ORE Probabilities

Here are some calculations of probability for the ORE (One Roll Engine) system. All probabilities are in percents. In all cases, the probability is of getting that result or better. For example, the probability of getting a Height of at least 7 rolling 4d is 20.56%.

To get the probability of rolling exactly a Height of 7 on 4d and no better, subtract the probability immediately below: 20.56 - 15.51 = 5.05%.

Dice
Height 2 3 4 5 6 7 8 9 10
1 10.00 28.00 49.60 69.76 84.88 93.95 98.19 99.64 99.96
2 9.00 25.20 44.91 63.95 79.22 89.53 95.40 98.24 99.41
3 8.00 22.40 40.16 57.89 72.96 84.13 91.45 95.75 98.04
4 7.00 19.60 35.35 51.56 66.08 77.71 86.19 91.89 95.46
5 6.00 16.80 30.48 44.98 58.58 70.23 79.47 86.37 91.25
6 5.00 14.00 25.55 38.13 50.45 61.62 71.14 78.88 84.90
7 4.00 11.20 20.56 31.02 41.68 51.84 61.06 69.10 75.88
8 3.00 8.40 15.51 23.66 32.26 40.84 49.06 56.68 63.57
9 2.00 5.60 10.40 16.03 22.18 28.57 34.99 41.28 47.32
10 1.00 2.80 5.23 8.15 11.43 14.97 18.69 22.52 26.39

The Height results assume you always choose the set with the best Height. Height has the most variation in results. The spread starts out even, but skews towards higher Heights the more dice you roll (assuming you ignore lower sets). Very large Heights are not probable, even with lots of dice.

Dice
Width 2 3 4 5 6 7 8 9 10
2 10.00 28.00 49.60 69.76 84.88 93.95 98.19 99.64 99.96
3 0.00 1.00 3.70 8.56 15.76 25.16 36.27 48.33 60.42
4 0.00 0.00 0.10 0.46 1.27 2.73 5.02 8.31 12.70
5 0.00 0.00 0.00 0.01 0.05 0.18 0.43 0.89 1.63
6 0.00 0.00 0.00 0.00 0.00 0.01 0.02 0.06 0.15
7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01

Width has minimal variation in it. Most of the time you will get either Width 2 or 3. If you determine damage based on Width (as is the case in many ORE variants), damage is going to be based mostly on weapon strength. If you want a more variable damage system, you might derive damage from Height instead.

Of course, in the Width-based-damage ORE systems, where you hit matters a lot, so that limb-hits (Heights under 6) are relatively harmless, while head-hits (a Height of 10) can be an instant kill. If you use create an ORE variant that eliminates hit locations, though, you will probably also want to switch to a Height-based-damage system, leaving Width to control action speed.

Dice
Sets 2 3 4 5 6 7 8 9 10
1 10.00 28.00 49.60 69.76 84.88 93.95 98.19 99.64 99.96
2 0.00 0.00 2.80 12.16 29.44 51.62 72.78 88.02 96.15
3 0.00 0.00 0.00 0.00 1.22 6.86 20.29 41.29 64.66
4 0.00 0.00 0.00 0.00 0.00 0.00 0.69 4.61 15.61
5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.46

The Set probabilities assume you are trying to maximize the number of sets. For example, it assumes you treat a 4x7 set as a pair of 2x7 sets. If you have a -1d penalty for attempting a second action, the cutoff for when this is worth trying is about 7d or 8d. It's definitely not worth it for 5d or less.

Trying for three actions is only worth it if you can offset penalties, have something like a Master Die or are rolling 10d.

Note: If you want to double-check the logic I used, the "OreProbabilities.java" file contains the Java code of the program I used to generate the results. Click the "files" button below to see the attached file.

Unless otherwise stated, content on this page is licensed for reuse under either the Open Gaming License v1.0a or the Creative Commons Attribution 2.5 License. See the Licensing page for details.