With the introduction of Unearthed
Arcana, AD&D® game players were presented
with a new way to generate player
characters. One now selects the class of
the character first and then rolls a number
of six-sided dice for each ability, as
indicated by the chart accompanying
Method V on page 74. The probability of
rolling a given number is no longer given
by a standard bell curve and is not simple
to calculate. The DM needs to
have a better idea of what he is giving the
players by allowing this system to be used.
This article presents a set of tables listing
the various probabilities involved with this
new method of character generation.

A new notation is given here for rolling
a group of dice. When a number between
3 and 18 is generated using nine six-sided
dice, I suggest using the notation ?9d6s3?
instead of ?9d6.? The first digit represents
the number of dice to be rolled, the second
digit represents the type of die to be
used, and the third digit represents the
number of dice to be added together by
selecting the highest rolled numbers. In
the tables given here, the "Total" figure
refers to the number of different possible
rolls; the ?Times? column refers to the
number of times that particular number is
generated; and, the ?Probability? column
refers to the probability of generating that
particular number, given that a 100%
chance equals a probability figure of 1.

These tables were generated on a DEC
VAX computer system using a program
written in C. Good luck rolling those 18s!

Table 1: 3d6s3 (Total 216)

Number	Times	Probability
3	1	0.00462963
4	3	0.01388889
5	6	0.02777778
6	10	0.04629629
7	15	0.06944445
8	21	0.09722222
9	25	0.11574074
10	27	0.12500000
11	27	0.12500000
12	25	0.11574074
13	21	0.09722222
14	15	0.06944445
15	10	0.04629629
16	6	0.02777778
17	3	0.01388889
18	1	0.00462963

Table 2: 4d6s3 (Total 1,296)

Number	Times	Probability
3	1	0.00077160
4	4	0.00308642
5	10	0.00771605
6	21	0.01620370
7	38	0.02932099
8	62	0.04783951
9	91	0.07021605
10	122	0.09413581
11	148	0.11419753
12	167	0.12885803
13	172	0.13271604
14	160	0.12345679
15	131	0.10108025
16	94	0.07253087
17	54	0.04166667
18	21	0.01620370

Table 3: 5d6s3 (Total 7,776)

Number	Times	Probability
3	1	0.00012860
4	5	0.00064300
5	15	0.00192901
6	41	0.00527623
7	90	0.01157407
8	170	0.02186214
9	296	0.03806584
10	470	0.06044239
11	665	0.08551954
12	881	0.11329733
13	1055	0.13567387
14	1155	0.14853396
15	1111	0.14287551
16	935	0.12024177
17	610	0.07844650
18	276	0.03549383

Table 4: 6d6s3 (Total 46,656)

Number	Times	Probability
3	1	0.00002143
4	6	0.00012860
5	21	0.00045010
6	78	0.00167181
7	207	0.00443673
8	447	0.00958076
9	914	0.01959019
10	1677	0.03594393
11	2706	0.05799897
12	4135	0.08862750
13	5646	0.12101337
14	7056	0.15123457
15	7770	0.16653806
16	7551	0.16184413
17	5535	0.11863426
18	2906	0.06228567

Table 5: 7d6s3 (Total 279,936)

Number	Times	Probability
3	1	0.00000357
4	7	0.00002501
5	28	0.00010002
6	148	0.00052869
7	469	0.00167538
8	1141	0.00407593
9	2745	0.00980581
10	5747	0.02052969
11	10409	0.03718350
12	18159	0.06486840
13	27979	0.09994785
14	39277	0.14030707
15	48798	0.17431842
16	54096	0.19324417
17	44121	0.15761103
18	26811	0.09577546

Table 6: 8d6s3 (Total 1,679,616)

Number	Times	Probability
3	1	0.00000060
4	8	0.00000476
5	36	0.00002143
6	283	0.00016849
7	1052	0.00062633
8	2844	0.00169324
9	8117	0.00483265
10	19252	0.01146214
11	38648	0.02301002
12	76543	0.04557173
13	132168	0.07868941
14	206032	0.12266614
15	286501	0.17057529
16	358828	0.21363692
17	322812	0.19219393
18	226491	0.13484690

Table 7: 9d6s3 (Total 10,077,696)

Number	Times	Probability
3	1	0.00000010
4	9	0.00000089
5	45	0.00000447
6	547	0.00005428
7	2340	0.00023220
8	6948	0.00068944
9	23806	0.00236225
10	63612	0.00631216
11	140049	0.01389693
12	314245	0.03118223
13	604863	0.06001997
14	1037223	0.10292263
15	1607641	0.15952466
16	2257245	0.22398423
17	2222676	0.22055398
18	1796446	0.17825960