FUDGE Dice Probability Tables

Contents

Notation

These different methods use a special notation to differentiate them. Take the standard notation and append a .n, where n is the number of +1s on the die. Some dice have additional +2s, which would be denoted as an additional .m added after the .n. For example:

4dF

4dF = (-1,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/81        1.235   1.235 100.000
  -3       4/81        4.938   6.173  98.765
  -2      10/81       12.346  18.519  93.827
  -1      16/81       19.753  38.272  81.481
   0      19/81       23.457  61.728  61.728
   1      16/81       19.753  81.481  38.272
   2      10/81       12.346  93.827  18.519
   3       4/81        4.938  98.765   6.173
   4       1/81        1.235 100.000   1.235

  Chance of very low result ...............  18.519
  Chance of acceptable result (+/-1) ......  62.963
  Chance of very high result ..............  18.519

  Chance of hitting trait level exactly ...  23.457
  Chance of missing trait level ...........  76.543

3dF

3dF = (-1,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -3       1/27        3.704   3.704 100.000
  -2       3/27       11.111  14.815  96.296
  -1       6/27       22.222  37.037  85.185
   0       7/27       25.926  62.963  62.963
   1       6/27       22.222  85.185  37.037
   2       3/27       11.111  96.296  14.815
   3       1/27        3.704 100.000   3.704

  Chance of very low result ...............  14.815
  Chance of acceptable result (+/-1) ......  70.370
  Chance of very high result ..............  14.815

  Chance of hitting trait level exactly ...  25.926
  Chance of missing trait level ...........  74.074

2dF

2dF = (-1,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -2       1/9        11.111  11.111 100.000
  -1       2/9        22.222  33.333  88.889
   0       3/9        33.333  66.667  66.667
   1       2/9        22.222  88.889  33.333
   2       1/9        11.111 100.000  11.111

  Chance of very low result ...............  11.111
  Chance of acceptable result (+/-1) ......  77.778
  Chance of very high result ..............  11.111

  Chance of hitting trait level exactly ...  33.333
  Chance of missing trait level ...........  66.667

5dF padded

5dPadded

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/243       0.412   0.412 100.000
  -3       5/243       2.058   2.469  99.588
  -2      15/243       6.173   8.642  97.531
  -1      30/243      12.346  20.988  91.358
   0     141/243      58.025  79.012  79.012
   1      30/243      12.346  91.358  20.988
   2      15/243       6.173  97.531   8.642
   3       5/243       2.058  99.588   2.469
   4       1/243       0.412 100.000   0.412

  Chance of very low result ...............   8.642
  Chance of acceptable result (+/-1) ......  82.716
  Chance of very high result ..............   8.642

  Chance of hitting trait level exactly ...  58.025
  Chance of missing trait level ...........  41.975

4d6.1

(equivalent to 4d12.2)
4d6 = (-1,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/1296      0.077   0.077 100.000
  -3      16/1296      1.235   1.312  99.923
  -2     100/1296      7.716   9.028  98.688
  -1     304/1296     23.457  32.485  90.972
   0     454/1296     35.031  67.515  67.515
   1     304/1296     23.457  90.972  32.485
   2     100/1296      7.716  98.688   9.028
   3      16/1296      1.235  99.923   1.312
   4       1/1296      0.077 100.000   0.077

  Chance of very low result ...............   9.028
  Chance of acceptable result (+/-1) ......  81.944
  Chance of very high result ..............   9.028

  Chance of hitting trait level exactly ...  35.031
  Chance of missing trait level ...........  64.969

5d6.1

5d6 = (-1,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -5       1/7776      0.013   0.013 100.000
  -4      20/7776      0.257   0.270  99.987
  -3     165/7776      2.122   2.392  99.730
  -2     720/7776      9.259  11.651  97.608
  -1    1770/7776     22.762  34.414  88.349
   0    2424/7776     31.173  65.586  65.586
   1    1770/7776     22.762  88.349  34.414
   2     720/7776      9.259  97.608  11.651
   3     165/7776      2.122  99.730   2.392
   4      20/7776      0.257  99.987   0.270
   5       1/7776      0.013 100.000   0.013

  Chance of very low result ...............  11.651
  Chance of acceptable result (+/-1) ......  76.698
  Chance of very high result ..............  11.651

  Chance of hitting trait level exactly ...  31.173
  Chance of missing trait level ...........  68.827

6d6.1

6d6 = (-1,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -6       1/46656     0.002   0.002 100.000
  -5      24/46656     0.051   0.054  99.998
  -4     246/46656     0.527   0.581  99.946
  -3    1400/46656     3.001   3.582  99.419
  -2    4815/46656    10.320  13.902  96.418
  -1   10224/46656    21.914  35.815  86.098
   0   13236/46656    28.369  64.185  64.185
   1   10224/46656    21.914  86.098  35.815
   2    4815/46656    10.320  96.418  13.902
   3    1400/46656     3.001  99.419   3.582
   4     246/46656     0.527  99.946   0.581
   5      24/46656     0.051  99.998   0.054
   6       1/46656     0.002 100.000   0.002

  Chance of very low result ...............  13.902
  Chance of acceptable result (+/-1) ......  72.197
  Chance of very high result ..............  13.902

  Chance of hitting trait level exactly ...  28.369
  Chance of missing trait level ...........  71.631

4d8.1

4d8 = (-1,0,0,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/4096      0.024   0.024 100.000
  -3      24/4096      0.586   0.610  99.976
  -2     220/4096      5.371   5.981  99.390
  -1     936/4096     22.852  28.833  94.019
   0    1734/4096     42.334  71.167  71.167
   1     936/4096     22.852  94.019  28.833
   2     220/4096      5.371  99.390   5.981
   3      24/4096      0.586  99.976   0.610
   4       1/4096      0.024 100.000   0.024

  Chance of very low result ...............   5.981
  Chance of acceptable result (+/-1) ......  88.037
  Chance of very high result ..............   5.981

  Chance of hitting trait level exactly ...  42.334
  Chance of missing trait level ...........  57.666

4d8.2

(equivalent to 4d4.1)
4d8 = (-1,-1,0,0,0,0,+1,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4      16/4096      0.391   0.391 100.000
  -3     128/4096      3.125   3.516  99.609
  -2     448/4096     10.938  14.453  96.484
  -1     896/4096     21.875  36.328  85.547
   0    1120/4096     27.344  63.672  63.672
   1     896/4096     21.875  85.547  36.328
   2     448/4096     10.938  96.484  14.453
   3     128/4096      3.125  99.609   3.516
   4      16/4096      0.391 100.000   0.391

  Chance of very low result ...............  14.453
  Chance of acceptable result (+/-1) ......  71.094
  Chance of very high result ..............  14.453

  Chance of hitting trait level exactly ...  27.344
  Chance of missing trait level ...........  72.656

4d10.1

(equivalent to 4d20.2)
4d10 = (-1,0,0,0,0,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/10000     0.010   0.010 100.000
  -3      32/10000     0.320   0.330  99.990
  -2     388/10000     3.880   4.210  99.670
  -1    2144/10000    21.440  25.650  95.790
   0    4870/10000    48.700  74.350  74.350
   1    2144/10000    21.440  95.790  25.650
   2     388/10000     3.880  99.670   4.210
   3      32/10000     0.320  99.990   0.330
   4       1/10000     0.010 100.000   0.010

  Chance of very low result ...............   4.210
  Chance of acceptable result (+/-1) ......  91.580
  Chance of very high result ..............   4.210

  Chance of hitting trait level exactly ...  48.700
  Chance of missing trait level ...........  51.300

4d10.2

(equivalent to 4d5.1)
4d10 = (-1,-1,0,0,0,0,0,0,+1,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4      16/10000     0.160   0.160 100.000
  -3     192/10000     1.920   2.080  99.840
  -2     928/10000     9.280  11.360  97.920
  -1    2304/10000    23.040  34.400  88.640
   0    3120/10000    31.200  65.600  65.600
   1    2304/10000    23.040  88.640  34.400
   2     928/10000     9.280  97.920  11.360
   3     192/10000     1.920  99.840   2.080
   4      16/10000     0.160 100.000   0.160

  Chance of very low result ...............  11.360
  Chance of acceptable result (+/-1) ......  77.280
  Chance of very high result ..............  11.360

  Chance of hitting trait level exactly ...  31.200
  Chance of missing trait level ...........  68.800

2d10.2.1

2d10 = (-2,-1,0,0,0,0,0,0,+1,+2):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/100       1.000   1.000 100.000
  -3       2/100       2.000   3.000  99.000
  -2      13/100      13.000  16.000  97.000
  -1      14/100      14.000  30.000  84.000
   0      40/100      40.000  70.000  70.000
   1      14/100      14.000  84.000  30.000
   2      13/100      13.000  97.000  16.000
   3       2/100       2.000  99.000   3.000
   4       1/100       1.000 100.000   1.000

  Chance of very low result ...............  16.000
  Chance of acceptable result (+/-1) ......  68.000
  Chance of very high result ..............  16.000

  Chance of hitting trait level exactly ...  40.000
  Chance of missing trait level ...........  60.000

2d10.3.1

2d10 = (-2,-1,-1,0,0,0,0,+1,+1,+2):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/100       1.000   1.000 100.000
  -3       4/100       4.000   5.000  99.000
  -2      12/100      12.000  17.000  95.000
  -1      20/100      20.000  37.000  83.000
   0      26/100      26.000  63.000  63.000
   1      20/100      20.000  83.000  37.000
   2      12/100      12.000  95.000  17.000
   3       4/100       4.000  99.000   5.000
   4       1/100       1.000 100.000   1.000

  Chance of very low result ...............  17.000
  Chance of acceptable result (+/-1) ......  66.000
  Chance of very high result ..............  17.000

  Chance of hitting trait level exactly ...  26.000
  Chance of missing trait level ...........  74.000

4d12.1

4d12 = (-1,0,0,0,0,0,0,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/20736     0.005   0.005 100.000
  -3      40/20736     0.193   0.198  99.995
  -2     604/20736     2.913   3.111  99.802
  -1    4120/20736    19.869  22.979  96.889
   0   11206/20736    54.041  77.021  77.021
   1    4120/20736    19.869  96.889  22.979
   2     604/20736     2.913  99.802   3.111
   3      40/20736     0.193  99.995   0.198
   4       1/20736     0.005 100.000   0.005

  Chance of very low result ...............   3.111
  Chance of acceptable result (+/-1) ......  93.779
  Chance of very high result ..............   3.111

  Chance of hitting trait level exactly ...  54.041
  Chance of missing trait level ...........  45.959

4d20.1

4d20 = (-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/160000    0.001   0.001 100.000
  -3      72/160000    0.045   0.046  99.999
  -2    1948/160000    1.218   1.263  99.954
  -1   23544/160000   14.715  15.978  98.737
   0  108870/160000   68.044  84.022  84.022
   1   23544/160000   14.715  98.737  15.978
   2    1948/160000    1.218  99.954   1.263
   3      72/160000    0.045  99.999   0.046
   4       1/160000    0.001 100.000   0.001

  Chance of very low result ...............   1.263
  Chance of acceptable result (+/-1) ......  97.474
  Chance of very high result ..............   1.263

  Chance of hitting trait level exactly ...  68.044
  Chance of missing trait level ...........  31.956

4d20.3

4d20 = (-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+1,+1,+1):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4      81/160000    0.051   0.051 100.000
  -3    1512/160000    0.945   0.996  99.949
  -2   10908/160000    6.817   7.813  99.004
  -1   37464/160000   23.415  31.228  92.187
   0   60070/160000   37.544  68.772  68.772
   1   37464/160000   23.415  92.187  31.228
   2   10908/160000    6.817  99.004   7.813
   3    1512/160000    0.945  99.949   0.996
   4      81/160000    0.051 100.000   0.051

  Chance of very low result ...............   7.813
  Chance of acceptable result (+/-1) ......  84.374
  Chance of very high result ..............   7.813

  Chance of hitting trait level exactly ...  37.544
  Chance of missing trait level ...........  62.456

2d20.2.1

2d20 = (-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+1,+2):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/400       0.250   0.250 100.000
  -3       2/400       0.500   0.750  99.750
  -2      33/400       8.250   9.000  99.250
  -1      34/400       8.500  17.500  91.000
   0     260/400      65.000  82.500  82.500
   1      34/400       8.500  91.000  17.500
   2      33/400       8.250  99.250   9.000
   3       2/400       0.500  99.750   0.750
   4       1/400       0.250 100.000   0.250

  Chance of very low result ...............   9.000
  Chance of acceptable result (+/-1) ......  82.000
  Chance of very high result ..............   9.000

  Chance of hitting trait level exactly ...  65.000
  Chance of missing trait level ...........  35.000

2d20.3.1

2d20 = (-2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+1,+1,+2):

   n                   P(n)    P(n-)   P(n+)
  ---                ------- ------- -------
  -4       1/400       0.250   0.250 100.000
  -3       4/400       1.000   1.250  99.750
  -2      32/400       8.000   9.250  98.750
  -1      60/400      15.000  24.250  90.750
   0     206/400      51.500  75.750  75.750
   1      60/400      15.000  90.750  24.250
   2      32/400       8.000  98.750   9.250
   3       4/400       1.000  99.750   1.250
   4       1/400       0.250 100.000   0.250

  Chance of very low result ...............   9.250
  Chance of acceptable result (+/-1) ......  81.500
  Chance of very high result ..............   9.250

  Chance of hitting trait level exactly ...  51.500
  Chance of missing trait level ...........  48.500