malraux
First Post
But because the 3d6 really converts to a yes/no result (ie you either hit or miss) you really only ever have 2 buckets. That's not a bell curve once you actually resolve the result.
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d20 vs. 3d6 "dice heresy" by Chris Sims
- Thread starter ggroy
- Start date
But because the 3d6 really converts to a yes/no result (ie you either hit or miss) you really only ever have 2 buckets. That's not a bell curve once you actually resolve the result.
Nifft
Penguin Herder
Is this a joke, or do you honestly not see the difference between 3d6 and tossing a coin?
Cheers, -- N
malraux
First Post
It's not a joke. But because the resolution is either success or failure, to a large extent the curve that generates the resolution isn't very important and can be mapped to a flat distribution. that is, if you are using a 3d6 method and hitting requires a 13 or greater, that's identical to the situation of using a d20 and needing a 15 or greater or rolling % and needing a 75 or greater.
Nifft
Penguin Herder
Uh-huh. Any curve of which you only sample two points is identical to a straight line, right?
Wrong, because when the points move along the curve, they don't move at all like they would on a straight line. Since we've been talking about the effects of small bonuses (+1 or +2) on the expected result, it's useless to confine ourselves to just two fixed points.
When we don't confine ourselves to just those two points, the shape of the PDF becomes important, and the "two bucket" outlook becomes less than useful.
Cheers, -- N
malraux
First Post
Right, the affect is different, but because we are only ever looking for a success or failure, there's never going to be a case that you can't model with a flat distribution.
If this were a system where degree of success mattered, then the bell curve matters; that is, if exceeding the target AC by 5 did extra damage, then your actual result is affected by using a d20 or 3d6. But DnD isn't one of those systems. Your result is never 16, your result is hit or miss.
pawsplay
Hero
Exactly. 3d6 is d20 is d%. You never get a "bell curve" for a given set of bonus vs. target. Changing to 3d6 only affects the significance of things that change the bonus vs. target relationship.
pawsplay
Hero
There is no difference. We are essentially talking about two coins... one is fairly true, the other favors heads (or tails) at whatever frequency.
The difference is in the marginal value of +1 at various points along the probability curve. In one case its flat, in the other +1 is more valuable closer to the center. You may be able to approximate any particular roll on a bell curve distribution by rounding to the nearest 5% and using a d20, but you can't model the relation between the points on the curve. At least not without creating a bell curve and doing a lot of work on any given in-game or character creation decision relating to your chances to hit.
It also has distorting edge effects. If you need an 18 to hit an opponent you can do so with 0.5% chance with 3d6 and 15% chance with d20. Even assumptions like a natural 20 always hits (and thus a natural 18 always hits on 3d6) make extremely high AC radically more valuable (as, if you can get out of the normally rooled range, hits are far elss common).
This takes mechanics that are already dangerous (stacking bonuses to make extremely high AC or, conversely, extremely high to hits) even more distorting and thus accelerates the benefits of hyper-optimization.
This is often an undesirable side effect
