4d4

4d4 is a dice notation indicating that four four-sided dice should be rolled and their results added together. Each four-sided die has faces numbered 1 through 4. The notation is commonly used in tabletop role-playing games and other gaming contexts to generate small to moderate random totals.

The total from four d4s can range from 4 to 16. The expected value (mean) of the sum is 10, since each die has an expected value of 2.5 and the dice are independent. The variance of a single d4 is (4^2 − 1)/12 = 15/12 = 1.25, so the sum’s variance is 5 and the standard deviation is about 2.24. The distribution is symmetric around 10 and is unimodal, with the center near 10 being the most probable.

There are 4^4 = 256 equally likely outcomes across the four dice, and the probability of any particular total is the number of outcome combinations that yield that total divided by 256.

Variations and notes: Some game systems modify dice behavior (exploding dice, re-rolls) but 4d4 in standard form refers to a straightforward sum of four d4s. The notation is part of a broader dice-notation convention such as Xdy, used to denote rolling an integer number of dice with a specified number of faces.