Dungeons and Dragons Roll Distributions

A Long Time Ago . . .

Rolling stats for D&D characters can be a trying time for a Dungeon Master. If too stringent of rules are applied to the rolling of dice, characters will be weak and players unhappy. However, if rules are too lax, the characters are overpowered and unrealistic (even for fantasy gaming).

Never again will a DM have to second-guess his decisions for die-rolling tactics! The charts below give probability distributions for six popular roll strategies.

When I calculated these in middle school, I was so proud of my little C program. For the sake of nostalgia, I keep the results online. Shockingly, this page gets at least a hit per day.

Purple:6 x 3d6
Gray:6 x 3d6, reroll 1s
Purple-blue:6 x (4d6, drop lowest)
Blue:7 x 3d6, reroll 1s, drop lowest
Green:7 x (4d6, drop lowest), drop lowest
Red:7 x (4d6, drop lowest, drop 1s)

D&D character stats roll probability distribution

D&D character stats roll cumulative probability distribution

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