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:
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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.84% | 31.37% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.84% | 31.37% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.77% | 31.07% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.77% | 31.07% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.73% | 30.92% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.73% | 30.92% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.72% | 30.87% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.72% | 30.87% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.71% | 30.84% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.71% | 30.84% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.69% | 30.77% |
| Busto | 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 | As |
| BJ | — | — | — | — | — | — | — | — | 7.69% | 30.77% |
| Busto | 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% |
También he encontrado valores diferentes para el caso de un número infinito de barajas y que el crupier se pare en las 17.
Tenga en cuenta que todas las columnas deben sumar 100 %. Pero esto no es cierto para las dos últimas columnas (dieces y ases) del diagrama. Tengo valores idénticos para las columnas 2 a 9 pero diferentes para el 10 y el as.
Por lo visto no has leído la descripción al principio de la página. Las columnas de As y Diez son después de que el crupier haya comprobado si hay blackjack y no lo tenga. Ese método es mucho más útil para la mayoría de los propósitos que incluir el blackjack en los totales normales.
Hola,
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]