fabula ultima check probability table
A post on reddit today made me wonder what actually the probabilities were of various types of result in the (excellent) Fabula Ultima RPG.
The basic mechanism for a check in Fabula is to roll two of the dice that represent your attributes, depending on the nature of the task - say, Might and Dexterity - add them together, and compare to a target number, usually 10. The attributes range from d6 to d12. In some cases, the effect varies according to the highest roll of the two dice - when attacking, for instance, damage is usually the highest roll plus a number. It's easy to calculate the average total from two dice, but the average highest roll is harder, so I automated it.
If the two dice match and both are 6+, that counts as a critical success, and if they're both 1, that's a fumble.
In many cases in Fabula, players get to pick which dice they use when choosing skills or equipment - e.g. if you have Might d12 you really want a weapon that attacks with Might + Might - so these numbers might be worth knowing first if you're that way inclined.
| Roll
| Mean total
| Mean highest die
| Critical
| Fumble
|
| [d6 + d6]
| 7
| 4.47
| 2.78%
| 2.78%
|
| [d6 + d8]
| 8
| 5.23
| 2.08%
| 2.08%
|
| [d6 + d10]
| 9
| 6.08
| 1.67%
| 1.67%
|
| [d6 + d12]
| 10
| 6.99
| 1.39%
| 1.39%
|
| [d8 + d8]
| 9
| 5.81
| 4.69%
| 1.56%
|
| [d8 + d10]
| 10
| 6.55
| 3.75%
| 1.25%
|
| [d8 + d12]
| 11
| 7.38
| 3.13%
| 1.04%
|
| [d10 + d10]
| 11
| 7.15
| 5%
| 1%
|
| [d10 + d12]
| 12
| 7.88
| 4.17%
| 0.83%
|
| [d12 + d12]
| 13
| 8.49
| 4.86%
| 0.69% |
While there's nothing too weird here there were a couple of things I noticed:
-
Any check using a low die is always going to have a low critical chance, and in fact the chance goes down the higher the other die is. For example, to critical with a d6 + d12 check, you have to roll a 6 on the d6 (1/6 chance) and a 6 on the d12 (1/12 chance) - half the probability compared to a d6 + d6 check. Critical changes do not simply go up as you add better dice either. The best chance works out to be with d10 + d10 - five rolls are criticals, double 6, 7, 8, 9, and 10, and the chance of each is 1/100. One might have guessed that d12 + d12 would be better, but there there are 7 criticals (doubles of 6 - 12) but the chance of each is 1/144.
tl;dr criticals are unpredictable, try to have similar dice and not a d6
- Highest roll also doesn't go up quite as one might expect, but in the other direction. Here, you want dice which aren't similar, and the effect of including a low die is less. A check of d6 + d12 beats d8 + d10 for highest die, even though they have the same mean sum.
You can find the script I used here: