Blackjack payouts and probabilities

Like any game of chance, blackjack comes with a built-in casino advantage: over a single session a player can finish ahead, but over the long run you will inevitably give back a portion of everything you wager. Exactly how much you lose depends both on the rules of the specific table¹ and on the size of the sample (the longer you play, the smaller the influence of variance — the closer your losses land to the average). Players who want to understand every nuance of their favourite game, though, tend to want to know exactly how blackjack payouts and probabilities work from a mathematical standpoint. This article is an attempt to give that detailed breakdown.

Blackjack payouts: 3:2 versus 6:5

Let’s set side bets aside straight away — they’re a separate topic that not every blackjack player cares about, and we cover them in a dedicated article. On the main bet, the most promising outcome is a natural blackjack — 21 on your first two cards. Some tables pay this hand at 3:2, others at 6:5, and that’s a fundamental difference any player who cares about their own bankroll should keep an eye on.

How the payout is calculated

The 3:2 and 6:5 figures express the ratio between your stake and the amount paid out when you draw a natural blackjack — the number after the colon is your stake, the one before it is your winnings. Translated into what bettors call decimal odds, a 3:2 payout means the player is looking at odds of 2.5 (you keep your stake and take one and a half times it in winnings), while 6:5 works out to just 2.2 (120% of your stake in winnings, plus the stake back). The examples in the table below make it very clear which is better, 3-to-2 or 6-to-5.

Seasoned blackjack players know that any rule which looks bad can, in theory, be offset by other, favourable rules. But 6:5 tells you you’ll be badly short-changed in exactly the situations where you’ve drawn the strongest hand possible.

The effect on the house edge

The house edge² in blackjack is very volatile, but on average it’s usually put at 0.5% — provided the player doesn’t guess their way through each hand and instead always follows basic strategy, i.e. makes the mathematically soundest plays³. A 0.5% house edge is only possible, though, when a natural blackjack pays 3:2; if the house only pays 6:5, that automatically adds roughly 1.39% to the edge. That’s why experienced players almost never sit at tables that pay 6:5 for a two-card 21 — the rule burns through your bankroll around four times faster.

Important: a 6:5 payout instead of 3:2 outweighs almost any favourable table rule. Before you buy chips, check the wording on the felt: a 6:5 table isn’t worth playing if there’s a 3:2 table open next to it.

Base blackjack probabilities

Because blackjack is played with a standard set of cards (decks of 52 with no jokers, from a single deck up to eight), the probability of every main way a hand can end is calculable. The table below shows clearly that the player’s and the dealer’s chances of winning differ: even though the player can use options like splitting and doubling that the dealer can’t, the house rep will win the hand more often.

The number of decks in play at a given table doesn’t change the probability of any one outcome. Over short runs (individual sessions), though, variance is unavoidable: a player may run hot or cold. Advanced players try to nudge their odds further by counting the cards left in the shoe (what’s left of the decks): if a big chunk of the low cards has already been dealt, leaving a majority of aces and ten-value cards, the chance of a blackjack goes up.

Important: the deck count doesn’t change the probability of an individual hand outcome — 42.22% to win, 8.68% to push and 4.83% for a natural are the same with one deck as with eight. What it does affect is the house edge — more on that below.

Dealer outcome probabilities

Playing blackjack, a player needs to understand not only the odds of drawing a strong hand themselves, but also the odds that the dealer will draw one. The dealer never plays by the same rules as the player: they don’t split, for instance, and they don’t double. On top of that, the dealer stops on 17 — though, depending on the table, either on hard 17 only or on soft 17 as well⁴. That last rule matters a great deal because of how it varies: you want tables where the dealer stops on soft 17, because that’s a fairly weak hand the dealer is voluntarily declining to safely improve.

How to read the table

In blackjack the player makes decisions based not only on the cards in their own hand but also on the dealer’s upcard. No single upcard actually guarantees the dealer a strong hand (a low card can be paired with that ten or ace, and a third card can then bust it), but you can calculate the bust probability from the first card shown. For the player, a dealer bust is the ideal outcome: as long as you haven’t busted yourself, you win, even with a very weak hand.

Dealer bust by upcard

The table looks at the dealer’s bust probability depending on which first card they show the table. The exact math can vary with a table’s specific rules, so to be precise: every probability here is for a single-deck game where the dealer stands on soft 17. All figures are also given after the dealer peek — i.e. after the dealer has checked whether they hold a natural blackjack⁵.

At first glance this may seem counterintuitive, but with a big card — an ace, any ten-value card, even a nine, eight or seven — the dealer’s bust probability is low: the second card will most likely bring them to the 17 threshold, where they stop. A two or a three is relatively promising for the dealer too — the second card won’t reach the 17 threshold yet, but they’ll still have plenty of room to take a third card without busting. A four, five or six as an upcard, by contrast, sets up a situation where the dealer busts: they risk falling just short of 17 and having to take a third card at a serious risk of going over.

House edge and the number of decks

The number of decks in blackjack directly affects how good the game is: even without deliberate card counting, on a single-deck game a player can notice the shoe skewing toward strong or weak cards, because the cards of the opposite value have mostly been dealt already. The table below shows how the house edge changes with the deck count — again with the dealer standing on soft 17 and with a dealer peek.

Additional rule nuances can adjust the figures shown here: for example, the dealer standing on hard 17 rather than soft 17 adds roughly 0.2% to the house edge, while the DAS rule (double after split) instead trims the edge by around 0.12%⁶.

Even less sense for the player is dealer blackjack insurance (Insurance): use it regularly and the house edge climbs to a stratospheric 7.4%. That option only has any real point if you’re an experienced card counter using the insurance bet strictly when the clear advantage lies with the player rather than the house. Other side bets also drive the house’s advantage sky-high — depending on the terms of the bet, the house edge can rise to 2–17%.

The probability of winning and losing streaks

Knowing the probability of winning and losing each individual hand, you can use the formula P(n) = p^n to work out the odds of lucky and unlucky streaks — several identical results in a row. The table below shows that seven losses in a row, for instance, is no great rarity: over any session that stretches to 2–3 hours, you’ll almost certainly run into one (remember variance).

The probability of a losing streak matters more to a thoughtful player than the probability of a winning one. It’s logical: you shouldn’t be counting on future wins anyway, and if they come, let them be a pleasant surprise; a losing streak, meanwhile, can drain a player’s entire bankroll in short order — especially one betting the Martingale system, doubling the next bet after every loss in the hope of clawing back all previous losses with a single win. We have a separate piece on how the Martingale system does (or rather, in practice, doesn’t) work in blackjack — read it to make an informed decision about whether to use it.

Important: a run of seven losses in a row (≈0.59%) is almost certain over a 2–3 hour session — and that’s exactly what breaks the Martingale: the bankroll or the table limit runs out before the saving win arrives.

How to use these numbers

The math this article has spent so long on actually has a practical payoff — it helps a player pick a table with the most favourable conditions and play without hurting themselves. Casinos often combine rules so that every table has both strengths and weaknesses, but broadly the math gives the player this list of pointers:

1. most important of all — choose a table that pays 3:2 for a natural blackjack, because a 6:5 payout means serious (and needless) losses, adding 1.39% to the house edge;
2. all else being equal, a dealer standing on soft 17 beats one standing on hard 17, at a cost of 0.2% in edge;
3. the fewer decks, the better the game — playing a single deck with a full set of other strong rules, you can expect a house edge of just around 0.15–0.17%;
4. dealer blackjack insurance, especially taken every time it’s offered, is a road to nowhere: you’re personally pushing the house edge up to about 7.4%;
5. side bets, insurance among them, should be treated purely as entertainment that demands a generous fee from the player: they dangle a huge potential win while actually raising the house’s long-run edge to 2–17%.

Finding a table with a perfect set of strong rules won’t be easy, so you’ll sometimes have to knowingly give something up; but now that you know how the main rule nuances affect the game’s math, you can make an informed choice. Keep the volatility of gambling in mind, though: in theory you can finish a single session ahead even on the worst rules, just as, conversely, you can lose your whole bankroll even when the rules seem to be in your favour.