2d5

2d5 refers to rolling two five-sided dice and adding the results. Each die is a fair polyhedral die with faces labeled 1 through 5. Five-sided dice exist in various shapes, commonly pentagonal trapezohedra, and they are used in some tabletop games and probability exercises. While not as ubiquitous as 2d6, 2d5 is a valid and used dice combination in systems that employ d5s or need a small, non-uniform range of outcomes.

The possible sums with two fair d5s range from 2 to 10. The number of combinations that yield each sum forms a symmetric, triangular distribution: 2 and 10 can occur in 1 way each, 3 and 9 in 2 ways each, 4 and 8 in 3 ways each, 5 and 7 in 4 ways each, and 6 in 5 ways. Therefore, with fair dice, the probability of each sum equals its count out of 25 (the total number of outcomes). The probabilities are 1/25 for 2 or 10, 2/25 for 3 or 9, 3/25 for 4 or 8, 4/25 for 5 or 7, and 5/25 for 6.

Statistical properties: the expected value (mean) of a single d5 is 3, so the expected sum of two independent d5 rolls is 6. The variance of a single d5 is 2, so the variance of the sum is 4, with a standard deviation of 2. The distribution is symmetric around 6 and forms a simple, unimodal shape.

In practice, 2d5 is used in some game systems and probability demonstrations where a modest, non-uniform range of outcomes is desired, or where two d5 dice are readily available.