Blackjack Odds and Probability: Dealer Bust and Winning Chances

A probability is the share of the time something happens, and it is the clearest way to read blackjack. A dealer bust probability of 42.28% (Chance that the dealer finishes with a bust when the up card is a 6. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) with a 6 showing means that, over a very large number of such hands, the dealer goes over 21 that share of the time. It does not say what the next hand will do.

Odds are the same idea written as a ratio, so "one in so many" and "so many to one" are two views of one number. A natural comes about one hand in 1 in 21.1 (The chance of a natural as one hand in so many. Rules: 6 decks. Worked out exactly from a full shoe.) hands, which is a probability of 4.75% (Chance that the first two cards dealt to a player are an ace and a ten-valued card. Rules: 6 decks. Worked out exactly from a full shoe.). Casinos pay bets using odds, and players think in probabilities, so keeping both in view helps when a payout is being compared with the chance of winning it.

Three families of probability decide how blackjack plays:

• The dealer's hand. The dealer has no choices. A hand below 17 must draw, a hand of 17 or more stands, so the final total depends only on the up card and the cards that follow.
• Your own draws. Every card you take has a known chance of busting you, set by your total and the cards left in the shoe.
• The deal itself. How often a natural appears, and how often a round ends ahead, level or behind.

Every figure below is a probability of one of those three things, for a named set of rules. Change the rules and the probability changes, which is why the deck toggle matters. The figures assume each round is dealt from a freshly shuffled shoe, the standard basis for stating blackjack odds.

The up card is the single most useful piece of information on the table, because the dealer's final total is a forced outcome. Only the first card is visible, but the whole range of finishing totals hangs on it. Use the explorer to see how the dealer's hand ends for each up card and each deck count.

Three patterns show up straight away. A 7, 8, 9 or ten-valued card is a strong start because it is already close to a finished hand, so the dealer's most likely outcome is to stand on the obvious total: 17 with a 7 (36.92% (Chance that the dealer finishes with a final total of 17 when the up card is a 7. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.)), 18 with an 8 (36.00% (Chance that the dealer finishes with a final total of 18 when the up card is a 8. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.)), 19 with a 9 (35.19% (Chance that the dealer finishes with a final total of 19 when the up card is a 9. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.)) and 20 with a ten-valued card (34.00% (Chance that the dealer finishes with a final total of 20 when the up card is a ten-valued card. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.)). An ace is different: it makes a natural 30.87% (Chance that the dealer finishes with a natural blackjack when the up card is an ace. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) of the time, and otherwise the dealer has a flexible soft hand that is hard to bust.

The weak up cards are the 2 to 6. A hand that starts from a small card cannot stop until it reaches 17, so the dealer is forced to keep drawing, and every extra card is another chance to go over 21.

Read the blackjack probability chart for the dealer card by card: the dealer busts in a little over a quarter of all hands. The exact share for this shoe is 28.19% (Chance that a dealer hand finishes with a bust, before any card is seen (every up card weighted by how often it comes up). Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.), but it hides a huge spread: the weakest up cards bust the dealer roughly four times in ten, and an ace far less often.

Why is the 6 the weakest up card? The most common hole card is ten-valued, and with a 6 showing that leaves a stiff 16 that must draw again. Most of the other hole cards leave a total below 17 too, so the dealer rarely stops on the first draw. That pushes the bust chance to 42.28% (Chance that the dealer finishes with a bust when the up card is a 6. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.). The 5 sits right behind it at 41.84% (Chance that the dealer finishes with a bust when the up card is a 5. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.), and the 4, 3 and 2 follow at 39.58% (Chance that the dealer finishes with a bust when the up card is a 4. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.), 37.42% (Chance that the dealer finishes with a bust when the up card is a 3. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) and 35.35% (Chance that the dealer finishes with a bust when the up card is a 2. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.). After that the curve falls off a cliff: a 7 busts only 26.19% (Chance that the dealer finishes with a bust when the up card is a 7. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.), because a ten-valued card already gives the dealer 17.

The exact ranking depends on the number of decks. With a single deck the 5 busts the dealer slightly more often than the 6 (42.89% (Chance that the dealer finishes with a bust when the up card is a 5. Rules: a single deck, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) against 42.08% (Chance that the dealer finishes with a bust when the up card is a 6. Rules: a single deck, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.)), The two are within one percentage point of each other either way, so a change in the shoe can swap them. In a six-deck shoe the 6 leads. The chart below follows the deck toggle, and marks the up card with the most busts for the deck count you pick.

The mirror of the dealer's problem is your own. A hard total of 11 or less can never bust on one more card, so hitting it costs nothing in bust risk. From 12 upward the risk climbs by about a thirteenth of the deck with every point, because each extra point of total turns one more card rank into a bust card.

A hard 12 busts only when the next card is a ten-valued card, which happens 30.80% (Chance of going over 21 when a two-card hard 12 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.) of the time. Hard 13 and 14 add one more rank each, reaching 38.48% (Chance of going over 21 when a two-card hard 13 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.) and 46.15% (Chance of going over 21 when a two-card hard 14 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.). A hard 15 busts 53.82% (Chance of going over 21 when a two-card hard 15 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.) of the time and a hard 16 busts 61.29% (Chance of going over 21 when a two-card hard 16 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.), which is why 16 has a reputation as the worst hand in blackjack: it is a weak total to stand on and it busts more often than not when hit. By hard 20 only an ace keeps you safe, and the bust chance is 92.26% (Chance of going over 21 when a two-card hard 20 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.).

Soft hands, those with an ace counted as 11, cannot bust on one card at all, because the ace simply drops back to 1. That is why a soft total can be drawn to freely while a hard total cannot. The ladder shows the bust chance for every hard two-card total from 12 to 20.

A natural is an ace with a ten-valued card as your first two cards. The probability is 4.75% (Chance that the first two cards dealt to a player are an ace and a ten-valued card. Rules: 6 decks. Worked out exactly from a full shoe.) with six decks, which is one hand in 1 in 21.1 (The chance of a natural as one hand in so many. Rules: 6 decks. Worked out exactly from a full shoe.). Sixteen of the cards in every deck are ten-valued and four are aces, so the combination is uncommon but far from rare over an evening of play.

The number of decks matters a little. With one deck the chance is 4.83% (Chance that the first two cards dealt to a player are an ace and a ten-valued card. Rules: a single deck. Worked out exactly from a full shoe.), and with eight it is 4.75% (Chance that the first two cards dealt to a player are an ace and a ten-valued card. Rules: 8 decks. Worked out exactly from a full shoe.). Fewer decks make a natural slightly more likely, because after you take an ace the chance that the next card is ten-valued is slightly higher when fewer cards are left. The difference is small, but it is one reason single-deck games are friendlier to the player.

The dealer faces the same odds, and the up card tells you a lot. With an ace showing, the dealer has a natural 30.87% (Chance that the dealer finishes with a natural blackjack when the up card is an ace. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) of the time, and with a ten-valued card showing, 7.72% (Chance that the dealer finishes with a natural blackjack when the up card is a ten-valued card. Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.). In games with a hole card the dealer checks for it immediately, so you learn the answer before you act.

The chance of winning a round is the number most people search for, and it is lower than most people expect. Measured over a large run of rounds with the reference rules, a player who follows the printed chart finishes ahead in 43.4% (Share of rounds in which a player finishes ahead (the round pays more than it cost), with 6 decks. Measured on 1,200,000 rounds dealt by the game engine from a freshly shuffled shoe to one player following the printed chart; standard error 0.045 points. Rules: 6 decks, dealer stands on soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender.) of rounds, level in 8.7% (Share of rounds in which a player finishes level (the bet comes back, or wins and losses on split hands cancel), with 6 decks. Measured on 1,200,000 rounds dealt by the game engine from a freshly shuffled shoe to one player following the printed chart; standard error 0.026 points. Rules: 6 decks, dealer stands on soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender.) and behind in 47.9% (Share of rounds in which a player finishes behind (the round loses money), with 6 decks. Measured on 1,200,000 rounds dealt by the game engine from a freshly shuffled shoe to one player following the printed chart; standard error 0.046 points. Rules: 6 decks, dealer stands on soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender.).

Finishing ahead less often than behind does not mean losing a large share of every bet. A winning round can pay more than a losing round costs, through a natural paid at 3 to 2, a double or a split, so the average loss per starting bet, the house edge, is much smaller than the gap between the shares.

A round counts as ahead when it pays more than it cost, level when the bet comes back or a split cancels out, and behind when it loses money. A hand that is doubled or split still counts as a single round. These shares are measured rather than worked out, so they carry a tiny margin of error, and they are printed to one decimal place for that reason.

The house edge for the reference rules is 0.41% (House edge per starting bet for six decks: the average loss per round as a share of the bet placed before the cards are dealt. Rules: 6 decks, dealer stands on soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender. The player follows the printed strategy chart for these rules from a full shoe, and never takes insurance or even money. A negative figure means the player is ahead.) per starting bet. It exists for one reason that beats all the others: the player acts first. If you bust, you lose immediately, before the dealer plays, even in the many cases where the dealer would have busted too. The dealer only ever has to act when you are still in the hand.

The rest of the game pushes back in the player's favour. The dealer has no choices, while you can double, split and choose when to stand, and a natural pays 3 to 2. The house edge is what is left after these effects are added up: acting first costs the player a great deal, and the natural bonus, doubling, splitting and free choice give most of it back.

That balance is sensitive to the details. The house edge is the sum of several large effects that nearly cancel, so a rule that shifts any one of them by a small amount shifts the total by a visible amount. A 6 to 5 natural payout cuts the bonus that balances acting first, and a dealer who hits soft 17 draws on hands that would otherwise have stood.

The house edge is also an average, not a forecast. Over a long run the average is what the player loses per unit bet. In a short session the result is dominated by the round-to-round swings in the shares above, and the house edge tells you very little about the next hour.

Rules are where the odds really change. Each row in the table is the reference rules with exactly one thing changed, and each house edge is worked out for the chart that suits those rules, so the comparison is fair.

The dealer hitting soft 17 is the most common difference between tables. It changes the house edge by +0.21 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: dealer hits soft 17. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.). The dealer actually busts a little more often, 28.58% (Chance that a dealer hand busts under these rules: dealer hits soft 17. 6 decks, the dealer hits soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) of hands instead of 28.19% (Chance that a dealer hand finishes with a bust, before any card is seen (every up card weighted by how often it comes up). Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.), but a soft 17 that draws usually lands on a better total, and the hands that do not bust finish higher. A natural paid at 6 to 5 instead of 3 to 2 changes the house edge by +1.36 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: blackjack pays 6 to 5. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), the largest single change in the table and the clearest reason to read the payout before sitting down.

Fewer decks help the player. Going to a single deck changes the house edge by -0.55 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: single deck. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), and a double deck by -0.21 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: double deck. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), while eight decks change it by +0.03 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: eight decks. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.). A smaller shoe makes naturals slightly more common and lets the cards in your own hand matter more, so the same rules are kinder to the player.

Smaller rules add up too. No doubling after a split changes the house edge by +0.14 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: no doubling after a split. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), doubling on only 10 and 11 by +0.19 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: double on 10 and 11 only. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), late surrender by -0.07 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: late surrender allowed. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), and resplitting aces by -0.07 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: aces may be resplit. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.). A game with no hole card, where a dealer natural takes every bet including doubles and splits, changes it by +0.11 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: no hole card, dealer natural takes every bet. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), while the version where a dealer natural takes the original bet only moves it by +0.00 points (Change in the house edge against the reference rules (6 decks, dealer stands on soft 17, blackjack pays 3 to 2) when only this changes: no hole card, dealer natural takes the original bet only. Positive means the house gains, negative means the player gains. The difference of two exact house edge figures.), the same as a game with a hole card.

Most mistakes at the table come from misreading what a probability is. A few come up again and again.

"The dealer is due a bust." Probabilities describe the long run, not the next hand. A dealer who has not busted in ten hands has the same chance of busting on the eleventh as any other. The exception is card counting, where actual cards removed from the shoe change the odds of the next card. The figures here assume a freshly shuffled shoe, so they contain no counting.

"The dealer busts so often that I can just stand." The dealer busts 28.19% (Chance that a dealer hand finishes with a bust, before any card is seen (every up card weighted by how often it comes up). Rules: 6 decks, the dealer stands on soft 17, and the dealer checks for blackjack with a hole card. Worked out exactly by following every possible order of cards from a full shoe, removing each card as it is drawn. The dealer's hole card counts as the first card the dealer draws, so a natural is one of the outcomes.) of hands, so most of the time the dealer finishes with a made hand between 17 and 21. Waiting for a bust fails more often than it works.

"A streak of losses means a win is coming." Each round is dealt from a shuffled shoe, so a run of losses leaves the next round's odds unchanged, apart from a tiny change in the shoe that is nowhere near enough to matter.

"Every hit is a coin flip." It is not. Your bust chance is zero on a soft hand and 92.26% (Chance of going over 21 when a two-card hard 20 takes one more card. Rules: 6 decks; the two cards of the hand are taken out of a full shoe before the next card is drawn, and the dealer up card is not removed. Worked out exactly for every two-card hand that makes the total.) on a hard 20, and every total in between carries its own risk, which is why the ladder above is worth reading.

The dealer tables, bust chances and natural chances are worked out by following every possible order of cards from a full shoe, removing each card as it is drawn, so nothing is estimated. The house edge figures use the same method and add the player's decisions. The shares of rounds that finish ahead, level or behind are the only measured figures: a single player follows the printed chart through thousands of rounds dealt by the game engine, and each deck count is checked against its exact house edge.