MidThreeD20

Ref: DnD35e

D&D Varant: Middle 3D20

In this version of DnD35e instead of rolling 1d20 for each 'test' you roll three and then pick the center value as your roll. This produces the same sort of bell curve as say using 3d6 but without all the messing around with rescaling and rebasing.

For threats, crits and fubles there are several options. The simplest is to just say that the threat range is now the crit range, this reduces the chance of a crit on average but quick to work out. The second is to say that 18 or greater is a '20' on a threat roll and 17 or greater is a '19-20', 16 is '18-20', 15 is '17-20'. After that the probs no longer work correctly ;)

The probs are:

       mid20    Prob % of
 TN    Prob    Eq or higher
       %   
  1    0.725    100
  2    2.075    99.275
  3    3.275    97.2
  4    4.325    93.925
  5    5.225    89.6
  6    5.975    84.375
  7    6.575    78.4
  8    7.025    71.825
  9    7.325    64.8
 10    7.475    57.475
 11    7.475    50
 12    7.325    42.525
 13    7.025    35.2
 14    6.575    28.175
 15    5.975    21.6
 16    5.225    15.625
 17    4.325    10.4
 18    3.275    6.075
 19    2.075    2.8
 20    0.725    0.725

Mid of 3d20

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 Average = 10.5    Spread = 4.48140602936

Lowest of 3d20

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 Average = 5.5125    Spread = 3.86760180861

Highest of 3d20

same as Low just inversed

Graph