Mathematica Chronica

There is very little math in Chronica Feudalis. There are no +4 modifiers to add or -2 penalties to take. Instead, your rolls are modified by adding or subtracting dice to and from your pool. You don’t even have to add any dice results together, you just keep the highest roll.

Chronica Feudalis attempts to make the most of the step-die resolution system. It allows for a predictable range of results and any ability’s rank always has a chance of success against any other rank. It’s relatively simple: there’s no adding or subtracting, and certainly no multiplication or division. It’s about comparing numbers. The real math is contained within the dice themselves.

This chart shows the chance of any die rank matching or exceeding an opposed roll. It takes into account the fact that, in Chronica Feudalis, ties go to the aggressor. The columns along the x-axis are aggressor’s die rank. Each colored line on the graph represents a different die rank for the opposed roll.

What we see here is basically what we intuitively get about step-die systems. Rolling bigger dice results in a larger chance of success. Rolling against larger dice results in a smaller chance of success. Many of us don’t care about the exact math, we just need to know that. But others of us feel the need to know our chances: it helps us to make decisions. There-in lies a problem with step-die systems, especially one like this with a roll-and-keep element. It’s difficult to decipher your chances on any particular roll. It’s hard to tell how much invoking a d8 aspect will help you or how much enduring a d6 penalty will hurt you. It certainly can’t contend with d100 percentile systems in this regard.

So this is a bit of an informal analysis on the system to show what all these funny-shaped dice are doing.

Lets say you’re playing a soldier and you get into a fight. You have the Brawl skill (punching and kicking) and the Strike skill (fighting with melee weapons) both ranked at d6. You start out by trying to punch your opponent. You’re not using a tool and your choose not to invoke an aspect. So you’re only rolling the d6 for your skill, nothing else. Each number on that six-sided die has an equal chance of coming up. Your possible results look like this:

It’s flat and linear. Although it becomes a little more interesting due to the fact that your target is trying to dodge out of the way, rolling his own die. You can look at the Opposed Roll Chart above to see what your chance are against variously skilled opponents.

Now let’s say your not getting your message across with your fists, so you draw your sword. Now, not only are you rolling a d6 skill, like before, but you are adding a d8 tool to your dice pool. You roll them together and take the highest result. This chart shows your possible results:

See what that did? First, you increased your possible range of results (from 6 to 8). Second, you dramatically altered your chances in the range where the two dice overlap (1-6). You have decreased your chances of rolling low and your chances progressively increase up to getting a 6. After the peak, the range in which only the d8 can reach, you can see our chances continue linearly.

So, what if we attack with our d6 skill, a d8 tool, and we decide to invoke our d8 Sword master aspect? Adding the additional d8 die to our roll, gives us these possible results:

Our range of results is still 1-8. Adding a third die has altered our progressive ramp into an exponential curve, which peaks first at 6 (where all three dice overlap) and then continues in a straighter acceleration to its next peak at 8 (where the two d8 continue to overlap).

So what can we learn from all this?

  • Rolling larger dice increases your chances for success.
  • Rolling more dice reduces your chance for whiffing (rolling low), increases your chances of rolling high, and therefor increases your chances for success.
  • Rolling 1 die gives us a linear graph of possible results.
  • Rolling 2 dice gives us a positive gradient where the ranges of the two dice overlap.
  • Rolling 3 dice gives us an exponentially positive gradient where the ranges of all three dice overlap.

Keep in mind, this is all coming from a man with an English degree who hasn’t taken a math course in over 10 years. If I’ve misused any terms or gotten my math wrong, I’d appreciate being let known. Feel free to further the discussion of the mathematics behind the mechanics of Chronica Feudalis by adding comments to this post.

  1. Just to follow up this entry :wink:

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