The flat curve

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The flat curve

Postby Daeruin » Mon Oct 29, 2012 2:43 am

I was browsing through the Codex today and came across a comment about "the dreaded flat curve" when talking about dice pools. What is that, exactly?
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Re: The flat curve

Postby Galloglaich » Tue Nov 06, 2012 4:45 am

That means when you roll a 20 sided die (or any single die) you are just as likely to roll a 1 or a 10 or a 20.

In real life we tend to expect that an average result is more likely than an outlier (i.e., really good - a 20 - or really bad - a 1). So for example when you roll 3 d6 to get your character attributes, you are much more likely to end up with numbers in the 8-12 range than in the lower end (near 3) or the higher end (near 18). In other words if you roll 6 stats probably 3 or 4 of them will be in that middle group of numbers. So this is more of a 'bell curve'. Like this:

Image

If you roll 4d6 and drop the lowest number, which is what most people actually do, you will skew the numbers a little more in your favor and the average die roll goes up a little, maybe say to the 9-14 range.

In the codex, the use of the "Free Dice" makes the very low numbers much less likely. I don't remember what the exact numbers are but rolling a natural 1 is very unlikely if you are taking the best of two dice on a D20. It goes from 20-1 (i.e. a 5% chance) to something like 400 to 1 or something.

So this lets you avoid the 'flat curve' where every probability is equally likely. Historically in RPG's the 'flat curve' is one reason why a lot of gamers and game designers didn't like the 20 sided die, because the D20 was used instead of using multiple dice of smaller size. But ... when you are rolling multiple dice you are much more likely to get an 'average' number somewhere in the middle of a probability curve (or skewed upward if you are dropping low numbers) which players tend to be more happy with.


Under the codex rules, which you have probably noticed if you have played the system, you can kind of 'make your own luck' by applying your Martial Pool intelligently and using Martial Feats and circumstantial rules to give yourself Free Dice. Thus you get the benefit of a wide range of possibilities (all 20 numbers on the d20) without the principle drawback, the flat curve.

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Re: The flat curve

Postby Daeruin » Tue Nov 06, 2012 7:17 pm

I see. Thanks for the explanation. The ability to make your own luck is one of the things I like best about Codex Martialis. Cool.
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