Wednesday, August 19, 2015

Staying Ahead of the Curve with Dual Dice Tables

Back in March I talked about how amazingly useful Tables can be.  I still fully believe that, but back then I just talked about your simple table where you roll X sided die usually with that many outcomes.  If you want something to be more likely then you just devote more sides of the dice to it, but that's not the only way a table can work.
2d6, behold the power of probability.  On the surface this is juts a range from 2-12, but it's not nearly as simple as that.  IT does mean there can only be 11 outcomes, but the likelihood of those outcomes are vastly different.  Without going into a ton of math the basics is the every number from 2-12 has a certain combination of two numbers from 1 to 6 that add up to that total.  This means that a 2 and a 12 only show up with double 1s or double 6s and thus are the rarest to show up while 6 can show up anywhere from 1+5 all the way up to 5+1.

Wait you might be saying, "isn't 1+5 and 5+1 the same and the short answer is in math of course, but in dice not at all".  The easiest way to imagine this is think about rolling two 6 sided dice one of them is blue and one of them is red.  Now a 5 and a 1 can both be rolls and they would add up to 6, but one time that could be a blue 5 and a red 1 while the other is a red 5 and a blue one.  This little difference actually tells a lot about how often a number can come up in a dual dice table.  Here is a quick breakdown of how many chances any number from 2-12 can come up.  The basic math stays the same with any dice size, but I'm only giving one example because A its enough to get the idea and B I'm not your servant.

2= One Combination (1+1)
3= Two Combinations (2+1 / 1+2)
4= Three Combinations (3+1 / 2+2 / 1+3)
5= Four Combinations (4+1 / 3+2 / 2+3 / 1+4)
6= Five Combinations (5+1 / 4+2 / 3+3 / 2+4 1+5)
7= Six Combinations (6+1 / 5+2 / 4+3 / 3+4 / 2+5 / 1+6)
8= Five Combinations (6+2 / 5+3 / 4+4 / 3+5 / 2+6)
9= Four Combinations (6+3 / 5+4 / 4+5 / 3+6)
10= Thee Combinations (6+4 / 5+5 / 4+6)
11= Two Combinations (6+5 / 5+6)
12= One Combination (6+6)

I also plotted you what those combinations fro two reasons.  First is to show my math for you unbelievers and yes I've had people claim that a two dice table is just and random as a one dice table. Second so you can see the curve.  The closer you get to the center of the table the more likely an outcome is.  Sure you could have a D20 table and make something use up 5 sides to make it more likely, but a 2d6 table has 36 (6 times 6) outcomes and that number 7 takes up 6 of them all on its own.  you want something to happen almost half the time but still have other options there the use 5-7 that's 16 of the 36 outcomes. Finally those 2 and 12 spots while yes there's only one number that can result in them that doesn't mean a one in 12 or 11 chance (I've also have players assume this too). Like I said there are 36 dice outcomes here so those two only have a 1 in 36 chance of happening.

Personally I lie this for tables without equal outcomes (like a crit table)  as much as I love the Lasting Wounds the new D&D 5th Edition has I don't like the fact that getting a minor scar, losing a hand, and cracking some ribs are just as likely (ok that's if you add in a limp, but that also means cracking a rib is less likely to permanently losing something).  With a bell curve you can have limb loss, but say its 1 in 36 while just getting the wind knocked out of you is 6 in 36 or even 16.
Yes its a bit less random, but pure randomness isn't always good give there a chance for the crazy to happen but don't give it the same weight as the reasonable.

1 comment:

  1. Yep! That's exactly why I used 2d6 for my Death & Dismemberment table:

    For added fun, you can have a table that includes a 1 spot, and sometimes it's a flat 1d12, and other times 2d6. Or even 3d4, depending on the outcomes you want to encourage. I used this idea in my motivations table for wandering monsters: