12-sided dice (pack of 12)

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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. Everybody knows what a regular 6-sided die is, and, most likely, many of you have already played thousands of games where t used one (or more) But, did you know that there are different types of die? Out of the countless possibilities, the most popular dice are included in the Dungeons & Dragons dice set, which contains seven different polyhedral dice:

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. For example, let's say we have a regular die and y = 3. We want to rolled value to be either 6, 5, 4, or 3. The variable p is then 4 · 1/6 = 2/3, and the final probability is P = (2/3) n. P(r,n,s) = \frac{1}{s 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. It's somehow different than previously because only a part of the whole set has to match the conditions. This is where the binomial probability comes in handy. The binomial probability formula is: The dice probability calculator is a great tool if you want to estimate the dice roll probability over numerous variants. There are many different polyhedral dice included, so you can explore the likelihood of a 20-sided die as well as that of a regular cubic die. The probability of rolling at least X same values (equal to y) out of the set — the problem is very similar to the prior one, but this time the outcome is the sum of the probabilities for X=2, 3, 4, 5, 6, 7. Moving to the numbers, we have: P = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) = 0.11006 = 11.006%. As you may expect, the result is a little higher. Sometimes the precise wording of the problem will increase your chances of success.Before we make any calculations, let's define some variables which we'll use in the formulas. 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. 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. First of all, we have to determine what kind of dice roll probability we want to find. We can distinguish a few, which you can see in this dice probability calculator.

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. 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 · 1/6) n = (1/2) n. P ( r , n , s ) = 1 s n ∑ k = 0 ⌊ ( r − n ) / s ⌋ ( − 1 ) k ( n k ) ( r − s ⋅ k − 1 n − 1 ) \scriptsize 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. In other words, the probability P equals p to the power n, or P = p n = (1/s) n. 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 = 1.25·10 -4 in scientific notation). 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 · 20 = 0.0025.