Blackjack odds and probabilities

Blackjack odds start with the deck

Every probability in blackjack comes from counting cards. A standard deck has 52 cards in 13 ranks. Nine ranks (2 to 9 and the ace) have four cards each, but four ranks (10, jack, queen and king) all count as 10, so a 10-value card turns up 16 times in 52, or 30.8% of the time. Any other single value, such as a 6 or an ace, appears 4 times in 52, or 7.7%. Our page on blackjack card values covers the counting rules.

Most of the calculations below use the “infinite deck” shortcut, which treats every card as equally likely each time. It is close to the real figures for six or eight decks, and it is how many published analyses simplify the sums. Where deck count changes things noticeably, the exact figure is shown too. For the general idea of counting outcomes, see casino probability basics.

The odds of being dealt a blackjack

A natural needs one ace and one 10-value card in your first two cards, in either order. With a single deck: the chance the first card is an ace and the second a 10-value card is 4/52 × 16/51, and the reverse order has the same chance, so the total is 2 × 4/52 × 16/51 = 4.83%. More decks dilute the effect of removing the first card, and the figure drifts towards the infinite-deck value of 2 × 1/13 × 4/13 = 8/169.

That slightly higher single-deck figure is part of why fewer decks help the player, worth +0.48% for one deck against eight on Wizard of Odds’ rule-variation figures (opens in a new tab). See does the number of decks matter.

The chance that both you and the dealer have a natural in the same round is roughly 4.73% × 4.73%, about 0.22%, or once in around 450 rounds. When it happens, the hand is a push.

The odds the dealer has blackjack

The dealer’s up card changes everything. With an ace showing, the dealer needs a 10-value card underneath. On the infinite-deck shortcut that is 4/13, or 30.8%. From a full eight-deck shoe, ignoring your own cards, 128 of the remaining 415 cards are 10-value, also 30.8%.

With a 10-value card showing, the dealer needs an ace in the hole: 1/13, or 7.7%. From the same eight-deck shoe that is 32 aces in 415 cards, again 7.7%. With any other up card the dealer cannot have blackjack at all. This is why peek games check only when an ace or ten is showing. Our answer on whether the dealer can have blackjack with a 10 showing has more.

Your odds of busting when you hit

If you hit a hard total, you bust when the new card takes you over 21. Counting the ranks that do that gives a clean table. A hard 12 busts only on a 10-value card (4 ranks of 13). A hard 16 busts on 6, 7, 8, 9 or any 10-value card (8 ranks of 13). Soft totals cannot bust on one card, because the ace drops to 1. Read more on hard hands and soft hands.

These numbers do not tell you what to do on their own. Hard 16 busts 61.5% of the time if you hit, yet basic strategy still hits it against a dealer 7 or higher, because standing on 16 against those cards loses even more often. The chart weighs your bust risk against the dealer’s likely final total.

Why the 10-value cards drive the odds

With almost a third of the deck worth 10, the safest guess for any unseen card is “10”. That shapes the game in three ways:

• Dealer weak cards. A dealer with 4, 5 or 6 showing is often looking at 14, 15 or 16 after the hole card, and must draw again with a real chance of busting. That is why the chart stands on stiff hands against those cards.
• Doubling on 10 and 11. One more card has a 30.8% chance of being a 10-value card, landing you on 20 or 21.
• Insurance. It needs the dealer’s hole card to be a 10-value card at least one time in three to break even. At 30.8%, it falls short.

The same logic explains why the dealer soft 17 rule matters. A dealer who hits soft 17 has extra chances to improve, which costs the player 0.22% on Wizard of Odds’ figures.

Blackjack odds against the payouts

A bet is fair when the payout matches the true odds. Blackjack’s main bet does not pay one fixed price for one event, so its overall value comes from the house edge, which combines every outcome and decision. Insurance is a clean single-event example, so it shows the gap clearly.

Those edges come straight from the counts, as set out in Wizard of Odds’ blackjack basics (opens in a new tab). On the infinite deck, a £1 insurance bet wins £2 four times in 13 and loses £1 nine times, so the average return is (2 × 4 − 9) ÷ 13 = −1/13, a loss of about 7.7p per £1. Our page on true odds against payout odds applies the same method across casino games.

Side bet odds: one worked example

Side bet probabilities are rarely printed, but one is published in full. In Free Bet Blackjack, the Push 22 side bet pays 11 to 1 if the dealer finishes on exactly 22. With six decks and the dealer hitting soft 17, Wizard of Odds gives the probability (opens in a new tab) as 0.073536, about 7.35%. A £1 bet therefore returns £12 (stake included) 7.35% of the time: 12 × 0.073536 = 0.882, a loss of about 11.8p per £1, which is the 11.76% edge it lists.

Most other side bets work the same way: the payout looks large, but it sits below the true odds. See blackjack side bets for the main paytables and their edges.

How to work out blackjack odds yourself

1. Decide what event you want the chance of, such as busting on hard 14 or the dealer holding blackjack under an ace.
2. List the cards that make the event happen, counting all four 10-value ranks together.
3. Divide by the total number of possibilities: 13 ranks on the infinite-deck shortcut, or the exact number of unseen cards if you want precision.
4. For two-card events, multiply the chances of each card, and add the orders if either order works.
5. Compare the result with the payout: a bet paying X to 1 needs a chance above 1 in (X + 1) to be fair.
6. Remember the result is a long-run frequency, not a forecast for the next hand.

Odds do not remember previous hands

In RNG blackjack, the cards are reshuffled every round. Wizard of Odds notes that most online games shuffle after every hand, so the odds reset each time and the gambler’s fallacy applies in full: three dealer blackjacks in a row say nothing about the next round. See its online blackjack answers (opens in a new tab) and our page on independent events.

Live tables deal from a physical shoe, so the remaining cards do change as a shoe goes on. That is the theory card counting grew from, but shoes are reshuffled part-way through (Wizard of Odds reports that Lightning Blackjack’s eight-deck shoe is reshuffled after roughly four decks), and casinos can refuse service to suspected counters. Our card counting page covers it as history and theory only.

Overall blackjack odds: the house edge in context

Put every probability together with the payouts and decisions and you get the overall price of the game. With basic strategy, Wizard of Odds’ house edge list (opens in a new tab) gives 0.28% under liberal Vegas rules and 0.43% under Atlantic City rules, and a six-deck European game comes in at 0.62%. At 0.62%, a £10 hand costs about 6.2p on average, and 60 hands an hour about £3.72. A 6 to 5 payout adds 1.39%. These are among the best odds in the casino, which our best odds answer compares, but they still favour the house.

Short sessions vary a lot. You can finish an hour well up or well down, because a few doubles, splits or blackjacks swing results by many times the average cost. That swing is variance, and it does not change the long-run direction. Budget for the average cost and treat any win as luck.

Blackjack odds and our partner offers

Our partner offers are mainly built around slots. Blackjack and other table games are often excluded from bonus wagering or count for less, so the offers below do not improve blackjack odds. Check each casino’s table game lobby and terms. 18+ and terms apply.

• Casumo: a 50% bonus up to £100 for new customers who opt in and deposit at least £20; 10x wagering on the bonus within 7 days, a £5 maximum bet while it runs, and game, play and payment restrictions.
• 10bet Casino: a 100% match up to £25 for new UK customers who pick the casino welcome bonus and deposit within 7 days; wager it 10x on slots within 3 days, bonus winnings capped at £1,000, Skrill and Neteller excluded.
• Coral Casino: 100 free spins (10p each, selected games, no wagering on winnings) when new players deposit and bet £10 or more on slots; accept within 48 hours, valid 7 days, offer period 1 October 2026 to 1 February 2027, some payment methods excluded.

18+. Every casino game has a built-in house edge, so over time you should expect to lose what you stake. Set a budget before you play and stop when it’s gone: safer gambling tools and support. Free, confidential help: National Gambling Helpline 0808 8020 133.