### Critical Damage and Random Numbers

So I was thinking about critical hits, where some attacks do much more damage than others. Normally, this is just a 2x or 3x bonus. But what if you wanted occasional 30 or 200 times the damage? And what if you wanted to use this system for more than just damage? City sizes and skill checks and so forth. The random number generator would need to be on a continuous scale, instead of occasional discrete bonuses.

And more importantly, how would you balance this? It wouldn’t be fair if critical attacks greatly boosted DPS. Or if skill checks that were bursty gave an advantage.

So, basically, I wanted a random number generator with a consistent average value, and a variable range, without going negative. For simplicity, I used an exponential system. So, if the variance is 2, you can get numbers anywhere between 1/2 (0.5) and 2, with an average of 1. Or, if the variance is 471, you’ll get values between 1/471 (0.0021231…) and 471, but the average value will still be 1.

(more…)