The game Yahtzee is a dice game. The main objective is to score points by rolling five dice to make combinations.
From a mathematical perspective, the probability of making certain combinations guarantees success in the game. First, we can find the total number of combinations in the game, the image below shows them
Each fraction on the right represents the probability of each combination. Notice that there are just 7 ways to score out of 7776 possible combinations from the 5 dice.
An interesting probability fact is that there is 7056/7776 chance to get a pair or better on your first hand, which is equivalent to 90.74% (really high chance). However, the least probability to get a Yahtzee which has a score of 50 points.
In this way, the chances of getting a Yahtzee increase if we role again, and again, and again, because according to experimental probability theory, the repetition of the event increases the chances of success. The chart below shows this pattern.
As you can observe, in the first attempt, there's almost zero chance of getting a Yahtzee, but if we keep trying then that probability increases. After the 20th attempt, we start to get around 90% chances to get a Yahtzee.
Therefore, according to the probability theory, in order to get a Yahtzee, we must roll several times to increase our chances.