White Wolf System Probabilities

This table shows the approximate chances of botch/failure/success by degree on multiple d10 throws, for the benefit of the numbercrunching munchkin, calculated for between 1 and 9 dice. Also patterned are the rates at difficulty 7 through 10, showing the bizarre results arising from the White Wolf system when one of these difficulties is thrown in by a Storyteller to reflect a difficult task. Note the increasing odds of a botch near the beginning of the curve.

DIFFICULTY 6 (Standard)

Number of Dice
Botch
Fail
1
2
3
4
5
6
7
8
9
Most Likely Result
1
10%
40%
50%
1
2
9%
26%
40%
25%
1
3
7.6%
18.4%
31.5%
30%
12.5%
1
4
6.3%
13.6%
24.8%
29%
20%
6.3%
2
5
5.2%
10.4%
19.7%
26%
23.1%
12.5%
3.1%
2
6
4.3%
8.1%
15.7%
22.5%
23.5%
16.9%
7.5%
1.5%
3
7
3.5%
6.4%
12.6%
19.2%
22.3%
19.2%
11.6%
4.4%
0.8%
3
8
2.9%
5.1%
10.1%
16.2%
20.5%
20%
14.7%
7.6%
2.5%
0.4%
3
9
2.4%
4.1%
8.2%
13.6%
18.3%
19.7%
16.7%
10.6%
4.8%
1.4%
0.2%
4

  DIFFICULTY 7

Number of Dice
Botch
Fail
1
2
3
4
5
6
7
8
9
Most Likely Result
1
10%
50%
40%
Fail
2
11%
33%
40%
16%
1
3
10.3%
24.5%
34.8%
24%
6.4%
1
4
9.3%
19.2%
29.6%
26.5%
12.8%
2.6%
1
5
8.2%
15.5%
25.2%
26.4%
17.3%
6.4%
1%
2
6
7.3%
12.8%
21.4%
25%
19.8%
10.2%
3.1%
0.4%
2
7
6.4%
10.7%
18.3%
23%
20.9%
13.4%
5.7%
1.4%
0.2%
3
8
5.7%
9%
15.7%
21%
21%
15.6%
8.3%
3%
0.7%
0.07%
3
9
5%
7.6%
13.6%
18.9%
20.4%
17%
10.7%
4.9%
1.5%
0.3%
0.03%
3

DIFFICULTY 8

Number of Dice
Botch
Fail
1
2
3
4
5
6
7
8
9
Most Likely Result
1
10%
60%
30%
Fail
2
13%
42%
36%
9%
Fail
3
13.6%
32.4%
35.1%
16.2%
2.7%
1
4
13.3%
26.5%
32.4%
20.5%
6.5%
0.8%
1
5
12.7%
22.4%
29.4%
22.7%
10.1%
2.4%
0.3%
1
6
12%
19.3%
26.6%
23.5%
13.1%
4.5%
0.9%
0.1%
1
7
11.3%
16.9%
24.1%
23.4%
15.4%
6.7%
1.9%
0.3%
0.02%
1
8
10.6%
15%
21.9%
22.8%
16.9%
8.8%
3.2%
0.8%
0.1%
0.007%
2
9
9.9%
13.4%
19.9%
21.9%
17.9%
10.7%
4.6%
1.4%
0.3%
0.04%
0.002%
2

DIFFICULTY 9

Number of Dice
Botch
Fail
1
2
3
4
5
6
7
8
9
Most Likely Result
1
10%
70%
20%
Fail
2
15%
53%
28%
4%
Fail
3
17.5%
42.7%
30.6%
8.4%
0.8%
Fail
4
18.7%
36%
30.8%
12.1%
2.2%
0.2%
Fail
5
19.2%
31.4%
30%
14.8%
4%
0.6%
0.03%
Fail
6
19.4%
28%
28.7%
16.8%
5.8%
1.2%
0.1%
0.006%
1
7
19.3%
25.3%
27.4%
18.1%
7.6%
2%
0.3%
0.03%
0.001%
1
8
19.1%
23.2%
26%
18.9%
9.1%
3%
0.6%
0.1%
0.007%
0.0003%
1
9
18.8%
21.4%
24.8%
19.3%
10.4%
4%
1%
0.2%
0.02%
0.002%
0.00005%
1

DIFFICULTY 10

Number of Dice
Botch
Fail
1
2
3
4
5
6
7
8
9
Most Likely Result
1
10%
80%
10%
Fail
2
17%
66%
16%
1%
Fail
3
22%
56%
19.5%
2.4%
0.1%
Fail
4
25.7%
48.7%
21.4%
3.9%
0.3%
0.01%
Fail
5
28.4%
43.3%
22.4%
5.3%
0.6%
0.04%
0.001%
Fail
6
30.5%
39.1%
22.8%
6.5%
1%
0.1%
0.005%
0.0001%
Fail
7
32.1%
35.8%
22.8%
7.6%
1.5%
0.2%
0.01%
0.0006%
0.00001%
Fail
8
33.4%
33.2%
22.6%
8.5%
2%
0.3%
0.03%
0.002%
0.00006%
0.000001%
Botch
9
34.5%
31.1%
22.2%
9.3%
2.5%
0.4%
0.05%
0.004%
0.0002%
0.000007%
0.0000001%
Botch

Also here is the little lame VB.NET proglet I used to come up with these results. If you want to try and improve it (hey, I've been using VB for all of 2 days) the source code for Form1.VB is here.

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