Basically, if you are like most people who are competitive, you are always looking to improve your score in any game. In this particular instance, you are looking to improve your Yahtzee score. The way to do so is to play as close as possible to the optimal strategy as you can get.

In mathematical terms, “optimal strategy” is the method of play that maximizes the expected score for a game. In a player’s terms, it is simply the best way to play that tells you the correct play for every possible position in the game. If properly instructed, a computer can already do this, and would eventually play a perfect game of Yahtzee. However, there are two problems with this. The first is time. Even the most sophisticated computers can’t play fast enough to crunch the numbers in anything approaching a reasonable time period. The second problem is that even if a computer did play a perfect game, would you even realize it? Since in Yahtzee we do not know in advance what we are actually trying to accomplish, it is hard to know the outcome we are going to get.

In order to get the optimal strategy for Yahtzee, each possible position in every single path of the game that it could take would have to be considered. Yet the greatest counting tool, the computer, wouldn’t even be effective enough to do this. That means that there is only one way to do this. The number of necessary calculations has to be reduced to a more reasonable figure. Basically you have to analyze the game in reverse. By actually starting at the point where all the score boxes have been filled and working back in time towards the first roll it is possible for perfect choices to be made when faced with any decision encountered during a Yahtzee game. This is called “dynamic programming” which thankfully has already been done by the experts in the game of Yahtzee. Otherwise, it would take you about 50,000 hours of non-stop work to figure it out.

The end result of all this mathematics and computations is that with optimal play your expected score in order to achieve an optimal game would be 254.6 points. There are no approximations in this number. No matter where you are in the game or what the current state of your score card, the perfect play can always be determined. It is truly the precise recipe for playing each and every hand in every imaginable situation.

The value of 254.6 points is also important. Knowing that it comes about by playing optimally means that there is no possible way that your average score in the long run can ever exceed 254.6. If someone claims to have an average score of 300, either they haven’t played many games or they are a little prone to exaggeration.