Saturday, February 25, 2012

Lines and Curves

(D'oh. Found this in my "drafts" folder. This post is part of the background for this one.)

A lot of times people will post, on reddit or elsewhere, that 3d6 is a "better" resolution roll than a d20 because the results fall along a bell curve. Whether or not this makes it better is a matter of choice,  but it never helps anyone's case when they follow up their opinion with a statement like "With a d20, a roll of twenty is just as likely as a one." That tells me they don't understand probability, because with a 3d6 roll, an eighteen is also just as likely as a three. I've even read this phrased as "with a d20, you're just as likely to roll under your target as you are over", which is patently untrue for any target number other than ten (Okay, "equal to or under".) But alas, some people on the internets are wrong, and you can't correct them all.

What they should be saying is, "with a d20, a roll of twenty is just as likely as a nineteen", which makes more sense; with 3d6, a roll of eighteen is not as likely as a seventeen, not even close: a seventeen is three times as likely. And a sixteen is twice as likely as that. But any number is equally as likely as any other number on a d20. If you need to roll, say, 16 or higher on a d20, that means you have a 25% chance of success, about what you'd have if you needed to roll a 13 or higher on 3d6. But if you make the d20 roll, any of the successful numbers is as likely as any of the others.

To me, this means that a linear roll is best used only to determine flat, binary, yes-or-no questions: Did I hit him? Do we find anything? Did I die from the poison? Conversely, it shouldn't be used to determine degrees of success. If a question ever contains the words "by how much" or "by how many", a 3d6 (or other bell curve friendly) roll is usually more appropriate. D&D decouples the question of "how much" from the success roll in most cases; whether this is a good thing or a bad thing is mostly a matter of taste, but there's no reason that the one roll must, as a matter of course, influence the second.

I mention this because I'm at best ambivalent about rewarding a "natural" twenty with a critical hit or a "natural" one with a fumble in my OSR game. There simply is no logical reason why, assuming an attack was successful, one equally likely number should be rewarded over any of the other equally likely numbers.

Of course, if you find that the arbitrary inclusion of massive damage or horrible fumbles increases the enjoyment of your game, who am I to say otherwise? But that's my reasoning.


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