Below is a graph and table showing the exact odds of a dealer's end-hand given his show card. One thing to keep in mind when playing: if the dealer is dealt a show-card of an ace and you're being asked to hit or to stand, you know that his hole card is not a ten. If it were, he'd have a blackjack, and you'd have already lost.

This graph was computed with the following rules:

• 6-deck shoe
• dealer hits on a soft 17
• zero-high-card-count (a fresh shoe)
• No charlie rule.

These are the most common house variations in low stakes games. In higher stakes you usually see house rules that favor the house less. The data was computed with this simulator. It was rendered in SAS.

Show Card 17 18 19 20 21 Blackjack Bust
10 3.44% 3.44% 3.44% 10.46% 1.07% 2.37% 6.54%
2 1.00% 1.05% 1.01% 0.97% 0.92% 0.00% 2.74%
3 0.97% 1.01% 0.97% 0.94% 0.90% 0.00% 2.90%
4 0.94% 0.96% 0.94% 0.91% 0.87% 0.00% 3.07%
5 0.91% 0.95% 0.91% 0.86% 0.84% 0.00% 3.23%
6 0.89% 0.88% 0.88% 0.85% 0.81% 0.00% 3.38%
7 2.84% 1.06% 0.60% 0.61% 0.57% 0.00% 2.01%
8 0.99% 2.77% 0.99% 0.53% 0.53% 0.00% 1.87%
9 0.93% 0.90% 2.71% 0.93% 0.47% 0.00% 1.76%
A 0.44% 1.10% 1.10% 1.10% 0.51% 2.37% 1.07%

Interesting fact: The rarest dealer-hand is getting seven aces for soft 17, and then hitting and getting a 5 for a hard 12, and then getting 5 more aces for a hard 17. The odds of this are slightly less than 0.00000000000001509%.