Dealer bust probability by upcard

The dealer busts roughly three hands in ten, but that average hides a wide spread: a dealer showing a 6 busts about 42% of the time while a dealer showing an ace busts under 17%. Every basic-strategy decision rests on this table, because the choice between hitting and standing on a stiff hand is really a bet on whether the dealer will break first.

The six-deck S17 dealer outcome table

The table below is the Wizard of Odds dealer-odds table for six decks with the dealer standing on soft 17 (S17), US peek rules. The figures are conditional on the dealer having already checked for and not found a blackjack, so the ace and 10 rows exclude natural 21s. Each row sums to 1.

The full-precision figures (for example 0.422842 for a 6 busting) are in the source table and in this site’s machine-readable copy at /data/dealer-outcomes.json. The “All upcards” row weights each upcard by how often it appears and, because of the peek condition, counts the 10 and ace rows only when no natural was present.

Why the dealer busts most against a 5 or 6

The dealer has no choices. With a 5 or 6 showing, the hole card and first draw are both forced, and the arithmetic is unforgiving:

• A 6 plus any card from 6 to 10 gives a stiff total of 12 to 16 that must be hit again. Those ranks are 8 of the 13 card values (four 10-value ranks plus 6, 7, 8, 9), so about 62% of hole cards leave the dealer stuck on a hand that busts with the next 10.
• A 5 behaves the same way with a hole card of 7 to 10, and a 6 in the hole makes 11, which then needs another draw.

The 6 edges out the 5 (42.28% against 41.84%) because 6 + 10 is already 16, the worst stiff, whereas 5 + 10 is 15 and has a slightly better chance of surviving a draw. The pattern is visible across the row: the 6 lands on exactly 17 more often (16.57%) than any other small card, because so many of its hands stop the moment they reach 17 rather than drawing further.

Why a 2 or 3 is a weak spot, not a bust card

Players often lump 2 through 6 together as “bust cards”. The table shows that is too generous. A dealer 2 busts 35.35% of the time and a 3 busts 37.42%, both well short of the 5 and 6.

The reason is flexibility. A 2 plus a 10 is only 12; the dealer can draw a 2 through 9 without busting and often needs two or three draws to reach 17. More draws mean more chances to land on 17 to 21 before the 10s do their damage. The practical effect is in the strategy chart: against a 2 or 3 you still stand on 13 to 16, but you hit a 12 and you double fewer hands than you would against a 5 or 6. The basic strategy guide sets out the full pattern.

Why a 7 through ace is strong

From 7 upwards the dealer usually makes a hand in one draw. Each of 7, 8, 9 and 10 has a single most likely outcome, which is the upcard plus 10:

This is why basic strategy tells you to hit stiff hands against a 7 or higher: standing on 14 against a 7 only wins when the dealer busts (26.19%), while the dealer stops on 17 or better the remaining 73.81% of the time.

The ace is strong for a different reason. Its bust rate is the lowest of all (16.70%) because the dealer can count it as 1 or 11, and its outcomes from 17 to 20 are almost flat at around 18.9% each. Even after the peek has ruled out a natural, an ace up is the single worst card for the player to see.

How the table feeds basic strategy

Standing on a stiff hand means your only route to a win is a dealer bust. The expected value of standing is therefore roughly 2 × P(dealer busts) − 1. Against a 10:

2 × 0.2302 − 1 = −0.5395, or a loss of about 54p per £1 staked.

Against a 6 the same arithmetic gives 2 × 0.4228 − 1 = −0.1543, a loss of about 15p per £1. The exact numbers in a strategy engine differ by a few thousandths because your own cards are removed from the shoe, but the shape of the decision is set by this table. The EV of hard 16 vs 10 article follows one hand through the full comparison, and the player bust probability article supplies the other half of the trade-off.

What changes under other rules

• Dealer hits soft 17 (H17). The Wizard of Odds six-deck H17 table gives an overall bust rate of 30.00% against 29.60% for S17. The dealer busts slightly more but makes 18 to 21 more often, which costs the player about 0.22% in the Wizard’s rule-variation figures. The ace and 6 rows move the most, because those are the upcards that produce soft 17s.
• Deck count. The effect is small. The all-upcard bust rate for S17 moves from 29.80% in a single deck to 29.59% in eight decks in the same source.
• No peek (European rules). When the dealer does not check for blackjack, a natural becomes one of the possible final hands. The Wizard’s European-rules tables show an all-upcard bust rate of 28.18% for eight decks S17, with naturals accounting for 4.75% of hands.
• Before the peek. If you want the probability of a dealer blackjack on an ace or 10 upcard, use the insurance maths article rather than this table, which has already conditioned that event away.

Related reading

• Player bust probability when hitting
• Expected value of hard 16 vs 10
• Basic strategy
• Strategy chart