Probability of Getting a Blackjack
Blackjack is one of the few casino games where the math actually matters. If you understand the odds, you make better decisions, choose better tables, and avoid the traps that quietly raise the house edge. One of the most useful numbers to know is the probability of getting a blackjack (a natural 21 made with your first two cards).
On this page
- What Counts as a Blackjack
- Why the Probability Matters
- What Is the Probability of Getting a Blackjack
- Simple Way to Think About It
- Why 3:2 vs 6:5 Changes Everything
- From natural frequency to the cost of a lower payout
- How Card Counting Changes Blackjack Frequency
- Dealer Blackjacks and Pushes
- Worked example: an average is not a deadline
- Worked example: one known removed card changes the calculation
- How to Use This Information at the Table
- Common Mistakes Players Make
- Bottom Line
- FAQ: Probability of Getting a Blackjack
This matters because a natural blackjack usually pays 3:2, which improves the return compared with a lower natural payout. That premium alone does not make the full game favorable to the player. The more often you get paid 3:2 on naturals, the more your long-term results improve. That is also why table rules and blackjack payouts matter so much.
What Counts as a Blackjack
A blackjack (also called a natural) is a two-card hand made up of:
- An Ace
- Any 10-value card (10, Jack, Queen, or King)
If you draw to 21 in three or more cards, it is still 21, but it is not a blackjack. That hand is paid even money if it wins. The extra payout only applies to a natural.
After splitting, an ace and a ten-value card normally count as 21 rather than a natural with the special payout. Check any variant-specific exceptions.
Why the Probability Matters
The chance of getting a blackjack drives part of your expected return. In a standard game, naturals are what create the “bonus payout” edge for the player side of the game. If a casino changes the payout from 3:2 to 6:5, your blackjacks are worth less, and the house edge jumps.
That is why smart players check payouts before they even sit down. A flashy table with side bets and a low minimum can still be a bad game if the blackjack payout is poor. If you are comparing games, start with payout rules, then move on to deck count and dealer rules. You can use our blackjack house advantage guide for a deeper breakdown.
What Is the Probability of Getting a Blackjack
From a complete standard single deck, before conditioning on any exposed cards, the probability of a natural on the initial two cards is:
64 / 1326 = 4.8265%
That means you will get a blackjack about once every 20.7 hands on average in a single-deck game.
In multi-deck games, the probability is slightly lower. For example:
- Single deck: about 4.83%
- Double deck: about 4.78%
- Six deck: about 4.75%
- Eight deck: about 4.75%
The difference is small, but over thousands of hands it matters. This is one reason players who care about long-term results often prefer stronger single- or double-deck rules when they can find them.
Simple Way to Think About It
There are two ways to make a blackjack:
- You get an Ace first, then a 10-value card
- You get a 10-value card first, then an Ace
In a fresh single deck:
- There are 4 Aces
- There are 16 ten-value cards
- There are 52 total cards
So the math is built from those combinations. You do not need to memorize the full formula to benefit from it, but it helps to understand that blackjack odds are not random guesswork. They come directly from the composition of the deck.
Why 3:2 vs 6:5 Changes Everything
Players sometimes underestimate how much a payout change hurts. A 3:2 payout means a $10 blackjack wins $15. A 6:5 payout means that same hand wins only $12. On paper it looks like a small difference. In real play, it adds up fast because blackjacks show up regularly.
If you are getting a natural around once every 20 to 21 hands, the casino is shaving value from one of the best outcomes in the game. Over a long session, that can wipe out any benefit you thought you had from a lower minimum or a convenient table.
Whenever possible, avoid 6:5 tables. If you want to compare rule quality, our blackjack variations page is a good place to start.
From natural frequency to the cost of a lower payout
The 3:2 premium is paid only when your natural wins. Here is a fresh six-deck calculation under conventional rules where two naturals push, with no side bets, insurance or bonuses. All probabilities are before any cards are known.
- There are 24 aces, 96 ten-value cards and 312 cards. Your natural probability is 2 × 24 × 96 ÷ (312 × 311), approximately 4.74895%.
- Given your natural, 23 aces and 95 ten-value cards remain among 310 cards. The dealer-natural probability is 2 × 23 × 95 ÷ (310 × 309), approximately 4.56206%.
- Your natural wins rather than pushes with probability 4.74895% × (1 − 0.0456206), approximately 4.53230% of initial hands.
Changing a winning natural from 3:2 to 6:5 removes 0.3 initial betting units of profit. Multiplying 0.3 by 0.0453230 gives an expected-return reduction of approximately 1.35969 percentage points. At a fixed 10-unit initial wager, that is about 0.13597 units of additional expected loss per hand under this comparison, not a guaranteed loss on each hand.
Multiplying the payout difference by all naturals would overstate the cost because tied naturals earn neither premium. These figures isolate the payout change, not the game’s complete house edge. Different rules or remaining-card information require a matching calculation. Compare affordable stakes as well as percentages; a better payout does not justify exceeding your budget.
How Card Counting Changes Blackjack Frequency
In a neutral shoe, the probability stays close to the numbers above. But in a card-counting context, the probability of getting a blackjack is not fixed. It changes with deck composition.
Counting observes composition; it does not change the cards. With A aces, T ten-value cards and C total cards remaining, the two-card natural probability without other conditioning information is 2AT ÷ [C(C − 1)]. A positive count is only a summary and does not identify all those quantities. An ace-neutral count especially needs separate ace information; if no aces remain, natural probability is zero even if many tens remain.
This is one of the core ideas behind counting. You are tracking when the remaining cards create better conditions than average. If you are learning that process, practice with a blackjack card counting trainer before trying to apply it in a live game.
Dealer Blackjacks and Pushes
Your blackjack does not automatically win if the dealer also has one. In that case, the hand is a push (tie) and your original bet is returned. That is another reason not to overestimate the value of naturals. They are great, but they are still part of a larger system of probabilities and rules.
Also remember:
- Insurance is a separate side wager and usually a poor bet for non-counters
- A 21 made in more than two cards is not paid as blackjack
- Some variants change payouts or side rules in ways that reduce value
Worked example: an average is not a deadline
Imagine independent rounds that each start from a complete single deck. With p = 64 ÷ 1326, the chance of receiving no natural in 20 rounds is (1 − p)20 ≈ 37.18%. The chance of at least one natural is the complement, about 62.82%. Even after 20 rounds without one, the next independent round still starts with the same 4.8265% probability.
This example assumes a fresh reset each round. It must not be applied unchanged to consecutive rounds from a persistent shoe: removed cards can change the next hand’s probability. In either model, a natural is not owed to you after a certain number of hands. The long-run average of roughly one per 20.7 single-deck hands is not a repayment schedule or a reason to increase your stake.
Worked example: one known removed card changes the calculation
Start with a standard single deck and suppose exactly one removed card is known to be an ace, with no other conditioning information. The remaining pack has A = 3 aces, T = 16 ten-valued cards and C = 51 cards. The next two-card natural probability is 2 × 3 × 16 ÷ (51 × 50), about 3.7647%.
If instead the only known removed card is a ten-value, the calculation is 2 × 4 × 15 ÷ (51 × 50), about 4.7059%. Both are lower than the fresh-pack 4.8265%. Removing an ace and removing a ten do not have identical effects. A dealer peek, exposed upcard or additional known cards can introduce further information; use the appropriate conditional model rather than substituting a vague “high-card-rich” label.
These examples follow the remaining-card formula above. For the fresh-pack deck-count values and their mathematical derivation, see Michael Shackleford’s blackjack probability analysis. The deck-count guide explains the difference between a reset and a continuing shoe.
How to Use This Information at the Table
Knowing the probability of getting a blackjack is useful, but it should lead to practical decisions:
1) Check the payout first
Always verify whether the table pays 3:2 or 6:5. This is one of the quickest ways to avoid a weak game.
2) Learn basic strategy
The probability of naturals helps, but basic strategy is still the foundation. If you want a refresher, start with our how to play blackjack guide and then review basic blackjack strategy.
3) Avoid side bets if you care about long-term results
Many side bets look exciting but come with a much higher house edge than the main blackjack game. If your goal is better expected value, focus on the core hand first. Our blackjack side bets page explains why.
4) Don’t chase blackjacks
Blackjacks happen at a predictable average rate over time, but not on a schedule. You may go many hands without one, then get several close together. Do not raise bets randomly because you “feel one coming.” That is how bankroll discipline breaks down.
Common Mistakes Players Make
- Ignoring the payout: Playing 6:5 because the table looks fun or has a lower minimum.
- Confusing 21 with blackjack: A drawn 21 is not a natural and does not pay extra.
- Using bad table selection: Choosing games with poor rules and heavy side-bet focus.
- Overvaluing streaks: Thinking a table is “cold” or “hot” instead of trusting the math.
Bottom Line
The probability of getting a blackjack is one of the most useful pieces of blackjack math because it directly connects to one important part of the game’s expected return. From a fresh standard pack, natural frequency averages roughly one per 20 to 21 hands; a particular session need not match that rate. That is frequent enough that payout rules matter a lot.
If you remember only one thing, make it this: prefer 3:2 over otherwise comparable 6:5 rules without exceeding an affordable stake. The probability of naturals is built into the game, but how much the casino pays you for them depends on the table you choose.
FAQ: Probability of Getting a Blackjack
What is the average probability of getting a blackjack?
From a complete standard pack without other known cards, your chance of an initial natural is around 4.75% to 4.83%, depending on deck count. Removed-card information and nonstandard variants can change it.
How often do you get a blackjack in blackjack?
On average, about once every 20 to 21 hands.
Does deck count change blackjack probability?
Yes. Single-deck games have a slightly higher blackjack probability than six- or eight-deck games, but the difference is small compared with payout and rule differences.
Does card counting increase your chance of getting a blackjack?
Counting does not change the cards. It can help identify composition changes, but natural probability depends on the remaining aces and ten-value cards, not merely on a positive count.
Why is 3:2 better than 6:5?
Because 6:5 pays less on each qualifying winning natural than 3:2. A natural that pushes against the dealer does not earn either premium. Over time, that increases the house edge by a noticeable amount.
