Friday, September 7, 2012

For my upcoming Gold and Glory campaign I was considering using d24 and d30 for some attack rolls.  For some weapons like black powder pistols, rayguns, and hvy crossbows. And I've been using roll two d20's and take the lower / higher roll in place of various +4 bonuses (like vs invisible or vs unawares).

I was curious what comparative odds where.  So, I wrote a litte test program using my Die Python dice library.

      2d20(worst)    2d20(best)     d20+2          d20+4          d24            d30
 1 -> 9.75%   9.75%  0.24%   0.24%  0.00%   0.00%  0.00%   0.00%  4.19%   4.19%  3.36%   3.36%
 2 -> 9.28%  19.03%  0.76%   1.00%  0.00%   0.00%  0.00%   0.00%  4.20%   8.38%  3.34%   6.69%
 3 -> 8.69%  27.72%  1.25%   2.26%  4.98%   4.98%  0.00%   0.00%  4.16%  12.54%  3.38%  10.07%
 4 -> 8.25%  35.97%  1.75%   4.01%  4.97%   9.96%  0.00%   0.00%  4.17%  16.71%  3.33%  13.40%
 5 -> 7.77%  43.74%  2.25%   6.25%  5.03%  14.98%  5.02%   5.02%  4.15%  20.86%  3.29%  16.69%
 6 -> 7.22%  50.95%  2.76%   9.02%  5.00%  19.99%  5.01%  10.03%  4.14%  25.00%  3.32%  20.01%
 7 -> 6.76%  57.71%a 3.25%  12.27%  5.01%  25.00%  5.00%  15.03%  4.17%  29.17%  3.34%  23.35%
 8 -> 6.27%  63.98%  3.77%  16.03%  5.03%  30.03%  4.98%  20.01%  4.19%  33.36%  3.34%  26.70%
 9 -> 5.74%  69.72%  4.25%  20.28%  5.02%  35.05%  4.97%  24.97%  4.18%  37.54%  3.35%  30.04%
10 -> 5.25%  74.97%  4.73%  25.01%  4.98%  40.03%  4.99%  29.96%  4.18%  41.71%  3.34%  33.39%
11 -> 4.74%  79.71%  5.26%  30.27%  4.96%  44.99%  5.00%  34.96%  4.14%  45.85%  3.33%  36.71%
12 -> 4.26%  83.97%  5.74%  36.00%  4.99%  49.99%a 4.97%  39.93%  4.15%  50.00%a 3.33%  40.04%
13 -> 3.76%  87.73%  6.23%  42.23%a 4.96%  54.95%  4.98%  44.91%  4.17%  54.18%  3.34%  43.39%
14 -> 3.27%  91.00%  6.76%  48.99%  5.03%  59.99%  5.05%  49.96%a 4.16%  58.34%  3.34%  46.73%
15 -> 2.75%  93.76%  7.31%  56.30%  4.97%  64.96%  4.99%  54.94%  4.17%  62.51%  3.30%  50.03%a
16 -> 2.25%  96.00%  7.71%  64.01%  5.00%  69.95%  5.02%  59.96%  4.18%  66.70%  3.34%  53.37%
17 -> 1.77%  97.77%  8.27%  72.27%  5.03%  74.98%  5.02%  64.98%  4.18%  70.88%  3.36%  56.74%
18 -> 1.24%  99.01%  8.72%  80.99%  5.04%  80.02%  5.02%  70.00%  4.16%  75.04%  3.34%  60.07%
19 -> 0.74%  99.75%  9.21%  90.20%  5.00%  85.02%  5.00%  75.00%  4.15%  79.19%  3.34%  63.41%
20 -> 0.25% 100.00%  9.80% 100.00% 14.98% 100.00% 25.00% 100.00% 20.81% 100.00% 36.59% 100.00%

Percentages are off a few 100ths cause results were rolled (1,000,000 times each) rather than calculated.  It ends at 20 cause any natural roll >= 20 is a critical. The d20+2 and d20+4 only crit on 20, 5%, but was interesting to compare the 20 or above's.  If not obvious d20 has 5% chance for any roll. Assuming GameScience ;)

I'm no longer so sure I like 2d20(best/worst) as general mechanic. Kind of extreme, less than 7 (or more than 14) 50% of the time.  All the other rolls are strictly linear and 50% is in the middle of range.  Linear curve (except stats) is one of the things that make D&D, D&D.

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