Sandcat - Comparison of dice rolling methods

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Comparison of 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.

	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	Total	Expectation
* Method 1 - roll 3d6	1	3	6	10	15	21	25	27	27	25	21	15	10	6	3	1			216	10.5
Method 2 - roll 3d6 twice, keep highest set	1	15	84	300	825	1911	3425	5103	6561	7375	7161	5655	4020	2508	1281	431			46656	12.176311728395
Method 5** - roll 4d6, drop lowest die	1	4	10	21	38	62	91	122	148	167	172	160	131	94	54	21			1296	12.244598765432
* Method DS1 - roll 5d4			1	5	15	35	65	101	135	155	155	135	101	65	35	15	5	1	1024	12.5
Method DS5 - roll 6d4, drop lowest die			1	6	21	56	120	217	341	471	575	620	583	476	330	185	75	19	4096	13.80615234375

Notes:

** 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)