Dice are the backbone of D&D. In theory, the game could be played without dice, but combat and the such would then depend solely on the DM's discretion. Dice come with a numerous amount of sides. There are d4, d6, d8, d10, d12, and d20. There are other sized dice sets, but they are not used in standard D&D games. The D&D system of dice-rolling is call d20. D20 is the most frequently rolled dice (followed by d6), which is used for combat, skill rolls, and all other checks. The twenty sides adds increased variability in the rolls.
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