There's a game called Cthulhutech which has a dice-based problem resolution system.
I'll use a notation of nd+b where relevant, where "n" is the number of 10-sided dice (giving a value from 1 to 10), and b is the skill bonus.
The first part is simple: The result of a roll is (initially), the highest of all dice.
The next complication is that if any number appears multiple times, the result is the sum of all copies: i.e, if I roll 3d+0 getting [5,5,9], the result is 10 (5+5).
The final complexity is that rolling a series of (at least 3) contiguous numbers results in the sum of all of them: i.e., rolling 5d+0 getting [2,4,5,6,10] is 15 (4+5+6).
The final result is the highest of all three possibilities, so 2d+0 => [2,2,10] is 10.
So, multiple related questions:
- Is it possible to find a probability function for this (That would be f(n,b,t) represents P(nd+b>=t) where n is the number of dice, b is the bonus, and t is the target. (Or, equivalently, p(nd>=t-b))).
- Since I can pay a certain amount of skill points in order to raise either n or b, is it valid to take df/dt vs df/db to decide which option is better?