Average Hits per Dealer Upcard
Lukas Steiner,
Willkommen! Now that I've exhausted my supply of German, let's get to your question.
Since you didn't specify, I assumed a 6D, S17 game. I ran ten 400-million-round CVData sims. Each sim involved a single player playing 6 spots of "never bust" strategy: this ensured that the dealer would always have to complete her hand. In each sim I selected a different dealer upcard and counted the number of times the dealer had the selected upcard and the number of cards in the dealer's final hand.
The data below show, given that the dealer has the indicated upcard, the percentage of the time the dealer's final hand (assuming completion) will consist of the indicated number of cards. Notice that I accounted separately for BJ's and other 2-card hands. I also assumed that the "More than 7 card" category is in fact exactly 8 cards: although this assumption is not true, it should be close enough, especially since the percentage of such hands is so small.
| Up | BJ | 2-card | 3-card | 4-card | 5-card | 6-card | 7-card | >7-card | Avg. Cards | Avg. Hits |
| A | 30.84560% | 30.87233% | 14.73108% | 16.86145% | 5.77756% | 0.84258% | 0.06600% | 0.00340% | 2.6951 | 0.6951 |
| X | 7.72238% | 53.65501% | 32.68459% | 5.48736% | 0.43408% | 0.01634% | 0.00024% | | 2.4503 | 0.4503 |
| 9 | | 53.66143% | 37.41085% | 8.02287% | 0.85462% | 0.04901% | 0.00121% | 0.00002% | 2.5622 | 0.5622 |
| 8 | | 46.24830% | 41.86122% | 10.53279% | 1.27311% | 0.08183% | 0.00271% | 0.00004% | 2.6709 | 0.6709 |
| 7 | | 38.56793% | 46.03111% | 13.36095% | 1.88772% | 0.14601% | 0.00612% | 0.00015% | 2.7903 | 0.7903 |
| 6 | | 7.72424% | 72.80686% | 16.52711% | 2.68537% | 0.24379% | 0.01227% | 0.00036% | 3.1496 | 1.1496 |
| 5 | | | 69.24764% | 26.19317% | 4.11893% | 0.41569% | 0.02372% | 0.00085% | 3.3578 | 1.3578 |
| 4 | | | 61.02336% | 32.33712% | 5.94789% | 0.64522% | 0.04468% | 0.00173% | 3.4636 | 1.4636 |
| 3 | | | 52.90631% | 37.44685% | 8.53440% | 1.02960% | 0.07890% | 0.00394% | 3.5794 | 1.5794 |
| 2 | | | 45.20803% | 41.60312% | 11.44531% | 1.60022% | 0.13562% | 0.00769% | 3.6988 | 1.6988 |
The last two columns show the average total number of cards in the dealer's hand, and the average number of hit cards, which is, after all, what you requested.
Hope this helps!
Dog Hand
