The probability of rolling exactly X same values (equal to y) out of the set - imagine you have a set of seven 12-sided dice, and you want to know the chance of getting exactly two 9s. If we take identical conditions ( s=6, y=3) and apply them in this example, we can see that the values 1, 2, & 3 satisfy the rules, and the probability is: P = (3

The probability of rolling all the values equal to or lower than y – this option is almost the same as the previous one, but this time we are interested only in numbers that are equal to or lower than our target.

1/6 = 2/3, and the final probability is P = (2/3) n.

We want to rolled value to be either 6, 5, 4, or 3. For example, let's say we have a regular die and y = 3. The probability of rolling all the values equal to or higher than y – the problem is similar to the previous one, but this time p is 1/s multiplied by all the possibilities which satisfy the initial condition. And if you are interested in rolling the set of any identical values - not just three 15s, but three of any number - you simply multiply the result by the total die faces: P = 0.000125 If we consider three 20-sided dice, the chance of rolling 15 on each of them is: P = (1/20) 3 = 0.000125 (or P = 1.25♱0 -4 in scientific notation). In other words, the probability P equals p to the power n, or P = p n = (1/s) n. The probability of rolling the same value on each die – while the chance of getting a particular value on a single die is p, we only need to multiply this probability by itself as many times as the number of dice.

There is a simple relationship – p = 1/s, so the probability of getting 7 on a 10-sided die is twice that of a 20-sided die. n – the number of dice, s – the number of individual die faces, p – the probability of rolling any value from a die, and P – the overall probability for the problem. We can distinguish a few, which you can see in this dice probability calculator.īefore we make any calculations, let's define some variables which we'll use in the formulas. Well, the question is more complex than it seems at first glance, but you'll soon see that the answer isn't that scary! It's all about maths and statistics.įirst of all, we have to determine what kind of dice roll probability we want to find.

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