Dealer bust odds with a 3 showing
Dealer shows a 3: they bust 37.39% of the time under stand-on-soft-17 rules (37.67% if the table hits soft 17). Exact figures, computed by full recursion — here is everything that upcard can become.
| Final hand | Probability (S17) | Probability (H17) |
|---|---|---|
| 17 | 13.50% | 12.63% |
| 18 | 13.05% | 13.20% |
| 19 | 12.56% | 12.71% |
| 20 | 12.03% | 12.18% |
| 21 | 11.47% | 11.62% |
| Bust | 37.39% | 37.67% |
What it means for your hand
A borderline bust card: 37.39% is high, but not high enough to protect every stiff. This is why 12 against a 2 or 3 is a hit while 13 stands — the two most-missed plays at any table — and why doubles here are selective rather than automatic. US peek rules assumed: a dealer blackjack ends the round before decisions, so naturals are excluded from the table. See the full upcard comparison or the strategy chart this number feeds into.
Hands this upcard decides
12 vs 3Full verdict with odds and EV13 vs 3Full verdict with odds and EV9 vs 3Full verdict with odds and EV
Frequently asked
How often does the dealer bust with a 3?
37.39% of the time under stand-on-soft-17 rules, 37.67% if the dealer hits soft 17 — exact recursion values, conditioned on no dealer blackjack.
What is the dealer's most likely final hand with a 3?
A bust — 37.39% of rounds.