Starting Hand Odds
How often you are dealt blackjack, a pair, a stiff hand or a doubling hand, counted exactly for 1, 2, 6 and 8 decks.
Every hand of blackjack starts with two cards, and the odds of each kind of starting hand can be counted exactly. Unlike most of the figures on this site, these are calculated for real decks, card by card without replacement, so you can see what the number of decks in the shoe actually changes.
Starting hand odds by number of decks
| Shoe | Blackjack | How often | Pair (same rank) | Hard 12 to 16 | Hard 11 | Hard 10 |
|---|---|---|---|---|---|---|
| 1 deck | 4.83% | 1 in 20.7 | 5.88% | 38.8% | 4.83% | 4.07% |
| 2 decks | 4.78% | 1 in 20.9 | 6.80% | 38.6% | 4.78% | 4.11% |
| 6 decks | 4.75% | 1 in 21.1 | 7.40% | 38.5% | 4.75% | 4.13% |
| 8 decks | 4.75% | 1 in 21.1 | 7.47% | 38.5% | 4.75% | 4.13% |
How often you are dealt blackjack
A blackjack needs an ace and one of the sixteen ten-value cards in each deck. In a single deck that happens 4.83% of the time, about once every 21 hands. In a six deck shoe it is 4.75%, about once every 21 hands.
The single deck figure is higher because once you hold an ace, the remaining deck is slightly richer in tens than a big shoe is. It is a small difference, but it is one of the reasons single deck games are worth more to the player, and one of the reasons casinos that deal them often pay 6 to 5 on blackjack to take the value back. See house edge by rules for what that payout costs.
Pairs
You will be dealt a pair of the same rank 7.4% of the time from a six deck shoe, roughly once in 14 hands. From a single deck it is only 5.9%, because once the first card is dealt only three of its rank remain. Split decisions therefore come up a little more often in shoe games.
Stiff hands are the most common hand you hold
A hard total of 12 through 16 is dealt about 39 percent of the time. More than one hand in three, in other words, arrives as the awkward total that can bust on the next card but rarely wins by standing. That is the most important number on this page for your results: the stiff-hand rows of the strategy chart are where you spend most of your playing life, so they are where small errors add up fastest.
The doubling hands
Hard 11 is dealt 4.75% of the time and hard 10 4.13%, so between them roughly one hand in eleven is a prime doubling hand. Those are the rounds where you are a clear favourite, and the cost of mistakes page shows how much is given up by playing them timidly.
How the counting works
Each figure divides the number of two-card combinations that make the hand by the total number of two-card combinations in the shoe. A six deck shoe has 312 cards and 48,516 possible two-card hands. Ninety-six of the cards are ten-value and twenty-four are aces, so 2,304 of those hands are blackjacks, which is where the 4.75% comes from.
Every two-card total, six deck shoe
Here is the full distribution of two-card totals from a six deck shoe, blackjack excluded. Hard totals include pairs, such as 8 and 8 counted as hard 16. Hard 20 is by far the most common single total because it can be made from any two of the ninety-six ten-value cards.
| Starting hand | Chance | About once in |
|---|---|---|
| Hard 4 | 0.57% | 1 in 176 |
| Hard 5 | 1.19% | 1 in 84 |
| Hard 6 | 1.76% | 1 in 57 |
| Hard 7 | 2.37% | 1 in 42 |
| Hard 8 | 2.94% | 1 in 34 |
| Hard 9 | 3.56% | 1 in 28 |
| Hard 10 | 4.13% | 1 in 24 |
| Hard 11 | 4.75% | 1 in 21 |
| Hard 12 | 8.88% | 1 in 11 |
| Hard 13 | 8.31% | 1 in 12 |
| Hard 14 | 7.69% | 1 in 13 |
| Hard 15 | 7.12% | 1 in 14 |
| Hard 16 | 6.51% | 1 in 15 |
| Hard 17 | 5.94% | 1 in 17 |
| Hard 18 | 5.32% | 1 in 19 |
| Hard 19 | 4.75% | 1 in 21 |
| Hard 20 | 9.40% | 1 in 11 |
| Pair of aces | 0.57% | 1 in 176 |
| Soft 13 (A,2) | 1.19% | 1 in 84 |
| Soft 14 (A,3) | 1.19% | 1 in 84 |
| Soft 15 (A,4) | 1.19% | 1 in 84 |
| Soft 16 (A,5) | 1.19% | 1 in 84 |
| Soft 17 (A,6) | 1.19% | 1 in 84 |
| Soft 18 (A,7) | 1.19% | 1 in 84 |
| Soft 19 (A,8) | 1.19% | 1 in 84 |
| Soft 20 (A,9) | 1.19% | 1 in 84 |
Notice how rare the very low totals are. Hard 4 needs a pair of 2s, and hard 5 needs a 2 and a 3, so together they come up less than one hand in a hundred. The middle totals from 12 to 17 are each dealt five to eight percent of the time, which is why they matter so much to your results.
Frequently asked questions
What are the odds of getting blackjack on any hand?
From a six deck shoe, 4.75%, or about one hand in 21. The dealer gets one just as often.
What are the odds of being dealt two aces?
From six decks, 0.57%, about once in 176 hands. Always split them.
Do more decks make blackjacks rarer?
Very slightly, as the first table shows. The bigger effect of extra decks is on the house edge, through many small changes in the odds of each decision.
How are these odds calculated?
By counting every possible pair of cards in the shoe, without replacement, and dividing the number that make each hand by the total number of pairs.
How these numbers were made: every figure on this page is calculated, not quoted. Our blackjack engine works out the exact expected value of every hand for an infinite deck, which lands within about a tenth of a percent of a 6 to 8 deck shoe. It assumes the dealer checks for blackjack, one split per hand, and split aces receiving one card each.
A note on risk. Basic strategy reduces the house edge to roughly half a percent. It does not remove it. Nothing here is gambling advice or a prediction of results. If gambling has stopped being entertainment, the National Problem Gambling Helpline is 1-800-522-4700, or ncpgambling.org.