Tuesday, March 20, 2012

boring dice charts

Back in the day brand new Lords of Creation boxed sets came with three kinds of dice: a twenty sider, a ten sider and a sixer.  The d10 and d20 were Zocchi dice, but I think the d6's might have been cheap cubes with pips.  I don't quite remember.

One oddity in LoC and nowhere else was that the game occasionally called for a 2-16 result, but did not come with any eight siders.  An early chapter of the rulebook explained how to use the dice, as is customary in many RPGs up until this day.  To get a 2-16 result it instructed you to roll d10+d6.

I've long wanted to know exactly how the change of dice from 2d8 to d10+d6 affects the probabilities involved and the other day I finally sat down and did the math.  Here are the results, represented visually.

Using d10+d6 instead of 2d8 flattened out the bell curve. 2d8 peaks at a roll of 9, just the way seven is the most common roll on) 2d6. With the d10+d6 combine all numbers from 7 to 11 all have an equal chance of occurring, exactly 10% chance for each.

The only other place I recall seeing this sort of set-up is Uncle Gary's new and improved wandering monster charts in the back of the Monster Manual II. He uses d12+d8 in lieu of 2d10 to create charts with many equally common monsters in the middle.

This chart shows the differences between the two methods for "roll some number or less" type situations. I don't think LoC actually uses d10+d6 for these situations, but it wouldn't be more than 3% off from a 2d8 test for any given target number.

As always, feel free to double check my numbers by doing the math yourself.


  1. Anonymous4:53 PM

    I use anydice dot com for this sort of thing and 1d10 + 1d6 looks flat to me!

    One think I noticed playing with the site: 1d4 + 1d6 + 1d8 is pretty similar to 3d6. Close enough to use as a quick substitute if they're aren't tons of dice around. Purists will note that the bell curve isn't quite as steep but I think it's handy anyway.

  2. I am fond of Alternity, and its system for providing dice as modifiers. D&D has +1, -3, whereas Alternity would have something like +1d4, -1d6 (it actually has +1, -3 type modifiers as well but I actually wish it did not)

    There were a few pages of charts that showed the probabilities for different dice combinations which are similar to what you have produced above.

  3. Anydice is nice.

    I also like SmallRoller. (http://www.fnordistan.com/smallroller.html) It installs on your local machine rather than being a web app.

    As for the curves with flat middles, they can be useful. I actually really like the MM2 encounter table method, though it's better suited for special locations than a general random encounter table, IMHO.

  4. Handy to know when making charts. I am wondering what 3d4 or d4+d8 would replace the old 2d6 standby. I am a big fan of the 2d6 charts from b/x like morale, turning undead, emcountet reactions, etc. Your blog has so much cool and useful site. Thanks

  5. Huh. My intuitive thought about d6+d10 was that it would match 2d8 exactly. Interesting to see that it is slightly different. Come to think of it, there are 64 possible results in 2d8, but only 60 in d6+d10.