naturals, and the dealer will bust in about 28 of the rounds. The longest losing streak will average 5.85 hands, and 51.1% of such stretches contain a streak of at least 6. These are averages. The spread around them is wide, which is why a bad hour is not evidence of anything.
Insurance: the odds behind the offer
When the dealer shows an ace, you are offered insurance, a side bet that pays 2 to 1 if the hole card is a ten. It is fair only if the hole card is a ten one time in three, a 33.33% chance. The real chance with an ace showing is 30.87%, so the bet costs 7.40% of the insurance stake at six decks, which is −0.073955 per unit insured. The usual stake is half your bet, so each time you take it you give up about 3.7% of your original wager.
An ace is up on 1 hand in 13, which makes insurance common. Over 100 hands, always taking it costs about 0.28 units of your starting bet. “Even money” on a natural is the same bet. Our comparison of every casino bet by cost puts that cost next to other side bets and games.
Using the numbers
Odds like these answer how often, not what to do. Basic strategy is the set of actions that uses the dealer-bust table above. You can check any hand against it with the strategy chart tool, and practise the plays until they are automatic with the trainer.
What we could not verify, and our assumptions
- Independent rounds. Streak figures treat each round as independent. In a real shoe, consecutive hands are very slightly correlated through the cards, which we expect to be small but have not measured.
- Rule set. Everything is for six decks, late surrender, double after split, split to four hands, no resplit of aces and a peeking dealer. Other rules, including a no-hole-card game, change the numbers. We did not compute them.
- Win and loss definition. A round is a loss if its net result is negative, so a lost double, a surrender or a net-losing split count as one loss each. Other definitions, such as counting each split hand, would give different streaks.
- Simulated shares. The 42.43%, 49.08% and 8.50% shares are from a seeded simulation with a standard error well under a tenth of a point, not exact calculations. The pace of 70 hands an hour behind the “14 hours” figure is an assumption, not measured at any table.
- Insurance. The 7.40% cost ignores your own cards. Holding tens makes it slightly worse, holding none slightly better.
- One outside source. Only the Wizard of Odds win, push and loss split was fetched and compared for this page. Dealer bust and natural figures match the same site’s published values through our engine’s tests, but we did not re-fetch those pages.
- Fair shoe. Everything assumes a properly shuffled shoe with no card counting and no continuous shuffler effects.
Rerun it yourself
Run node research/studies/s5-blackjack-odds/run.mjs with plain Node 22. It rewrites the JSON behind every chart and table on this page in about 13 seconds and fails if any validation check does not pass.