The best thing about Yahtzee is that every game is different. No matter what you do you will never play the same game twice. A lot of that has to do with the statistics of the game. It just means that there are numbers and some odds involved in this game, although you certainly don’t have to memorize them. However, they do give you a better understanding of the underlying complexity of the game that seems so simply when you play it.

Let’s start with the roll of the dice. When you roll five dice, you will see many different outcomes. Mathematicians call each of these outcomes a “combination.” A combination is a grouping of elements in which order does not matter. If we wanted to, we could list all of the possible combinations of the dice, but since there are 252 distinct combinations that may be rolled with five dice, let’s just say that it would talk a while! Basically the combinations would range from 1-1-1-1-1 to 6-6-6-6-6.

Not all of these combinations are equally likely though. For example, if you look at the last two combinations 5-6-6-6-6 and 6-6-6-6-6, you may think that the Yahtzee is harder to get and therefore less likely. If you think that then you would be correct. The fact is to get a Yahtzee you would have to roll each of the same number, and in this example it would be a 6. On the other hand, 5-6-6-6-6 has five possible ways of occurring. One way is for one die to be a 5 and the rest to be the 6’s. Another way is for the second die to be a 5 and the rest 6’s, and so on until you have five ways of rolling that combination. So, for a roll of five dice, the hand of 5-6-6-6-6 is in fact five times more likely than the hand of 6-6-6-6-6.

Essentially you are saying that the hand of 5-6-6-6-6 has five times the weight of 6-6-6-6-6. A weight can be similarly be assigned to each of the other 252 combinations. For example, a hand of 1-2-3-4-5 is 120 times more likely as a hand of 6-6-6-6-6 and so forth.

Again, this may sound confusing to you, but it is actually just common sense. If you have more numbers you can roll then you have more chances to roll them. That is why it seems so easy to fill up the Upper Section of the score card as compared to the Lower Section.