Ellye
2009-09-11, 11:19 PM
While trying to decide what kind of dice to use in my own RPG system, I've put together a quick probability table for rolls in multiple die. Since it might be useful to someone else perhaps, I decided that there's no harm in posting it here.
First column is the target number, second column is the probability of getting exact that number and third column is the probability of getting a number equal to or lower than that number.
====================
2D4 2D4 2D4 2D4
====================
{table=head]Roll|==|<=
2|6.25|6.25
3|12.5|18.75
4|18.75|37.5
5|25|62.5
6|18.75|81.25
7|12.5|93.75
8|6.25|100[/table]
UNIQUE ROLLS: 16
====================
2D6 2D6 2D6 2D6
====================
{table=head]Roll|==|<=
2|2.77778|2.77778
3|5.55556|8.33333
4|8.33333|16.6667
5|11.1111|27.7778
6|13.8889|41.6667
7|16.6667|58.3333
8|13.8889|72.2222
9|11.1111|83.3333
10|8.33333|91.6667
11|5.55556|97.2222
12|2.77778|100[/table]
UNIQUE ROLLS: 36
====================
2D8 2D8 2D8 2D8
====================
{table=head]Roll|==|<=
2|1.5625|1.5625
3|3.125|4.6875
4|4.6875|9.375
5|6.25|15.625
6|7.8125|23.4375
7|9.375|32.8125
8|10.9375|43.75
9|12.5|56.25
10|10.9375|67.1875
11|9.375|76.5625
12|7.8125|84.375
13|6.25|90.625
14|4.6875|95.3125
15|3.125|98.4375
16|1.5625|100[/table]
UNIQUE ROLLS: 64
====================
2D10 2D10 2D10 2D10
====================
{table=head]Roll|==|<=
2|1|1
3|2|3
4|3|6
5|4|10
6|5|15
7|6|21
8|7|28
9|8|36
10|9|45
11|10|55
12|9|64
13|8|72
14|7|79
15|6|85
16|5|90
17|4|94
18|3|97
19|2|99
20|1|100[/table]
UNIQUE ROLLS: 100
====================
2D12 2D12 2D12 2D12
====================
{table=head]Roll|==|<=
2|0.694444|0.694444
3|1.38889|2.08333
4|2.08333|4.16667
5|2.77778|6.94444
6|3.47222|10.4167
7|4.16667|14.5833
8|4.86111|19.4444
9|5.55556|25
10|6.25|31.25
11|6.94444|38.1944
12|7.63889|45.8333
13|8.33333|54.1667
14|7.63889|61.8056
15|6.94444|68.75
16|6.25|75
17|5.55556|80.5556
18|4.86111|85.4167
19|4.16667|89.5833
20|3.47222|93.0556
21|2.77778|95.8333
22|2.08333|97.9167
23|1.38889|99.3056
24|0.694444|100[/table]
UNIQUE ROLLS: 144
====================
2D20 2D20 2D20 2D20
====================
{table=head]Roll|==|<=
2|0.25|0.25
3|0.5|0.75
4|0.75|1.5
5|1|2.5
6|1.25|3.75
7|1.5|5.25
8|1.75|7
9|2|9
10|2.25|11.25
11|2.5|13.75
12|2.75|16.5
13|3|19.5
14|3.25|22.75
15|3.5|26.25
16|3.75|30
17|4|34
18|4.25|38.25
19|4.5|42.75
20|4.75|47.5
21|5|52.5
22|4.75|57.25
23|4.5|61.75
24|4.25|66
25|4|70
26|3.75|73.75
27|3.5|77.25
28|3.25|80.5
29|3|83.5
30|2.75|86.25
31|2.5|88.75
32|2.25|91
33|2|93
34|1.75|94.75
35|1.5|96.25
36|1.25|97.5
37|1|98.5
38|0.75|99.25
39|0.5|99.75
40|0.25|100[/table]
UNIQUE ROLLS: 400
====================
3D4 3D4 3D4 3D4 3D4
====================
{table=head]Roll|==|<=
3|1.5625|1.5625
4|4.6875|6.25
5|9.375|15.625
6|15.625|31.25
7|18.75|50
8|18.75|68.75
9|15.625|84.375
10|9.375|93.75
11|4.6875|98.4375
12|1.5625|100[/table]
UNIQUE ROLLS: 64
====================
3D6 3D6 3D6 3D6 3D6
====================
{table=head]Roll|==|<=
3|0.462963|0.462963
4|1.38889|1.85185
5|2.77778|4.62963
6|4.62963|9.25926
7|6.94444|16.2037
8|9.72222|25.9259
9|11.5741|37.5
10|12.5|50
11|12.5|62.5
12|11.5741|74.0741
13|9.72222|83.7963
14|6.94444|90.7407
15|4.62963|95.3704
16|2.77778|98.1481
17|1.38889|99.537
18|0.462963|100[/table]
UNIQUE ROLLS: 216
====================
3D8 3D8 3D8 3D8 3D8
====================
{table=head]Roll|==|<=
3|0.195313|0.195313
4|0.585938|0.78125
5|1.17188|1.95313
6|1.95313|3.90625
7|2.92969|6.83594
8|4.10156|10.9375
9|5.46875|16.4063
10|7.03125|23.4375
11|8.20313|31.6406
12|8.98438|40.625
13|9.375|50
14|9.375|59.375
15|8.98438|68.3594
16|8.20313|76.5625
17|7.03125|83.5938
18|5.46875|89.0625
19|4.10156|93.1641
20|2.92969|96.0938
21|1.95313|98.0469
22|1.17188|99.2188
23|0.585938|99.8047
24|0.195313|100[/table]
UNIQUE ROLLS: 512
====================
3D10 3D10 3D10 3D10
====================
{table=head]Roll|==|<=
3|0.1|0.1
4|0.3|0.4
5|0.6|1
6|1|2
7|1.5|3.5
8|2.1|5.6
9|2.8|8.4
10|3.6|12
11|4.5|16.5
12|5.5|22
13|6.3|28.3
14|6.9|35.2
15|7.3|42.5
16|7.5|50
17|7.5|57.5
18|7.3|64.8
19|6.9|71.7
20|6.3|78
21|5.5|83.5
22|4.5|88
23|3.6|91.6
24|2.8|94.4
25|2.1|96.5
26|1.5|98
27|1|99
28|0.6|99.6
29|0.3|99.9
30|0.1|100[/table]
UNIQUE ROLLS: 1000
====================
3D12 3D12 3D12 3D12
====================
{table=head]Roll|==|<=
3|0.0578704|0.0578704
4|0.173611|0.231481
5|0.347222|0.578704
6|0.578704|1.15741
7|0.868056|2.02546
8|1.21528|3.24074
9|1.62037|4.86111
10|2.08333|6.94444
11|2.60417|9.54861
12|3.18287|12.7315
13|3.81944|16.5509
14|4.51389|21.0648
15|5.09259|26.1574
16|5.55556|31.713
17|5.90278|37.6157
18|6.13426|43.75
19|6.25|50
20|6.25|56.25
21|6.13426|62.3843
22|5.90278|68.287
23|5.55556|73.8426
24|5.09259|78.9352
25|4.51389|83.4491
26|3.81944|87.2685
27|3.18287|90.4514
28|2.60417|93.0556
29|2.08333|95.1389
30|1.62037|96.7593
31|1.21528|97.9745
32|0.868056|98.8426
33|0.578704|99.4213
34|0.347222|99.7685
35|0.173611|99.9421
36|0.0578704|100[/table]
UNIQUE ROLLS: 1728
====================
3D20 3D20 3D20 3D20 3D20
====================
{table=head]Roll|==|<=
3|0.0125|0.0125
4|0.0375|0.05
5|0.075|0.125
6|0.125|0.25
7|0.1875|0.4375
8|0.2625|0.7
9|0.35|1.05
10|0.45|1.5
11|0.5625|2.0625
12|0.6875|2.75
13|0.825|3.575
14|0.975|4.55
15|1.1375|5.6875
16|1.3125|7
17|1.5|8.5
18|1.7|10.2
19|1.9125|12.1125
20|2.1375|14.25
21|2.375|16.625
22|2.625|19.25
23|2.85|22.1
24|3.05|25.15
25|3.225|28.375
26|3.375|31.75
27|3.5|35.25
28|3.6|38.85
29|3.675|42.525
30|3.725|46.25
31|3.75|50
32|3.75|53.75
33|3.725|57.475
34|3.675|61.15
35|3.6|64.75
36|3.5|68.25
37|3.375|71.625
38|3.225|74.85
39|3.05|77.9
40|2.85|80.75
41|2.625|83.375
42|2.375|85.75
43|2.1375|87.8875
44|1.9125|89.8
45|1.7|91.5
46|1.5|93
47|1.3125|94.3125
48|1.1375|95.45
49|0.975|96.425
50|0.825|97.25
51|0.6875|97.9375
52|0.5625|98.5
53|0.45|98.95
54|0.35|99.3
55|0.2625|99.5625
56|0.1875|99.75
57|0.125|99.875
58|0.075|99.95
59|0.0375|99.9875
60|0.0125|100[/table]
UNIQUE ROLLS: 8000
First column is the target number, second column is the probability of getting exact that number and third column is the probability of getting a number equal to or lower than that number.
====================
2D4 2D4 2D4 2D4
====================
{table=head]Roll|==|<=
2|6.25|6.25
3|12.5|18.75
4|18.75|37.5
5|25|62.5
6|18.75|81.25
7|12.5|93.75
8|6.25|100[/table]
UNIQUE ROLLS: 16
====================
2D6 2D6 2D6 2D6
====================
{table=head]Roll|==|<=
2|2.77778|2.77778
3|5.55556|8.33333
4|8.33333|16.6667
5|11.1111|27.7778
6|13.8889|41.6667
7|16.6667|58.3333
8|13.8889|72.2222
9|11.1111|83.3333
10|8.33333|91.6667
11|5.55556|97.2222
12|2.77778|100[/table]
UNIQUE ROLLS: 36
====================
2D8 2D8 2D8 2D8
====================
{table=head]Roll|==|<=
2|1.5625|1.5625
3|3.125|4.6875
4|4.6875|9.375
5|6.25|15.625
6|7.8125|23.4375
7|9.375|32.8125
8|10.9375|43.75
9|12.5|56.25
10|10.9375|67.1875
11|9.375|76.5625
12|7.8125|84.375
13|6.25|90.625
14|4.6875|95.3125
15|3.125|98.4375
16|1.5625|100[/table]
UNIQUE ROLLS: 64
====================
2D10 2D10 2D10 2D10
====================
{table=head]Roll|==|<=
2|1|1
3|2|3
4|3|6
5|4|10
6|5|15
7|6|21
8|7|28
9|8|36
10|9|45
11|10|55
12|9|64
13|8|72
14|7|79
15|6|85
16|5|90
17|4|94
18|3|97
19|2|99
20|1|100[/table]
UNIQUE ROLLS: 100
====================
2D12 2D12 2D12 2D12
====================
{table=head]Roll|==|<=
2|0.694444|0.694444
3|1.38889|2.08333
4|2.08333|4.16667
5|2.77778|6.94444
6|3.47222|10.4167
7|4.16667|14.5833
8|4.86111|19.4444
9|5.55556|25
10|6.25|31.25
11|6.94444|38.1944
12|7.63889|45.8333
13|8.33333|54.1667
14|7.63889|61.8056
15|6.94444|68.75
16|6.25|75
17|5.55556|80.5556
18|4.86111|85.4167
19|4.16667|89.5833
20|3.47222|93.0556
21|2.77778|95.8333
22|2.08333|97.9167
23|1.38889|99.3056
24|0.694444|100[/table]
UNIQUE ROLLS: 144
====================
2D20 2D20 2D20 2D20
====================
{table=head]Roll|==|<=
2|0.25|0.25
3|0.5|0.75
4|0.75|1.5
5|1|2.5
6|1.25|3.75
7|1.5|5.25
8|1.75|7
9|2|9
10|2.25|11.25
11|2.5|13.75
12|2.75|16.5
13|3|19.5
14|3.25|22.75
15|3.5|26.25
16|3.75|30
17|4|34
18|4.25|38.25
19|4.5|42.75
20|4.75|47.5
21|5|52.5
22|4.75|57.25
23|4.5|61.75
24|4.25|66
25|4|70
26|3.75|73.75
27|3.5|77.25
28|3.25|80.5
29|3|83.5
30|2.75|86.25
31|2.5|88.75
32|2.25|91
33|2|93
34|1.75|94.75
35|1.5|96.25
36|1.25|97.5
37|1|98.5
38|0.75|99.25
39|0.5|99.75
40|0.25|100[/table]
UNIQUE ROLLS: 400
====================
3D4 3D4 3D4 3D4 3D4
====================
{table=head]Roll|==|<=
3|1.5625|1.5625
4|4.6875|6.25
5|9.375|15.625
6|15.625|31.25
7|18.75|50
8|18.75|68.75
9|15.625|84.375
10|9.375|93.75
11|4.6875|98.4375
12|1.5625|100[/table]
UNIQUE ROLLS: 64
====================
3D6 3D6 3D6 3D6 3D6
====================
{table=head]Roll|==|<=
3|0.462963|0.462963
4|1.38889|1.85185
5|2.77778|4.62963
6|4.62963|9.25926
7|6.94444|16.2037
8|9.72222|25.9259
9|11.5741|37.5
10|12.5|50
11|12.5|62.5
12|11.5741|74.0741
13|9.72222|83.7963
14|6.94444|90.7407
15|4.62963|95.3704
16|2.77778|98.1481
17|1.38889|99.537
18|0.462963|100[/table]
UNIQUE ROLLS: 216
====================
3D8 3D8 3D8 3D8 3D8
====================
{table=head]Roll|==|<=
3|0.195313|0.195313
4|0.585938|0.78125
5|1.17188|1.95313
6|1.95313|3.90625
7|2.92969|6.83594
8|4.10156|10.9375
9|5.46875|16.4063
10|7.03125|23.4375
11|8.20313|31.6406
12|8.98438|40.625
13|9.375|50
14|9.375|59.375
15|8.98438|68.3594
16|8.20313|76.5625
17|7.03125|83.5938
18|5.46875|89.0625
19|4.10156|93.1641
20|2.92969|96.0938
21|1.95313|98.0469
22|1.17188|99.2188
23|0.585938|99.8047
24|0.195313|100[/table]
UNIQUE ROLLS: 512
====================
3D10 3D10 3D10 3D10
====================
{table=head]Roll|==|<=
3|0.1|0.1
4|0.3|0.4
5|0.6|1
6|1|2
7|1.5|3.5
8|2.1|5.6
9|2.8|8.4
10|3.6|12
11|4.5|16.5
12|5.5|22
13|6.3|28.3
14|6.9|35.2
15|7.3|42.5
16|7.5|50
17|7.5|57.5
18|7.3|64.8
19|6.9|71.7
20|6.3|78
21|5.5|83.5
22|4.5|88
23|3.6|91.6
24|2.8|94.4
25|2.1|96.5
26|1.5|98
27|1|99
28|0.6|99.6
29|0.3|99.9
30|0.1|100[/table]
UNIQUE ROLLS: 1000
====================
3D12 3D12 3D12 3D12
====================
{table=head]Roll|==|<=
3|0.0578704|0.0578704
4|0.173611|0.231481
5|0.347222|0.578704
6|0.578704|1.15741
7|0.868056|2.02546
8|1.21528|3.24074
9|1.62037|4.86111
10|2.08333|6.94444
11|2.60417|9.54861
12|3.18287|12.7315
13|3.81944|16.5509
14|4.51389|21.0648
15|5.09259|26.1574
16|5.55556|31.713
17|5.90278|37.6157
18|6.13426|43.75
19|6.25|50
20|6.25|56.25
21|6.13426|62.3843
22|5.90278|68.287
23|5.55556|73.8426
24|5.09259|78.9352
25|4.51389|83.4491
26|3.81944|87.2685
27|3.18287|90.4514
28|2.60417|93.0556
29|2.08333|95.1389
30|1.62037|96.7593
31|1.21528|97.9745
32|0.868056|98.8426
33|0.578704|99.4213
34|0.347222|99.7685
35|0.173611|99.9421
36|0.0578704|100[/table]
UNIQUE ROLLS: 1728
====================
3D20 3D20 3D20 3D20 3D20
====================
{table=head]Roll|==|<=
3|0.0125|0.0125
4|0.0375|0.05
5|0.075|0.125
6|0.125|0.25
7|0.1875|0.4375
8|0.2625|0.7
9|0.35|1.05
10|0.45|1.5
11|0.5625|2.0625
12|0.6875|2.75
13|0.825|3.575
14|0.975|4.55
15|1.1375|5.6875
16|1.3125|7
17|1.5|8.5
18|1.7|10.2
19|1.9125|12.1125
20|2.1375|14.25
21|2.375|16.625
22|2.625|19.25
23|2.85|22.1
24|3.05|25.15
25|3.225|28.375
26|3.375|31.75
27|3.5|35.25
28|3.6|38.85
29|3.675|42.525
30|3.725|46.25
31|3.75|50
32|3.75|53.75
33|3.725|57.475
34|3.675|61.15
35|3.6|64.75
36|3.5|68.25
37|3.375|71.625
38|3.225|74.85
39|3.05|77.9
40|2.85|80.75
41|2.625|83.375
42|2.375|85.75
43|2.1375|87.8875
44|1.9125|89.8
45|1.7|91.5
46|1.5|93
47|1.3125|94.3125
48|1.1375|95.45
49|0.975|96.425
50|0.825|97.25
51|0.6875|97.9375
52|0.5625|98.5
53|0.45|98.95
54|0.35|99.3
55|0.2625|99.5625
56|0.1875|99.75
57|0.125|99.875
58|0.075|99.95
59|0.0375|99.9875
60|0.0125|100[/table]
UNIQUE ROLLS: 8000