Dice system
From FiranMUX
FiranMUX originally used the Storyteller dice system (often called WoD dice, as they were used in the first-edition World of Darkness RPG games) as its task resolution method. In the Storyteller system, ten-sided-dice are used to generate results.
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How Storyteller (or WoD) dice work
A player will have one or more dice to roll, collectively called their dice pool. The number of dice in their dice pool is determined by the relevant skills and attributes of their character for the task they are attempting; for instance, to make a crystal goblet glassmaking and coordination are combined together. The better the character is at this task, the more dice they will have in the dice pool.
To determine a result, all dice in the dice pool are rolled against that task's target difficulty. For each die in the pool, the roll is compared to the target difficulty and used to add up a number of successes.
- If the roll is >= the target difficulty, add 1 success to the total.
- If the roll is 1, subtract 1 success to the total.
- If the roll is neither of these, do not change the total.
For example, a character has 3 coordination and 2 glassmaking and wishes to attempt to create a crystal goblet. The target difficulty set for making crystal goblets is 7, and the character's dice pool is 3 + 2 = 5. She will then roll 5 d10's to generate her result.
If she rolls 2 8 4 7 1, then her result is +2 successes for the 2 rolls >= the target difficulty of 7, and -1 success for the roll of 1, for a total of 1 success.
Often success totals are grouped into different result categories:
- Bonus - An exceptionally successful task attempt, usually attained by 4 or more successes.
- Success - A successful task attempt, usually attained by 1 to 3 successes.
- Failure - An unsuccessful task attempt, usually attained by 0 successes.
- Botch - A ruinously unsuccessful task attempt, usually attained by a negative number of successes.
Problems with standard Storyteller
Range was an issue with this dice system; if 4 successes is a better result than 1 success, then naturally -4 successes connotes a much worse result than -1 success. However, a character with a dice pool of 1 (implying they are very bad at that task) can not roll any worse of a result than -1 because they're only rolling 1 die. In contrast, a character with a dice pool of 10 (implying they are one of the absolute best) can roll a minimum of -10 (although this is very unlikely). Thus you had a system where the better you were, the worse you could (and sometimes did) screw up.
Similarly, it is clear that one could not roll a standard 'bonus' result without a dice pool of at least 4.
A second problem is that botches for some difficulties became more likely with higher dice pools, despite the overall expected average result rising.
Example of botch chance rising with larger dice pool
Also, with a dice pool of 1, the target difficulty has no effect on the chance to botch: it is always the chance of rolling a 1 on a d10, which is 10%.
Finally, at 10 difficulty a character has an equal chance of success+bonus and botching, because only a roll of 10 gives +1 per die and only a roll of 1 gives -1 per die, and the chances of rolling either one 10% for each.
The dice > diff modification
Due to the effects of some of these problems but the constraints imposed by building the game to a good size around the Storyteller system already, a modifcation to the rolling function was made known as dice over diff.
All rolls were made as before, but after the result was computed a secondary check was made on the result. If a character's dice pool was larger than its target difficulty (i.e. 8 dice rolled at 7, etc) then these changes were made to the results:
- If the total result was 0 (i.e. a failure) it was changed to 1 (a success).
- If the total result was -1 or less (i.e. a botch) it was changed to 0 (a failure).
Therefore having more dice than the difficulty rolled at became known as being botchproofed and was highly sought after for task rolling.
Problems with dice > diff
Botchproofing was somewhat unbalancing in effect, as by and large for tasks with potentially dangerous consequences (such as healing), a character would not be selected to do it without being unable to botch, a largely OOC situation since it was not directly based on a character's skill levels.
In addition, botchproofing tended to create a major lift in effectiveness between the last nonbotchproofed dice pool and the first botchproofed dicepool, essentially making that particular skill or attribute point worth 2 or 3 in relative effect.
Example of the dice > diff 'lift'
Botchproofing also did not address the general fundamental problems of the rolling mechanics and the other problems with botching.
Dice over diff botch rate chart
'Newdice'
Because of the fundamental problems in rolling dice in this manner, it was decided to replace simulated rolling of actual dice with a probability table. Instead of rolling dice, every roll would be replaced by a d1000 roll and compared to a table of probabilities for the given dice and difficulty.
An example of this is given for a 6 dice, 6 diff roll listing the d1000 roll and equivalent result:
- 1: 7 successes
- 2 to 13: 6 succs
- 14 to 70: 5 succs
- 71 to 223: 4 succs
- 224 to 477: 3 succs
- 478 to 743: 2 succs
- 744 to 918: 1 success
- 919 to 985: 0 succs
- 986 to 999: -1 succs
- 1000: -2 succs
In order to populate this table, a formula was written to generate probabilities that were close to the results of the WoD dice without exhibiting any of the bad botch-related behavior. Botch results were strictly to decrease with increasing dice, and increase with increasing difficulty. In addition, the range of botches was not to increase with increasing dice.
Newdice botch chart (contrast with dice over diff botch chart above)
Newdice approximate mechanics
This is an explanation of how the forumla works in dice terms. This is not exact because the formula is able to "roll" non-geometric dice (i.e. you won't find a 7 1/2 sided die in your gaming store anytime soon) but serves to convey the idea.
Newdice uses "good" dice and "bad" dice. The "good" dice pool is much like the original WoD dice pool, with two major differences:
- There is a bonus die for all rolls.
- There are no 'botch results.
The 'good' dice pool for a 7@7 roll would therefore look like this:
The blue is the bonus die, plus 7 green dice. Each roll at or better than the difficulty is +1 success. All other results count as 0.
The 'bad' dice pool functions this way:
- There are always three dice.
- A roll of 1 counts as a botch, and is -1 to the success total. Any other result counts as 0.
- As the difficulty goes up, the number of sides on the die goes down.
This is a 10 diff bad dice pool: 
This is a 7 diff bad dice pool: 
This is a 4 diff bad dice pool: 
Combining the positive results the good dice and the negative results from the bad dice results in a total successes score.
The Firan Dice Utility Page
The Firan Dice Utility Page has a number of graph and table generating things to show how the rolls behave between a number of different probability sets (the old unmodified WoD dice, the dice-over-diff WoD dice, 'newdice', proposed newdice revisions, etc).
