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Skill Function.
Dec. 14th, 2009 03:43 pmIts a tiny breakthrough, but I'm now able to present to you (thanks to WolframAlpha) the Proposed Skill Function for a possible future role-playing game. It resembles the function (tanh(x)+1)/2 which it was modeled after, but is (somewhat) more amenable to mental calculation.
The function gives the probability in succeeding in a skill roll that has an abstract bonus of X. N and K govern the rate at which bonuses improve your chances. For every +K bonus, your chance of failure drops by a factor of N. So, with N=2 and K=10, every +10 bonus halves the chance of failure and every -10 penalty halves the chance of success. At +10 the chance of success is 3/4, at +20 its 7/8, at +30 its 15/16 and so on. There is no limit to how high or low the bonuses can go, and your chance of success is always higher than 0 and lower than 1.
N=2 and K=10 are one possible set of parameters I could use in a game, but another option is N=10,K=10. In this scenario, die rolls are made by rolling a D10 to generate successive digits in a value between 0 and 1, until its clear if a roll has succeeded or failed. Then, a +10 bonus or better means .9 or less succeeds, a +20 means .99 or less succeeds, +30 means .999 or less, etc. By the same token a -10 penalty means that .1 or less succeeds, a -20 means .01 or less succeeds, -30 means .001 or less, etc.
NOTE: Oops. I get different numbers than expected for N=10. Not sure where I went wrong, but it still basically does what I want.
The function gives the probability in succeeding in a skill roll that has an abstract bonus of X. N and K govern the rate at which bonuses improve your chances. For every +K bonus, your chance of failure drops by a factor of N. So, with N=2 and K=10, every +10 bonus halves the chance of failure and every -10 penalty halves the chance of success. At +10 the chance of success is 3/4, at +20 its 7/8, at +30 its 15/16 and so on. There is no limit to how high or low the bonuses can go, and your chance of success is always higher than 0 and lower than 1.
N=2 and K=10 are one possible set of parameters I could use in a game, but another option is N=10,K=10. In this scenario, die rolls are made by rolling a D10 to generate successive digits in a value between 0 and 1, until its clear if a roll has succeeded or failed. Then, a +10 bonus or better means .9 or less succeeds, a +20 means .99 or less succeeds, +30 means .999 or less, etc. By the same token a -10 penalty means that .1 or less succeeds, a -20 means .01 or less succeeds, -30 means .001 or less, etc.
NOTE: Oops. I get different numbers than expected for N=10. Not sure where I went wrong, but it still basically does what I want.
