Yahtzee seems to be an easy game, but if you want to play it at a professional level, it isn’t what it looks at a first glance. In this document I assume you are already familiar with the game. If you are not, please read this first.
Note: for better understanding we will call “boxes” the different options you can store your combinations into: Ones, Twos, Threes, Fours, Fives, Sixes, Three of a kind, Four of a Kind, Full House, Small Straight, Large Straight, Yahtzee, Chance.
There are mainly three key elements one should understand when playing this game:
A. If there are rolls left in the actual turn: which dice does he/she has to save/fix before the next roll in order to get the best combination at the end of the turn?
B. If there are no more rolls in the actual turn: which available box is the best for the current combination?
C. How can we take into account the upper section bonus and the extra Yahtzee bonus?
If you can answer these three questions, you are a top Yahtzee player.
I worked for about half a year on a program which plays Yahtzee and finally, I managed to build a program which calculated in about one day the exact theoretical outcome of the game. During this calculation the program built a database with all necessary data to play the game. As a result, the Professinoal Yahtzee player was created and all three questions above had been answered both from theoretical and statistical point of view.
Please note that the method of calculation was not that the program played random games and generated the results, but the exact probabilities and probabilistic values were calculated.
The final program (P-Yahtzee professional) is a perfect game player. From statistical point of view there is no possibility to play this game better on a long term. The P-Yahtzee professional advises you during game play where to place your dice combination in order to obtain the maximum possible points (Hint window).
For the reasons mentioned above, I consider now the Yahtzee game solved.
Would you like to understand the answers to the questions above? Read the theory & steps described here.