Die Roll Stats

I have often wondered the statistical differences between 2d6 and 3d4. They both have a maximum of 12, but both the minimums and the averages are higher with 3d4. This is especially applicable for character generation. As a DM/GM/super-powerful narrator, I decide how the characters get to roll up their attributes. Do they use 3d6 like 2nd edition, or perhaps 4d6, dropping the lowest? My old method even let you reroll ones and that left you with an even higher average with more of a tendency of higher numbers.

I wrote this analyzer so you can see the differences between whatever type of rolling method you pick. I don't suggest you use a high number of dice, otherwise it will take significantly longer to generate statistics. My machine bombs out at about 10 dice.

Sample rolls for character generation: 3d6, 4d4 + 2, 6d3, 4d6, drop lowest, 4d6, reroll 1s, drop lowest (really it rolls 4d5 and adds 1, but that's effectively the same), 3d6, drop the highest (penalty of some sort).

Dice Roll String:

Feel free to try out your own die rolling strings, like "5d4 + 3" or "6d8". The "d" must be lowercase. To drop the lowest x dice, use an uppercase D, like "4d6D1" means to roll 4d6 and drop the lowest 1 die.

Besides the links above, I have also seen these ideas:

  • 4d6, drop lowest, reroll if max < 14 or reroll if the sum of the modifiers is < 1
  • 5d6D2 (5d6, drop the two lowest rolls)
  • Roll up 12 characters using the 3d6 method, then pick the best character
  • Roll 3d6 six times, then pick the best result. Roll each attribute in order – do not assign numbers to stats as you see fit.
  • Roll a pool of 12 scores using 3d6, pick the best 6 scores.

I have also been contacted about making some stats that would be useful for Legend of the Five Rings (L5R). In there, you have a stat and a skill. when you roll against that, you keep a number of 10-sided dice equal to your stat. You can also "roll up" by rolling again when you roll a ten and adding the new roll to the ten. You can continue rolling up as long as you keep rolling tens.

I wrote up a small c program to only do the rolling of 1-10 10 sided dice and keeping just the highest digit, then averaging the rolls. Let me know if you would like alternate die roll stats and I will see what I can do to help out.

  1. Rolling 1d10, keeping the highest: average roll of 5.5
  2. Rolling 2d10, keeping the highest: average roll of 7.15
  3. Rolling 3d10, keeping the highest: average roll of 7.975
  4. Rolling 4d10, keeping the highest: average roll of 8.4667
  5. Rolling 5d10, keeping the highest: average roll of 8.79175
  6. Rolling 6d10, keeping the highest: average roll of 9.021595
  7. Rolling 7d10, keeping the highest: average roll of 9.1919575
  8. Rolling 8d10, keeping the highest: average roll of 9.32268667
  9. Rolling 9d10, keeping the highest: average roll of 9.425695015
  10. Rolling 10d10, keeping the highest: average roll of 9.5085658075
A pigeon's feathers are heaver than its bones. Tyler Akins <>
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