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Dice rolling methods

This little examination was done to compare character creation methods from AD&D 2nd edition. However, playing 3rd ed. or 3.5 does not prevent you from using these good old methods - they still work.

The table below shows how many ways there are to throw each number for each method.
DS1 and DS5 are method I and method V from DarkSun.

 34567891011121314151617181920 TotalExpectation
* Method 1 - roll 3d613610152125272725211510631   21610.5
Method 2 - roll 3d6 twice, keep highest set115843008251911342551036561737571615655402025081281431   4665612.176311728395
** Method 5 - roll 4d6, drop lowest die141021386291122148167172160131945421   129612.244598765432
* Method DS1 - roll 5d4  1515356510113515515513510165351551 102412.5
Method DS5 - roll 6d4, drop lowest die  1621561202173414715756205834763301857519 409613.80615234375



  • ** Method 5 is the standard character creation method in D&D 3.x

  • Since most of these methods skew the probability curve, including the standard deviation is pointless
  • * denotes symmetrical probability curve (all others are skewed)
  • A red background denotes the maximum (ways to roll this number) for that method. Obviously, you'll roll these numbers the most.
  • Those with symmetry are symmetric around the red background
  • Method 5 is skewed in favor of lower values (compare the values surrounding the red background)(!!!!)
  • Methods 2 and DS5 are skewed in favor of higher values(!!)

see all probability curves (one graph per curve)

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