In order to solve this question I developed a program which calculated the best combination of the dice to be saved for each combination of the following items:
- Current combination of dice (ex. 1,3,5,5,6) = what rolled the player last.
- Current combination of unused boxes (ex, Ones & Sixes & Chance) = possible choices.
- Number of rolls left in the current turn (2 or 1).
- Points/score already achieved in the Upper Section.
- Current status of the Yahtzee box (U, Y, 0).
The result is really a huge database which contains pre-calculated “best combination of the dice to be saved” for each game stage. With this database the P-Yahtzee professional became a very strong player, achieving an average score of 254.33 points, very close to the theoretical 254.40 value!
See here two examples what is best to save before the next roll.
When playing with P-Yahtzee against the computer you will notice that the program changes quite frequently the saved dice after the first and second roll.