🎲 Dice Probability

A dice pool has sides^dice outcomes — 10d20 is 10¹³, all countable exactly with integer arithmetic, which is what this page does: convolve one die at a time and read off the counts. No randomness, no simulation error, and the percentages are true fractions of the count, so the answer cannot change between visits. The mean and most-likely total come out of the same table.

Why the curve peaks where it does

A total is not an outcome — it is a set of outcomes, and the middle of the range has the most ways to be built: 7 on 2d6 arrives six ways (1+6 through 6+1) while 2 and 12 arrive once each, so the counts form a triangle that rounds toward a bell as dice pile up (the central limit theorem, arriving at a board-game table). The “at least” column is what game rules usually need: P(≥ 7) on 2d6 is 21/36 = 58.33%, not 50%, because the peak itself counts — the same asymmetry that makes 7 both the most-rolled total and the number gamblers pay you to avoid.

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