Optimal Strategy for the 12 / 10 position in Jail Blackjack
| ----- | 12 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | ----- | ----- | 6/11 | 2/11 | ----- | ----- | ----- | ----- | ----- | ----- | ----- | 3/11 |
| 0 | 6/11 | 8/11 | 2/3 | 0.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 2/11 | 2/3 | 0.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | ----- | 0.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
| 3 | 3/11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 4 | ----- | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| 5 | ----- | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 6 | ----- | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 7 | ----- | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | ----- | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 9 | ----- | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | ----- | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Explanatory notes:
First row - possible moves by the 1st player (blue).
First column - possible moves by the 2nd player (blue).
Second row - probability of the 1st player making the corresponding move, under the optimal strategy (yellow).
Second column - probability of the 2nd player making the corresponding move, under the optimal strategy (yellow).
The matrix elements - the value of the corresponding outcome for the 2nd player. Naturally, the value of the outcome corresponding to "0" moves by both players is the value of the position itself.