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I remember seeing somewhere (possibly on this board) that opposed tests are massively weighted towards the side with even slightly higher stats. The person posting had a house rule that all opposed tests are made with a target number of 4, so the only difference is the number of dice. I was curious how true this was. So I decided to run a simulation.
I've got two orthogonal rule variations that I used - various target number calculations and a modified rule-of-six where every 6 above the target number counts as an extra success. I went up to 12 because I was interested, and didn't go above that because I wasn't. This isn't any fancy mathematical proof, it's just the result of doing 100,000 tries and checking the results. (Ties don't count, it just retries it.) That's why none of the identical-stat results are precisely 50%. :)
The target number options include standard opposed tests, target number of 4, and target number of 2 + opponent/2, which I added to see how well it worked. (Badly.)
| CODE | Modified rule-of-six off
Standard opposed target
1 2 3 4 5 6 7 8 9 10 11 12
01 49.84 97.00 99.67 99.96 99.99 100.00 99.99 100.00 100.00 100.00 100.00 100.00
02 3.08 49.86 95.79 99.56 99.96 99.99 99.99 100.00 100.00 100.00 100.00 100.00
03 0.30 4.29 49.74 87.96 97.85 99.74 99.91 99.97 99.99 99.99 100.00 100.00
04 0.03 0.49 12.11 49.91 84.21 97.41 98.50 99.39 99.77 99.92 99.98 99.99
05 0.00 0.04 2.17 15.89 49.93 85.38 89.59 94.41 97.18 98.75 99.51 99.87
06 0.00 0.00 0.20 2.65 14.60 50.04 56.42 68.75 79.37 87.70 93.77 97.71
07 0.00 0.00 0.10 1.51 10.27 43.62 49.93 63.68 75.45 85.32 92.52 97.16
08 0.00 0.00 0.01 0.59 5.59 31.01 36.57 50.21 63.98 76.43 87.09 94.91
09 0.00 0.00 0.00 0.21 2.89 20.69 24.38 36.08 50.02 64.60 79.41 91.29
10 0.00 0.00 0.00 0.07 1.27 12.32 14.81 23.41 34.65 49.91 67.26 84.83
11 0.00 0.00 0.00 0.02 0.52 6.24 7.44 12.65 20.48 32.41 49.94 73.05
12 0.00 0.00 0.00 0.00 0.14 2.40 2.80 4.93 8.69 15.26 27.13 49.76
Modified rule-of-six on
Standard opposed target
1 2 3 4 5 6 7 8 9 10 11 12
01 50.22 91.11 98.37 99.63 99.93 99.99 99.99 99.99 100.00 100.00 100.00 100.00
02 8.67 50.14 89.47 97.95 99.63 99.96 99.98 99.99 100.00 100.00 100.00 100.00
03 1.66 10.52 50.00 83.17 95.86 99.35 99.69 99.89 99.95 99.99 100.00 100.00
04 0.34 2.14 17.02 50.03 80.79 95.74 97.30 98.74 99.41 99.78 99.94 99.98
05 0.06 0.35 4.12 19.22 49.75 82.41 87.09 92.42 95.76 97.86 99.09 99.71
06 0.00 0.03 0.63 4.17 17.36 49.83 55.98 67.38 77.35 85.70 92.05 96.91
07 0.00 0.01 0.28 2.70 12.92 43.89 50.10 61.92 73.47 82.90 90.71 96.28
08 0.00 0.00 0.11 1.21 7.71 32.63 37.81 49.92 62.54 74.93 85.19 93.76
09 0.00 0.00 0.03 0.56 4.18 22.87 26.64 37.33 50.05 63.69 77.42 89.94
10 0.00 0.00 0.01 0.20 2.11 14.49 16.87 25.28 35.62 49.94 65.99 83.45
11 0.00 0.00 0.00 0.06 0.93 7.80 9.28 14.78 22.62 33.96 49.77 71.99
12 0.00 0.00 0.00 0.01 0.31 3.12 3.66 6.22 10.02 16.65 28.03 50.15
Modified rule-of-six off
Target number 4
1 2 3 4 5 6 7 8 9 10 11 12
01 50.07 79.95 91.70 96.28 98.26 99.13 99.60 99.82 99.89 99.95 99.97 99.99
02 19.95 50.04 72.68 85.66 92.25 96.08 97.86 98.88 99.38 99.66 99.82 99.88
03 8.36 27.28 49.93 68.72 81.43 89.26 93.79 96.42 97.98 98.84 99.37 99.62
04 3.70 14.36 31.33 49.91 66.33 78.34 86.45 91.59 94.99 96.95 98.19 98.87
05 1.69 7.38 18.35 33.64 50.07 64.51 76.06 84.21 89.61 93.44 95.81 97.42
06 0.85 3.87 10.66 21.73 35.26 49.76 63.15 73.92 82.29 88.08 92.20 94.90
07 0.39 2.15 6.29 13.59 24.08 36.84 50.04 62.08 72.06 80.33 86.52 90.75
08 0.19 1.18 3.54 8.31 15.75 25.98 37.73 50.29 61.21 71.02 79.01 85.02
09 0.09 0.58 2.01 5.10 10.15 17.64 27.28 38.71 50.18 60.49 70.04 77.61
10 0.05 0.34 1.11 3.07 6.57 11.85 19.70 28.81 39.08 49.83 59.80 69.13
11 0.02 0.16 0.69 1.84 4.16 7.85 13.51 20.94 29.81 39.90 49.99 59.48
12 0.01 0.08 0.38 1.11 2.59 5.15 9.24 14.66 22.40 30.94 40.39 50.07
Modified rule-of-six on
Target number 4
1 2 3 4 5 6 7 8 9 10 11 12
01 49.96 75.92 88.12 93.78 96.71 98.17 98.92 99.43 99.67 99.80 99.89 99.93
02 23.71 49.91 69.50 81.64 88.93 93.33 96.02 97.47 98.57 99.07 99.44 99.66
03 11.73 30.36 49.91 65.70 77.46 85.38 90.55 93.88 96.02 97.39 98.41 98.93
04 6.22 18.30 34.00 49.99 63.85 74.48 82.42 87.92 91.88 94.59 96.39 97.65
05 3.23 10.95 22.34 36.19 50.10 62.27 72.29 80.07 85.98 90.07 93.16 95.20
06 1.78 6.57 14.69 25.59 37.47 50.01 61.26 70.47 77.92 84.01 88.33 91.63
07 1.03 4.03 9.39 17.67 27.70 39.09 50.29 60.12 69.22 76.47 82.34 86.92
08 0.60 2.45 6.19 12.08 19.91 29.37 39.23 50.08 59.67 67.89 75.06 80.83
09 0.36 1.48 3.90 8.18 14.13 22.06 30.86 40.46 50.02 59.27 66.84 73.97
10 0.18 0.89 2.51 5.48 10.05 15.96 23.47 31.99 41.08 49.94 58.66 66.25
11 0.09 0.51 1.53 3.53 6.97 11.54 17.63 25.03 33.05 41.41 49.94 58.13
12 0.04 0.33 1.02 2.39 4.77 8.26 13.16 18.91 26.11 33.75 42.05 50.08
Modified rule-of-six off
Target number 2 + n/2
1 2 3 4 5 6 7 8 9 10 11 12
01 49.84 97.70 99.68 99.96 99.99 100.00 100.00 100.00 100.00 100.00 100.00 100.00
02 2.18 49.99 81.07 96.15 98.58 99.74 99.89 99.98 99.99 99.99 99.99 100.00
03 0.33 18.73 50.26 87.67 95.06 99.10 99.63 99.97 99.99 99.99 99.99 100.00
04 0.04 3.97 12.04 49.97 66.56 90.48 94.39 99.21 99.56 99.71 99.84 99.94
05 0.00 1.39 5.01 33.78 49.99 84.22 90.24 98.59 99.21 99.52 99.75 99.89
06 0.00 0.23 0.82 9.43 15.50 49.95 59.59 89.94 92.56 94.57 96.10 97.99
07 0.00 0.09 0.36 5.59 9.67 40.49 50.20 86.85 90.15 92.68 94.61 97.23
08 0.00 0.01 0.02 0.83 1.39 10.13 13.30 49.96 55.84 60.70 65.04 75.56
09 0.00 0.00 0.01 0.45 0.77 7.37 9.84 44.60 50.01 55.25 59.94 71.52
10 0.00 0.00 0.00 0.27 0.44 5.37 7.34 39.43 44.80 49.98 54.89 67.35
11 0.00 0.00 0.00 0.16 0.25 3.89 5.36 35.04 40.11 45.32 50.04 63.30
12 0.00 0.00 0.00 0.06 0.09 2.04 2.72 24.44 28.19 32.33 36.57 49.94
Modified rule-of-six on
Target number 2 + n/2
1 2 3 4 5 6 7 8 9 10 11 12
01 50.13 93.19 98.31 99.65 99.90 99.98 99.99 99.99 100.00 100.00 100.00 100.00
02 6.70 50.21 74.99 92.86 96.68 99.19 99.61 99.93 99.97 99.98 99.99 99.99
03 1.66 24.60 49.86 83.00 91.21 97.92 99.00 99.83 99.91 99.96 99.98 99.99
04 0.37 7.15 16.99 49.86 63.45 87.22 91.53 98.35 98.97 99.32 99.61 99.79
05 0.08 3.39 8.80 36.54 49.97 81.06 86.93 97.44 98.43 98.97 99.28 99.71
06 0.02 0.82 2.09 12.84 19.09 49.85 58.41 87.46 90.26 92.38 94.14 96.67
07 0.01 0.36 1.01 8.40 13.05 41.86 49.70 83.97 87.78 90.23 92.48 95.64
08 0.00 0.07 0.12 1.69 2.48 12.57 15.81 50.32 54.78 59.62 63.47 73.53
09 0.00 0.02 0.07 1.05 1.59 9.86 12.51 45.17 49.97 54.43 58.83 69.44
10 0.00 0.00 0.03 0.62 1.02 7.58 9.55 40.71 45.31 50.10 54.26 65.60
11 0.00 0.00 0.01 0.38 0.67 5.79 7.34 36.47 41.12 45.36 49.88 62.03
12 0.00 0.00 0.00 0.17 0.29 3.31 4.27 26.75 30.14 34.39 37.94 49.97 |
Thoughts: Yes, it's pretty bad. 4-vs-5 is an 85% win for 5. Adding the modified rule-of-6 brings it down to 80%. That's still not great. With a target number of 4, it's a 66% win for 5 (and a 63% win if you add the modifed rule-of-6.)
It's much better when you get above 6, but if you often have people with skills of 6 doing opposed checks, you need to rethink your game balance IMHO. :)
The weird 2+n/2 target number didn't work out as well as I was hoping, combining the bad parts of both. 4-vs-5 ends up equivalent to target-number-of-4, 5-vs-6 is nasty, and 3-vs-4 is nasty (though not as bad as the original opposed number tests). Stupid stairsteps. If we were using d12s this would work much better, I think.
Hmmm . . . well, maybe I'll try that later.
Whether you prefer the standard exaggerated differences or the target-of-4 downplayed differences probably depends on what kind of a game you're running. It's fun to be overpowered and rampage, and it's also fun (in a different way) to defeat enemies who are incredibly powerful compared to you. It's probably more realistic to have it be more random.
I think personally I'll stick to target-of-4 except when I need to override it for dramatic purposes.
If anyone has other statistical breakdowns they'd like me to run, let me know. I find these things kind of fun. :)
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Opposed test statistical study
Oct 29 2004, 12:56 PM
ZorbaTHut Opposed test statistical study Oct 29 2004, 12:56 PM
