It is time to check whether the dice is unbiased or not. Now, with the help of the online game, we can determine the performance of the algorithm for throwing a dice by computing the sum of rolling two dice.
In the article on “Possible Outcomes of Rolling Two Dice“, we studied the probability for rolling a certain number or moving a certain distance. Even though this analysis is extremely interesting in a Backgammon game, it is not useful to check if a dice is unbiased or not. Instead, here we will compute the sum of two dice and determine the probability of each number. Thus, the sum of two dice must satisfy the following conditions:
- It has a value between 2 and 12
- The value with the highest probability is 7
- The values with the second highest probability are 6 and 5, etc
Therefore, when we plot the probability of each number versus the number we expect to get a triangle. The vertex of that triangle is at number 7.
In the following chart, we plot the theoretical value (black line), and the one from the online games. If these two lines concise, the dice is unbiased, and we can not complain that it favors one or the other player.