#### Saelorn

##### Hero

I've been thinking about system mechanics recently, and I realized that I have difficulty intuiting the mathematical implications of a count-the-successes type system, such as used in World of Darkness or Shadowrun. In something like D&D, it's easy to see how a +1 to hit compares to +1 AC and get a rough estimate for probabilities. Likewise with GURPS, where both the attack roll and the defense roll are independent of each other and have a direct percentage chance of succeeding, it's easy to intuit the combined probabilities.

How do probabilities compare when you're rolling a bunch of dice and counting successes, if both the attacker and the defender get to roll? If you need a 7 or higher on a d10 to count as a success, and the attacker is rolling nine dice against the defender's five dice, what is the chance that the defender will roll more successes? Has anyone seen a big chart somewhere?