Dice Roller

Each die gets its own independent random draw between 1 and the number of sides selected, generated fresh every time you roll -- there's no seeding or pattern carried over between dice or between separate rolls, so results are not reproducible and every roll is a genuinely new random outcome. Rolling the same dice configuration twice in a row will typically produce two different results, exactly as physical dice would.

The theoretical average for any single die is the midpoint of its face values -- 3.5 for a d6, 10.5 for a d20 -- and multiplying that by the number of dice gives the expected sum for a multi-dice roll. The actual possible range is much wider than that average suggests, though: two d6 dice can land anywhere from 2 (both dice show 1) to 12 (both show 6), even though the expected average sum is 7.

Only the final total -- the modifier is applied as a flat addition or subtraction after all the individual dice have already been rolled and summed, so it shifts every possible outcome by the same fixed amount without changing which values are more or less likely to come up on the dice themselves. A +5 modifier on 2d6 shifts the possible total range from 2-12 up to 7-17, but the underlying probability shape (more likely to land in the middle than at the extremes) stays the same.

Yes -- this calculator caps the number of dice at 100 per roll. That's a practical display and performance limit rather than a probability rule; there's nothing mathematically special about 100 dice, it's simply capped to keep the individual-rolls display and calculation manageable for a single roll.