AnyDice Classic Archive 16
Interpolating distributions
Suppose you're using a 1d20 mechanic, but would like to curve the distribution, while keeping the same 1-20 value range. Take Median is a nice solution for that, for example 3d20m1. But what if that curves too much for your taste?
You can interpolate between dice mechanics! You do this by varying which dice mechanic you use, either by alternating between then or by rolling a die to decide which to use each time. You can do this in one roll, for example:
Roll a d4, a red (or whatever that distinguishes it) d20, and two additional d20. If the d4 shows a 1 or a 2, your result is the value of the red d20. Otherwise, your result is the middle value of the three d20.
You can adjust the flatness of the distribution by changing how the d4 dictates which mechanic to use. With a d4, you can produce a 3:1, a 1:1, or a 1:3 selection ratio.
By interpolating mechanics you can find distributions that are otherwise hard or impossible to get. For example, by rolling 3d20 and picking either the highest or the lowest value with a 1:1 ratio, you get a distribution where the extremes are more likely to be rolled than the average.
You can interpolate between any two mechanics, they needn't have the same value range. So, in a way, you can compromise between using 1d20 and 3d6.
You can modify this approach in multiple ways (one of which is actually exploding dice), but take care that the final mechanic is still playable!
Unfortunately, AnyDice 1 can't handle interpolated mechanics. AnyDice 2 will be able to hande it, but that's not very useful right now. Fortunately, it's not that hard to combine precalculated distributions in a spreadsheet, like I did for this post.
Wow, looks great. I can't wait for AnyDice2!
3d20m1 has a nice, gentle bell curve. I might end up using it in a few games to see how it goes. One question, though... if you had 3d20s, and one "red" one, and took the middle for all rolls EXEPT when the red one read 1 or 20 (in which case you went with the red) how would that look on a curve?
It would jerk the 1 and 20 up to 5%, while the rest of the 3d20m graph would sink and flatten a bit to compensate. So you get two steep peaks and a hill in between.
"3d20m1 has a nice, gentle bell curve." -- Actually 3d20m1 has a parabolic curve. 3d20 has a bell curve, and 2d20 has a pyramidal "curve". I'm not sure that these differences would have a palpable impact on play at the table...but the height of the curve sure does! It's great to be able to differentiate between high potential-but-unreliable characters and limited-but-steady types of characters.
Thanks for this tool Jasper, you rock!
My pleasure!
How much difference it makes mostly depends on how the roll is interpreted in the system you use. But you're right that the difference is mostly subtle.