Blackjack Dealer Outcome Probabilities
The dealer outcome probability charts on this page can be helpful in determining which of two tournament strategies is preferable. The values in these charts were calculated using a combinatorial analysis from a full deck after removing only the dealer’s upcard.
How to use the charts:
First, choose the game of interest:
- 1 Deck, Dealer stands on all 17s
- 1 Deck, Dealer hits soft 17
- 2 Decks, Dealer stands on all 17s
- 2 Decks, Dealer hits soft 17
- 4 Decks, Dealer stands on all 17s
- 4 Decks, Dealer hits soft 17
- 6 Decks, Dealer stands on all 17s
- 6 Decks, Dealer hits soft 17
- 8 Decks, Dealer stands on all 17s
- 8 Decks, Dealer hits soft 17
- Infinite Deck, Dealer stands on all 17s
- Infinite Deck, Dealer hits soft 17
Then look up the dealer upcard across the top, and read down the column to see the probability of each dealer outcome.
The probabilities of each outcome other than Blackjack assume that the dealer has checked the hole card and did not have blackjack. (Therefore, the columns under dealer Ten and dealer Ace add up to more than 100%. The rows other than blackjack add up to 100%.)
For example, in a 1D S17 game, if the dealer shows a Ten card up, he’ll have a blackjack 7.84% of the time. Now, after he checks and does not have blackjack, he’ll make a final total of twenty 35.69% of the time.
| Single Deck: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.84% | 31.37% |
| Bust | 35.30% | 37.56% | 40.28% | 42.89% | 42.08% | 25.99% | 23.86% | 23.34% | 23.25% | 16.98% |
| 17 | 13.90% | 13.03% | 13.10% | 11.97% | 16.69% | 37.23% | 13.09% | 12.19% | 12.42% | 18.38% |
| 18 | 13.18% | 13.09% | 11.42% | 12.35% | 10.65% | 13.86% | 36.30% | 10.39% | 12.25% | 19.09% |
| 19 | 13.18% | 12.38% | 12.07% | 11.69% | 10.72% | 7.73% | 12.94% | 35.74% | 12.44% | 18.87% |
| 20 | 12.39% | 12.33% | 11.63% | 10.47% | 10.07% | 7.89% | 6.83% | 12.23% | 35.69% | 19.17% |
| 21 | 12.05% | 11.60% | 11.51% | 10.63% | 9.79% | 7.30% | 6.98% | 6.11% | 3.96% | 7.51% |
| Single Deck: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.84% | 31.37% |
| Bust | 35.63% | 37.81% | 40.58% | 43.00% | 43.78% | 25.99% | 23.86% | 23.34% | 23.25% | 20.46% |
| 17 | 12.98% | 12.35% | 12.28% | 11.67% | 11.61% | 37.23% | 13.09% | 12.19% | 12.42% | 8.18% |
| 18 | 13.31% | 13.19% | 11.54% | 12.38% | 11.38% | 13.86% | 36.30% | 10.39% | 12.25% | 20.54% |
| 19 | 13.32% | 12.50% | 12.19% | 11.74% | 11.61% | 7.73% | 12.94% | 35.74% | 12.44% | 20.62% |
| 20 | 12.56% | 12.42% | 11.78% | 10.52% | 10.96% | 7.89% | 6.83% | 12.23% | 35.69% | 20.95% |
| 21 | 12.20% | 11.73% | 11.63% | 10.69% | 10.67% | 7.30% | 6.98% | 6.11% | 3.96% | 9.26% |
| Double Deck: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.77% | 31.07% |
| Bust | 35.33% | 37.48% | 39.85% | 42.25% | 42.21% | 26.11% | 24.16% | 23.09% | 23.11% | 16.81% |
| 17 | 13.94% | 13.28% | 13.07% | 12.10% | 16.62% | 37.05% | 12.97% | 12.09% | 12.24% | 18.64% |
| 18 | 13.33% | 13.07% | 12.02% | 12.28% | 10.62% | 13.82% | 36.12% | 11.20% | 12.16% | 18.99% |
| 19 | 13.07% | 12.46% | 12.10% | 11.73% | 10.67% | 7.80% | 12.90% | 35.41% | 12.25% | 18.89% |
| 20 | 12.40% | 12.18% | 11.64% | 10.90% | 10.12% | 7.88% | 6.89% | 12.11% | 36.39% | 19.03% |
| 21 | 11.93% | 11.54% | 11.31% | 10.73% | 9.75% | 7.34% | 6.96% | 6.10% | 3.84% | 7.65% |
| Double Deck: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.77% | 31.07% |
| Bust | 35.65% | 37.75% | 40.13% | 42.37% | 43.88% | 26.11% | 24.16% | 23.09% | 23.11% | 20.26% |
| 17 | 12.99% | 12.50% | 12.26% | 11.75% | 11.55% | 37.05% | 12.97% | 12.09% | 12.24% | 8.24% |
| 18 | 13.48% | 13.19% | 12.15% | 12.33% | 11.42% | 13.82% | 36.12% | 11.20% | 12.16% | 20.61% |
| 19 | 13.22% | 12.59% | 12.23% | 11.79% | 11.55% | 7.80% | 12.90% | 35.41% | 12.25% | 20.65% |
| 20 | 12.56% | 12.30% | 11.78% | 10.96% | 11.00% | 7.88% | 6.89% | 12.11% | 36.39% | 20.81% |
| 21 | 12.08% | 11.68% | 11.45% | 10.79% | 10.62% | 7.34% | 6.96% | 6.10% | 3.84% | 9.43% |
| 4 Decks: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.73% | 30.92% |
| Bust | 35.34% | 37.43% | 39.65% | 41.94% | 42.27% | 26.17% | 24.32% | 22.97% | 23.05% | 16.73% |
| 17 | 13.96% | 13.39% | 13.06% | 12.16% | 16.58% | 36.95% | 12.91% | 12.05% | 12.16% | 18.76% |
| 18 | 13.41% | 13.06% | 12.31% | 12.25% | 10.62% | 13.80% | 36.03% | 11.60% | 12.12% | 18.94% |
| 19 | 13.02% | 12.51% | 12.12% | 11.75% | 10.65% | 7.83% | 12.88% | 35.24% | 12.16% | 18.89% |
| 20 | 12.40% | 12.11% | 11.64% | 11.11% | 10.15% | 7.87% | 6.91% | 12.06% | 36.73% | 18.96% |
| 21 | 11.86% | 11.50% | 11.22% | 10.78% | 9.73% | 7.37% | 6.95% | 6.09% | 3.79% | 7.72% |
| 4 Decks: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.73% | 30.92% |
| Bust | 35.66% | 37.71% | 39.92% | 42.06% | 43.91% | 26.17% | 24.32% | 22.97% | 23.05% | 20.16% |
| 17 | 13.00% | 12.57% | 12.25% | 11.80% | 11.52% | 36.95% | 12.91% | 12.05% | 12.16% | 8.27% |
| 18 | 13.57% | 13.19% | 12.44% | 12.31% | 11.45% | 13.80% | 36.03% | 11.60% | 12.12% | 20.65% |
| 19 | 13.18% | 12.65% | 12.26% | 11.81% | 11.51% | 7.83% | 12.88% | 35.24% | 12.16% | 20.67% |
| 20 | 12.57% | 12.24% | 11.78% | 11.17% | 11.01% | 7.87% | 6.91% | 12.06% | 36.73% | 20.75% |
| 21 | 12.02% | 11.65% | 11.35% | 10.84% | 10.60% | 7.37% | 6.95% | 6.09% | 3.79% | 9.50% |
| 6 Decks: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.72% | 30.87% |
| Bust | 35.35% | 37.42% | 39.58% | 41.84% | 42.28% | 26.19% | 24.37% | 22.92% | 23.02% | 16.70% |
| 17 | 13.97% | 13.43% | 13.06% | 12.18% | 16.57% | 36.92% | 12.89% | 12.03% | 12.13% | 18.81% |
| 18 | 13.44% | 13.05% | 12.41% | 12.24% | 10.62% | 13.79% | 36.00% | 11.73% | 12.10% | 18.92% |
| 19 | 13.00% | 12.52% | 12.13% | 11.76% | 10.64% | 7.84% | 12.87% | 35.19% | 12.13% | 18.89% |
| 20 | 12.40% | 12.08% | 11.64% | 11.18% | 10.16% | 7.87% | 6.92% | 12.04% | 36.84% | 18.94% |
| 21 | 11.84% | 11.49% | 11.19% | 10.79% | 9.73% | 7.38% | 6.95% | 6.09% | 3.77% | 7.74% |
| 6 Decks: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.72% | 30.87% |
| Bust | 35.67% | 37.70% | 39.85% | 41.96% | 43.93% | 26.19% | 24.37% | 22.92% | 23.02% | 20.13% |
| 17 | 13.01% | 12.59% | 12.25% | 11.81% | 11.51% | 36.92% | 12.89% | 12.03% | 12.13% | 8.28% |
| 18 | 13.60% | 13.19% | 12.54% | 12.30% | 11.46% | 13.79% | 36.00% | 11.73% | 12.10% | 20.66% |
| 19 | 13.16% | 12.67% | 12.26% | 11.82% | 11.50% | 7.84% | 12.87% | 35.19% | 12.13% | 20.68% |
| 20 | 12.57% | 12.22% | 11.78% | 11.24% | 11.02% | 7.87% | 6.92% | 12.04% | 36.84% | 20.73% |
| 21 | 12.00% | 11.64% | 11.32% | 10.86% | 10.59% | 7.38% | 6.95% | 6.09% | 3.77% | 9.53% |
| 8 Decks: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.71% | 30.84% |
| Bust | 35.35% | 37.41% | 39.55% | 41.79% | 42.29% | 26.20% | 24.40% | 22.90% | 23.01% | 16.69% |
| 17 | 13.97% | 13.45% | 13.05% | 12.19% | 16.56% | 36.90% | 12.88% | 12.02% | 12.11% | 18.83% |
| 18 | 13.45% | 13.05% | 12.45% | 12.24% | 10.62% | 13.79% | 35.98% | 11.80% | 12.09% | 18.92% |
| 19 | 12.99% | 12.53% | 12.13% | 11.76% | 10.64% | 7.85% | 12.87% | 35.16% | 12.12% | 18.89% |
| 20 | 12.40% | 12.07% | 11.65% | 11.21% | 10.16% | 7.87% | 6.93% | 12.03% | 36.90% | 18.93% |
| 21 | 11.83% | 11.49% | 11.17% | 10.80% | 9.72% | 7.39% | 6.95% | 6.09% | 3.76% | 7.75% |
| 8 Decks: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.71% | 30.84% |
| Bust | 35.67% | 37.69% | 39.81% | 41.91% | 43.93% | 26.20% | 24.40% | 22.90% | 23.01% | 20.11% |
| 17 | 13.01% | 12.60% | 12.24% | 11.82% | 11.50% | 36.90% | 12.88% | 12.02% | 12.11% | 8.29% |
| 18 | 13.61% | 13.19% | 12.59% | 12.30% | 11.46% | 13.79% | 35.98% | 11.80% | 12.09% | 20.67% |
| 19 | 13.15% | 12.68% | 12.27% | 11.83% | 11.50% | 7.85% | 12.87% | 35.16% | 12.12% | 20.68% |
| 20 | 12.57% | 12.21% | 11.78% | 11.28% | 11.02% | 7.87% | 6.93% | 12.03% | 36.90% | 20.72% |
| 21 | 11.99% | 11.63% | 11.31% | 10.87% | 10.58% | 7.39% | 6.95% | 6.09% | 3.76% | 9.54% |
| Infinite Deck: Dealer stands on all 17s | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.69% | 30.77% |
| Bust | 35.36% | 37.39% | 39.45% | 41.64% | 42.32% | 26.23% | 24.47% | 22.84% | 22.98% | 16.65% |
| 17 | 13.98% | 13.50% | 13.05% | 12.23% | 16.54% | 36.86% | 12.86% | 12.00% | 12.07% | 18.89% |
| 18 | 13.49% | 13.05% | 12.59% | 12.23% | 10.63% | 13.78% | 35.93% | 12.00% | 12.07% | 18.89% |
| 19 | 12.97% | 12.56% | 12.14% | 11.77% | 10.63% | 7.86% | 12.86% | 35.08% | 12.07% | 18.89% |
| 20 | 12.40% | 12.03% | 11.65% | 11.31% | 10.17% | 7.86% | 6.94% | 12.00% | 37.07% | 18.89% |
| 21 | 11.80% | 11.47% | 11.12% | 10.82% | 9.72% | 7.41% | 6.94% | 6.08% | 3.74% | 7.78% |
| Infinite Deck: Dealer hits soft 17 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Outcome | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Ten | Ace |
| BJ | — | — | — | — | — | — | — | — | 7.69% | 30.77% |
| Bust | 35.67% | 37.67% | 39.71% | 41.77% | 43.95% | 26.23% | 24.47% | 22.84% | 22.98% | 20.07% |
| 17 | 13.01% | 12.63% | 12.24% | 11.84% | 11.48% | 36.86% | 12.86% | 12.00% | 12.07% | 8.30% |
| 18 | 13.65% | 13.20% | 12.73% | 12.29% | 11.48% | 13.78% | 35.93% | 12.00% | 12.07% | 20.69% |
| 19 | 13.13% | 12.71% | 12.28% | 11.84% | 11.48% | 7.86% | 12.86% | 35.08% | 12.07% | 20.69% |
| 20 | 12.57% | 12.18% | 11.79% | 11.38% | 11.03% | 7.86% | 6.94% | 12.00% | 37.07% | 20.69% |
| 21 | 11.96% | 11.62% | 11.26% | 10.89% | 10.57% | 7.41% | 6.94% | 6.08% | 3.74% | 9.57% |
I found different values for the case of infinite number of decks and dealer stand’s on all 17, too.
Please note, that all columns should yield 100 % in sum. But this is not true for the last two colums (tens and aces) of the diagram! I’ve got identical values for the columns 2 to 9 but different ones for 10 and ace.
Apparently you did not read the description at the top of the page. The Ace and Ten columns are after the dealer has checked for blackjack and did not have it. That method is far more useful for most purposes than including blackjack in the normal totals.
Hi,
I’ve worked out the odds of busting (given infinite decks and dealer stands on all 17s) and some of my figures differ to yours. I’m very confident mine are correct, I can send you my excel calculations to scrutinise if you like.
These are my results for dealer busting chances:
10 21.21%
9 22.84%
8 24.47%
7 26.23%
6 42.32%
5 41.64%
4 38.92%
3 36.17%
2 33.42%
A 11.53%
No, something is wrong with your calculations. Your numbers agree with mine for dealer upcards of 5,6,7,8, and 9, but are too low on all the other upcards.
If you want a second place to compare, see this thread and download the spreadsheet there:
https://www.blackjackinfo.com/knowledge-base/blackjack-theory-and-math/distribution-of-dealer-hands/
I need your excel calculations for my project.
Can you mail it to me?
mail: [email protected]