How Often Do You Get a Blackjack?
Updated
About one hand in 21. With six decks the exact figure is 4.75%, and it goes up as the deck count comes down — which turns out to be one of the reasons single-deck tables so often pay 6:5.
- Six decks: 4.75%, roughly one hand in 21.
- One deck: 4.83% — noticeably more often.
- The calculation is exact, not simulated: two ways to make it, ace first or ten first.
- A 3:2 payout on 4.75% of hands is worth about 1.425% compared with 6:5.
How the number is worked out
A blackjack is an ace with any ten-value card. There are two orders it can arrive in, so:
P = 2 × (aces ÷ cards) × (tens ÷ remaining cards)
With six decks that is 2 × (24 ÷ 312) × (96 ÷ 311) = 4.75%. No simulation, no approximation — this one you can check on paper.
| Decks | Chance of a blackjack | About one in |
|---|---|---|
| 1 | 4.83% | 20.7 hands |
| 2 | 4.78% | 20.9 hands |
| 4 | 4.76% | 21.0 hands |
| 6 | 4.75% | 21.1 hands |
| 8 | 4.75% | 21.1 hands |
Why fewer decks help
The second card is drawn from a shoe that is missing the first. In a single deck, taking an ace out leaves 16 tens among 51 cards — a ratio of 31.4%. In eight decks, taking one ace out barely changes anything, and the ratio is 30.8%.
That small edge is real money, because blackjacks pay more than even. It is also exactly why casinos so often attach a 6:5 payout to single-deck tables: the payout cut costs you far more than the deck reduction gives back.
When you both have one
It is a push. You get your bet back and nobody wins. That happens more often than people expect — roughly 0.23% of hands — and it is one of the reasons the win/lose/push split is not simply 50/50.
Keep reading
By Martin Kosek · every number on this site is computed by us, not copied.
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