
He went overloading on testing and coding and his name was
United Kingdom Redhill Surrey
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I would like to document some interesting flaws in the core action resolution mechanic in the Storyteller system. If you are familiar with this system, you can skip the introductory background that explains how it works.
Background
Characters have a number of Attributes and Abilities each of which is rated from 0 to 5. 2 is an average human score. 5 is the highest human potential. Some supernatural powers may raise the values beyond this maximum.
An action is typically tested by the appropriate combination of attribute and ability, adding the values together to calculate the size of the dice pool. This many tensided dice (with values read as 1 to 10) are rolled against a target difficulty. Each individual die rolling equal to or higher than the difficulty counts as a success. Each individual die rolling a 1 deducts one of these successes. Rolling more 1s than successes is called a botch; rolling a net total of 0 successes is a failure; a positive amount of successes is a success, with the number of net successes determining the degree of success (typically on a scale of 1 to 5).
Note that when the Storyteller system was revised in 1998, the definition of a botch changed subtly: a botch would only result if there was at least one 1 rolled, and no successes at all (as opposed to a greater number of 1s than successes).
So usually dice pool sizes range from one to ten dice. Even with supernatural powers, it is unusual that more than twenty dice are rolled.
A standard target difficulty number is 6, although the difficulty can range from 2 to 10.
Flaw: Difficulty 2
Any individual die roll can only be a success (+1) or a botch (1). This means that when rolling an odd number of dice, it is impossible to fail; only to succeed or botch. But when rolling an even number of dice, one can succeed, fail, or botch.
This skews the probability distribution in odd ways:
Flaw: Probability of Botching It would be a reasonable assumption to make that as a character improves in their ability to perform a particular task, that the chance of a critical failure (botch) should decrease; or at least should not increase. However this is not always the case with the system as written: for a fixed target difficulty, the probability of botching can sometimes increase as your dice pool increases.
The specific ranges where this flaw occurs are...
Difficulty 2: the probability of botching when rolling an odd number of dice is higher than when rolling one less die.
Difficulty 2: the probability of botching when rolling 3 dice is higher than when rolling 2 dice.
Difficulty 7: the probability of botching when rolling 2 or 3 dice is higher than when rolling 1 die.
Difficulty 8: the probability of botching when rolling 2 to 8 dice is higher than when rolling 1 die; the probability of botching when rolling 3 to 4 dice is higher than when rolling 2 dice.
Difficulty 9: the probability of botching when rolling 2 to 36 dice is higher than when rolling 1 die; the probability of botching when rolling 3 to 19 dice is higher than when rolling 2 dice; the probability of botching when rolling 4 to 12 dice is higher than when rolling 3 dice; the probability of botching when rolling 5 to 9 dice is higher than when rolling 4 dice; the probability of botching when rolling 6 to 7 dice is higher than when rolling 5 dice.
Difficulty 10: the probability of botching always increases, the more dice that you roll.
As mentioned above, the revised edition of the rules starting from 1998 fixed this bug. Instead, botches could only be rolled if there was at least one 1 rolled, and no successes at all (as opposed to a greater number of 1s than successes). This gave a maximum probability of botching of 10% for a dice pool of 1, with a reduced probability of botching as the dice pool increased. Probabilities of success were completely unaffected.
This was a fine solution, and completely fixed the problem (after only seven years of product sales).
Probability Distributions
Here are graphs for all difficulties; open them up for a larger view. The probabilities are also listed in a comment to each image, to 0.1%.
Difficulty 2: Difficulty 5: Difficulty 8: Difficulty 3: Difficulty 6: Difficulty 9: Difficulty 4: Difficulty 7: Difficulty 10:

Hans Messersmith
Canada Hamilton Ontario
With your head held high and your scarlet lies You came down to me from the open skies It's either real or it's a dream There's nothing that is in between
Twilight, I only meant to stay awhile Twilight, I gave you time to steal my mind Away from me.

Nice article Stelio.
Here is another article covering similar territory...
http://www.scribd.com/doc/46230301/d10Probability
It is of interest mostly because of the formulas it derives.

フィル
Australia Ashfield NSW
Promise me there won't be any squares at my funeral

Strange that some game designers don't do the maths as a matter of course. Not everyone's a mathematician, but hopefully there's a friend of a friend or an excel template or something to help with probability.



In addition to the revised Vampire probabilities (when you get around to them), I'd also be interested in a comparison to nWoD.

He went overloading on testing and coding and his name was
United Kingdom Redhill Surrey
Support comes in many forms: community involvement, forum posts, submitting data, running PbF games, wordofmouth advertising, financial donations... All these are vital to this site, and you have my sincere thanks for participating in any of them.
Currently: planning.

dysjunct wrote: In addition to the revised Vampire probabilities (when you get around to them), I'd also be interested in a comparison to nWoD. Article, graphs, and tabulated probabilities all updated to reflect the improvements introduced by the revised edition of the rules.
So... what are the full details of the nWoD mechanics?



I'm no expert, I've only played nWoD once, and I'm in my cups, but I think it is:
 basically the same, dots etc.  however target numbers are fixed. 8+ is always a success, 10s count as successes and get rerolled, with exploding possible.  number of successes is always degree of success, using the standard 1=marginal, 3=complete, etc.  situational difficulty substracts dice from the pool.  botching is only possible if lack of skill and/or difficulty reduces your pool to one die or fewer. In that case, you still get to roll a die, but a one is a botch.
Please correct, nWoD fans!

Samuel Sol
Brazil São Paulo SP
All engines full to awesome land!
*tap* *tap* Is this thing on?

This sounds a lot like Scion and Exalted, so I think it is correct for nWoD



That always annoyed me, too. I never played the new version, though.



