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1st Edition AD&D	-	Dragon #132	-	Dragon magazine

As a Dungeon Master, I have started a
number of campaigns over the last seven
years. Each time the players roll up new
characters, henchmen, or family members
of central characters, they ask the same
question: ?Which method are we using??

I immediately start agonizing over which
method of character generation will give
the players a fair chance of ?heroic?
scores, while not being ?Monty Hall? in
nature. To the end of helping DMs sort out
this question for themselves, this article
presents the statistical chances for rolling
each possible score (with a range of 3-18)
for each of the common character-generation
methods.

Page 11 of the Dungeon Masters Guide
offers four separate methods for rolling
up characters. Unearthed Arcana adds a
fifth alternative on page 74, though the
probabilities of rolling each score with
Method V have already been treated more
than adequately by Arthur J. Hedge III, in
his article "What are the Odds?" which
appeared in DRAGON® issue #117.

The four original methods described in
the DMG are as follows:

Method I: All scores are recorded and
arranged in the order the player desires.
Four six-sided dice are rolled and the lowest
die (or one of the lower) is discarded.

Method II: All scores are recorded and
arranged as in Method I. Three six-sided
dice are rolled 12 times and the highest six
scores are retained.

Method III: Scores rolled are according
to each ability category in this order:
strength, intelligence, wisdom, dexterity,
constitution, and charisma. Three six-sided
dice are rolled six times for each ability,
and the highest score for each category is
retained for that category.

Method IV: Three six-sided dice are
rolled to generate the six ability scores, in
order, for 12 characters. The player then
selects one set of scores and notes them
on the character record sheet.

One of the drawbacks of statistics is its
inability to adequately represent human
choice. For this reason, it is impossible to
give statistical values for the results of
Method IV, and it is excluded from this
article.

With the assistance of my computer,
Theresa (an Apple Macintosh), I have
managed to produce the following tables
for your examination. In each table,
column A represents the percent chance
of rolling a particular score exactly,
column B the chance of rolling that score
or lower, and column C the chance of
rolling that score or higher. Table I is supplied
for comparison; it shows the chance
of rolling each score with 3d6. Table II
demonstrates Method I, Table III demonstrates
Method II, and Table IV demonstrates
Method III.

All chances given as "0.00" represent a
chance under 1 in 20,000. It is worth
noting that the chance of rolling a natural
3 with Method III is 1 chance in
36,349,366,588,416.

APRIL 1988

Table I
3d6 Generation Method

Score	A	B	C
3	0.46	0.46	100.00
4	1.39	1.85	99.54
5	2.78	4.63	98.15
6	4.63	9.26	95.37
7	6.94	16.20	90.74
8	9.72	25.93	83.80
9	11.57	37.50	74.07
10	12.50	50.00	62.50
11	12.50	62.50	50.00
12	11.57	74.07	37.50
13	9.72	83.80	25.93
14	6.94	90.74	16.20
15	4.63	95.37	9.26
16	2.78	98.15	4.63
17	1.39	99.54	1.85
18	0.46	100.00	0.46

Table III
Method II

Score	A	B	C
3	0.00	0.00	100.00
4	0.00	0.00	100.00
5	0.00	0.00	100.00
6	0.00	0.00	100.00
7	0.03	0.03	100.00
8	0.34	0.37	99.97
9	2.42	2.79	99.63
10	8.33	11.12	97.21
11	17.34	28.46	88.88
12	20.55	49.01	71.54
13	19.07	68.08	50.99
14	13.65	81.73	31.92
15	9.12	90.85	18.27
16	5.55	96.40	9.15
17	2.69	99.09	3.60
18	0.91	100.00	0.91