A bust rate describes an upcard from the dealer's side. The more direct question: playing the chart, what is a round against this card worth on average, in percent of the bet? The exact answers rearrange some intuitions: the dealer's 7, which busts far less often than a 2 or a 3, is worth more to the player than either, and the dealer's ace is only the second worst upcard once the peek is done.
Two sources answer it, the Wizard of Odds exact table and our simulation of about 62 million rounds, and they agree closely wherever they measure the same thing.
Two sources, one table
The first is the Wizard of Odds exact table of expected values for every starting hand against every upcard (its blackjack appendix 9). Its rules: six decks, dealer stands on soft 17, resplits to four hands except aces, one card to split aces, double after split. Play is composition dependent from a full shoe, and the hand values cover rounds where the dealer has checked and does not have blackjack. The whole game is worth -0.4026 percent. Our own arithmetic on their table groups it by dealer upcard, weighting each hand by how often the deal produces it; with the dealer's blackjacks added back, the groups sum to that game value. Grouped by starting hand, the same table is behind our piece on which starting hands make and lose money.
The second is our simulation, the same engine as our article on what share of rounds you win, push and lose: about 62 million rounds through a six deck shoe with a cut card at 75 percent, basic strategy from the app's 4 to 8 deck chart, dealer stands on soft 17 and peeks, 3:2, double on any two cards, double after split, split to four hands, one card to split aces, no surrender. Its column below averages all rounds with that upcard, dealer blackjacks included. All values are in percent of the starting bet.
| Upcard | Share of all rounds, after the peek | Average result after the peek, Wizard of Odds grouped | Units per 100 rounds | Simulation, all rounds |
|---|---|---|---|---|
| 2 | 7.692 | +9.27 | +0.713 | +9.24 |
| 3 | 7.692 | +12.63 | +0.972 | +12.52 |
| 4 | 7.692 | +16.28 | +1.252 | +16.25 |
| 5 | 7.692 | +20.33 | +1.564 | +20.21 |
| 6 | 7.692 | +23.58 | +1.814 | +23.50 |
| 7 | 7.692 | +14.46 | +1.112 | +14.41 |
| 8 | 7.692 | +5.76 | +0.443 | +5.69 |
| 9 | 7.692 | -4.11 | -0.317 | -4.15 |
| 10 | 28.395 | -10.78 | -3.061 | -17.34 |
| Ace | 5.318 | -6.81 | -0.362 | -34.17 |
| Dealer blackjack | 4.749 | -95.44 | -4.532 | |
| Total | -0.4026 |
For the upcards 2 through 9 the two sources measure the same thing, because no dealer blackjack is possible, and they agree to within about 0.12 of a point on every row. In the dealer blackjack row, a player who also holds a natural pushes, which lifts the average from -100 to -95.44.
Ahead against 2 through 8, behind from 9 up
The player is ahead against every upcard from 2 through 8 and behind against the 9, the 10 and the ace. The best upcard is the 6 at +23.58, with the 5 next at +20.33; the climb from the 2 to the 6 goes 9.27, 12.63, 16.28, 20.33, 23.58, roughly three to four points per step. Then the value drops to 14.46 at the 7 and crosses zero between the 8 and the 9.
Weighted by frequency, the 6 brings +1.814 units per 100 rounds, the largest entry in the player's favor. That is an average over whole rounds: in the same table, a 10,3 standing against a 6 is still worth -15.43. The column by column logic is in our treatments of playing against a dealer 6 and playing against a dealer 7.
The 7 earns more than the 2 and the 3
The table's quietest surprise: the 7 busts far less often than the low cards, 26.2 percent against 35.4 for the 2 and 37.4 for the 3, per the exact dealer totals in what the dealer actually ends up with. Yet the 7 is worth +14.46 to the player, comfortably more than the 2 at +9.27 or the 3 at +12.63.
The resolution is that busting is not the only way a dealer pays out. A dealer showing 7 finishes on exactly 17 in 36.9 percent of rounds, more than any other total, and a 17 is a made hand the player's 18 beats and the player's 17 ties, as that article puts it. Against a 2 or a 3 the hands that do not bust spread almost evenly across 17 through 21, finishing on 19, 20 or 21 in 37.2 and 36.1 percent of rounds against 23.1 for the 7 (our sums from that table). The 7's value is consistent with that shape.
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The 10, the ace, and what the peek removes
After the peek, the 10 is the worse upcard: -10.78 against the ace's -6.81. The grouped values cover only rounds that survive the peek: a dealer blackjack ends the hand before the player acts, as our piece on the dealer peek rule explains.
Count the blackjacks back in and the ranking flips hard. In our simulation, which includes them, the ace is the worst upcard in the game by a wide margin at -34.17 percent of the bet per round, against -17.34 for the 10. The reason sits in the shares column: a dealer showing an ace has blackjack about 30.9 percent of the time, and a dealer showing a 10 about 7.7 percent, approximately one minus the after-peek share divided by the upcard's full share (5.318 over 7.692, and 28.395 over 30.769). Nearly a third of ace-up rounds end at the peek, still short of the one in three that insurance needs to break even at 2 to 1; our article on why basic strategy says never take insurance works that bet in full.
The 10 also does damage through sheer frequency. Ten-value cards are four of the thirteen ranks, so the 10 appears about four times as often as any other upcard and, even after the peek, accounts for 28.395 percent of all rounds, more than the 5 and 6 combined, and the 10's -3.061 units per 100 rounds is by far the largest negative entry among the upcards. The hand by hand versions are our guides to playing against a dealer 10 and playing against a dealer ace.
Where the house edge comes from
Add the units column up in three blocks. Against the upcards 2 through 9 the player earns +7.553 units per 100 rounds. The 10 and the ace, after the peek, take back 3.423. The dealer's blackjacks take 4.532 more. The sum, 7.553 minus 3.423 minus 4.532, is -0.402 units per 100 rounds, the -0.4026 game value up to rounding.
The house edge is not spread evenly; the eight upcards from 2 through 9 are, together, a net win for the player, and the whole edge, net, comes from the 10 and the ace, above all from the dealer's naturals. The 5 and the 6 together bring in 1.564 plus 1.814, or 3.378 units per 100 rounds, a little more than the 10 costs after the peek at 3.061.
One footnote: our simulation puts the whole game at -0.436 percent, as published in the win share article, against the exact table's -0.4026, a gap consistent with the simulation's cut card and total dependent chart against the exact table's full shoe and composition dependent play.
What the numbers are for
The bet is already on the table when the upcard appears, so this article offers no betting advice. What the table is for is understanding the chart: the upcard tells you which kind of round you are in, one the dealer loses on average or one they win. Against a 6 the chart stands on hard 12 through 16; against a 10, without surrender, it hits them, because there standing costs more. Our guide to reading the dealer upcard covers the bust rate logic, the upcard series summary sets all ten chart columns side by side, and how often the player and the dealer bust covers the bust race.
The values also assume correct play, the part practice controls. Rule changes move them: a different deck count, a dealer who hits soft 17, no double after split. The app's charts redraw for the rules you select, every decision comes back with instant feedback and an explanation, and the Pro upgrade adds accuracy heat maps by hand type and dealer upcard.
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Frequently asked questions
Which dealer upcard is best for the player in blackjack?
The 6. After the dealer has checked and does not have blackjack, a round against a 6 averages +23.58 percent of the starting bet under correct play, per our grouping of the Wizard of Odds expected value table. The 5 is next at +20.33. The player is ahead against every upcard from 2 through 8 and behind against the 9, 10 and ace.
Which dealer upcard is the worst for the player?
It depends on whether the dealer's blackjacks are counted. After the peek, a 10 is worse than an ace: -10.78 percent of the bet against -6.81. Counting the rounds where the dealer turns over a natural, the ace is worst by far, about -34 percent per round in our simulation against about -17 for the 10.
Why is a dealer 7 worth more to the player than a 2 or a 3?
The 2 and the 3 bust more often, 35.4 and 37.4 percent against 26.2 for the 7, yet the 7 averages +14.46 percent after the peek while the 2 manages only +9.27. That is consistent with the 7 finishing on exactly 17 in about 37 percent of rounds, a total a player 18 beats and a 17 ties, while a 2 or a 3 more often finishes on 18 through 21.
Where does the house edge in blackjack come from?
Net, from the dealer's 10 and ace. Against upcards 2 through 9 the player earns about 7.55 units per 100 rounds. The 10 and the ace, after the peek, take back about 3.42, and the dealer's blackjacks take 4.53 more, for a net of about -0.40 percent.
Why does the simulation make the ace look so much worse?
The two sources measure different rounds. The grouped exact values cover only rounds that survive the peek, where the ace is -6.81 percent of the bet. Our simulation averages every round with an ace up, including the roughly 30.9 percent in which the dealer has blackjack, which drags it to -34.17. The 10 moves less, from -10.78 to -17.34.