Savage Worlds Probability Trait and Wild Die the same
An interesting idea was brought up on the Savage Worlds forum about the possibility of adjusting the system so that instead of wild card characters rolling a d6 as the wild die, what if the wild die was the same as the trait die being rolled. This got me thinking, and since I'd already done up the chart and tables for rolling the normal way, how hard could this be. Turns out, not hard at all. About 15 minutes with excel and voila, here is the chart. A quick comparison of the 2 charts shows that the graphs aren't as smooth when the wild die is the same as the trait die (since the borders between results on the dice have the same probability, e.g. 4 and 5 on a D4, 6 and 7 on a D6, etc...). With the exception of the D4 Wild die, the others show a maximal change from the D6 Wild die at a target of 6, but this shift rapidly falls back off such that the probabilities almost become the same. The D4 has a maximal change at a target of 3. One of the details that was mentioned by Clint was that the Wild Die selection wasn't just based on the % success against the fixed number 4, but for trying to get close to 50% chance to hit someone with a Fighting die of the same type (e.g. d8 fighting vs a d8 fighting). If the Wild Die was the same as the Trait/Skill die, then these numbers shift. In most cases the chance of hitting someone with a fighting skill of the same type actually rises from 50% to closer to 65%. The D4 drops almost 20% from a 62.5% to a 43.75% chance to hit a Parry of 4. And here is the table of the probabilities.
d4 | d6 | d8 | d10 | d12 | |
1 | 100 | 100 | 100 | 100 | 100 |
2 | 93.75 | 97.22222222 | 98.4375 | 99 | 99.30555556 |
3 | 75 | 88.88888889 | 93.75 | 96 | 97.22222222 |
4 | 43.75 | 75 | 85.9375 | 91 | 93.75 |
5 | 43.75 | 55.55555556 | 75 | 84 | 88.88888889 |
6 | 33.984375 | 30.55555556 | 60.9375 | 75 | 82.63888889 |
7 | 23.4375 | 30.55555556 | 43.75 | 64 | 75 |
8 | 12.109375 | 25.84876543 | 23.4375 | 51 | 65.97222222 |
9 | 12.109375 | 20.98765432 | 23.4375 | 36 | 55.55555556 |
10 | 9.155273438 | 15.97222222 | 20.67871094 | 19 | 43.75 |
11 | 6.15234375 | 10.80246914 | 17.87109375 | 19 | 30.55555556 |
12 | 3.100585938 | 5.478395062 | 15.01464844 | 17.19 | 15.97222222 |
13 | 3.100585938 | 5.478395062 | 12.109375 | 15.36 | 15.97222222 |
14 | 2.33001709 | 4.576045953 | 9.155273438 | 13.51 | 14.69425154 |
15 | 1.556396484 | 3.669410151 | 6.15234375 | 11.64 | 13.4066358 |
16 | 0.779724121 | 2.758487654 | 3.100585938 | 9.75 | 12.109375 |
17 | 0.779724121 | 1.843278464 | 3.100585938 | 7.84 | 10.80246914 |
18 | 0.585079193 | 0.923782579 | 2.715682983 | 5.91 | 9.48591821 |
19 | 0.39024353 | 0.923782579 | 2.33001709 | 3.96 | 8.159722222 |
20 | 0.195217133 | 0.770116503 | 1.943588257 | 1.99 | 6.823881173 |
21 | 0.195217133 | 0.616331352 | 1.556396484 | 1.99 | 5.478395062 |
22 | 0.146430731 | 0.462427126 | 1.168441772 | 1.7919 | 4.123263889 |
23 | 0.097632408 | 0.308403826 | 0.779724121 | 1.5936 | 2.758487654 |
24 | 0.048822165 | 0.15426145 | 0.39024353 | 1.3951 | 1.384066358 |
25 | 0.048822165 | 0.15426145 | 0.39024353 | 1.1964 | 1.384066358 |
26 | 0.036617741 | 0.128559478 | 0.341504812 | 0.9975 | 1.269095883 |
27 | 0.024412572 | 0.102854197 | 0.292754173 | 0.7984 | 1.154058428 |
28 | 0.012206659 | 0.077145609 | 0.243991613 | 0.5991 | 1.038953993 |
29 | 0.012206659 | 0.051433714 | 0.195217133 | 0.3996 | 0.923782579 |
30 | 0.009155064 | 0.025718511 | 0.146430731 | 0.1999 | 0.808544185 |
31 | 0.006103422 | 0.025718511 | 0.097632408 | 0.1999 | 0.693238812 |
32 | 0.003051735 | 0.021432322 | 0.048822165 | 0.179919 | 0.577866459 |
33 | 0.003051735 | 0.017146041 | 0.048822165 | 0.159936 | 0.462427126 |
34 | 0.002288805 | 0.012859669 | 0.042720046 | 0.139951 | 0.346920814 |
35 | 0.001525873 | 0.008573204 | 0.036617741 | 0.119964 | 0.231347522 |
36 | 0.000762938 | 0.004286648 | 0.03051525 | 0.099975 | 0.115707251 |
37 | 0.000762938 | 0.004286648 | 0.024412572 | 0.079984 | 0.115707251 |
38 | 0.000572204 | 0.003572213 | 0.018309709 | 0.059991 | 0.106067538 |
39 | 0.000381469 | 0.002857776 | 0.012206659 | 0.039996 | 0.09642736 |
40 | 0.000190735 | 0.002143336 | 0.006103422 | 0.019999 | 0.086786718 |
41 | 0.000190735 | 0.001428893 | 0.006103422 | 0.019999 | 0.077145609 |
42 | 0.000143051 | 0.000714448 | 0.005340505 | 0.01799919 | 0.067504036 |
43 | 9.53674E-05 | 0.000714448 | 0.004577584 | 0.01599936 | 0.057861998 |
44 | 4.76837E-05 | 0.000595373 | 0.003814661 | 0.01399951 | 0.048219494 |
45 | 4.76837E-05 | 0.000476299 | 0.003051735 | 0.01199964 | 0.038576526 |
46 | 3.57628E-05 | 0.000357224 | 0.002288805 | 0.00999975 | 0.028933092 |
47 | 2.38419E-05 | 0.00023815 | 0.001525873 | 0.00799984 | 0.019289193 |
48 | 1.19209E-05 | 0.000119075 | 0.000762938 | 0.00599991 | 0.009644829 |
49 | 1.19209E-05 | 0.000119075 | 0.000762938 | 0.00399996 | 0.009644829 |
50 | 8.9407E-06 | 9.9229E-05 | 0.000667571 | 0.00199999 | 0.008841111 |
51 | 5.96046E-06 | 7.93832E-05 | 0.000572204 | 0.00199999 | 0.00803739 |
52 | 2.98023E-06 | 5.95374E-05 | 0.000476837 | 0.001799992 | 0.007233665 |
53 | 2.98023E-06 | 3.96916E-05 | 0.000381469 | 0.001599994 | 0.006429938 |
54 | 2.23517E-06 | 1.98458E-05 | 0.000286102 | 0.001399995 | 0.005626207 |
55 | 1.49012E-06 | 1.98458E-05 | 0.000190735 | 0.001199996 | 0.004822473 |
56 | 7.45058E-07 | 1.65382E-05 | 9.53674E-05 | 0.000999998 | 0.004018735 |
57 | 7.45058E-07 | 1.32305E-05 | 9.53674E-05 | 0.000799998 | 0.003214995 |
58 | 5.58794E-07 | 9.9229E-06 | 8.34465E-05 | 0.000599999 | 0.002411251 |
59 | 3.72529E-07 | 6.61527E-06 | 7.15256E-05 | 0.0004 | 0.001607504 |
60 | 1.86265E-07 | 3.30763E-06 | 5.96046E-05 | 0.0002 | 0.000803754 |
61 | 1.86265E-07 | 3.30763E-06 | 4.76837E-05 | 0.0002 | 0.000803754 |
62 | 1.39698E-07 | 2.75636E-06 | 3.57628E-05 | 0.00018 | 0.000736774 |
63 | 9.31323E-08 | 2.20509E-06 | 2.38419E-05 | 0.00016 | 0.000669795 |
64 | 4.65661E-08 | 1.65382E-06 | 1.19209E-05 | 0.00014 | 0.000602815 |
65 | 4.65661E-08 | 1.10254E-06 | 1.19209E-05 | 0.00012 | 0.000535836 |
66 | 3.49246E-08 | 5.51272E-07 | 1.04308E-05 | 1E-04 | 0.000468857 |
67 | 2.32831E-08 | 5.51272E-07 | 8.9407E-06 | 8E-05 | 0.000401877 |
68 | 1.16415E-08 | 4.59394E-07 | 7.45058E-06 | 6E-05 | 0.000334898 |
69 | 1.16415E-08 | 3.67515E-07 | 5.96046E-06 | 4E-05 | 0.000267918 |
70 | 8.73115E-09 | 2.75636E-07 | 4.47035E-06 | 2E-05 | 0.000200939 |
71 | 5.82077E-09 | 1.83757E-07 | 2.98023E-06 | 2E-05 | 0.000133959 |
72 | 2.91038E-09 | 9.18787E-08 | 1.49012E-06 | 1.8E-05 | 6.69796E-05 |