Monday, August 7, 2017

Easier way to replicate funky dice for DCC RPG using regular d6s

I recently came across the Dungeon Crawl Classics RPG and have been pretty hooked by the game since then.  The game introduces a lot of very interesting new mechanics into an over-troped hobby, most notably the magic system, the level-0 funnel, the Warrior's Might Deeds, and the dice chain, all of which bring back some of the spice of adventure and originality.

The dice chain is an original game mechanic.  While everyone who has played an RPG is familiar with a modified roll like d10+4 -- that is, roll a ten-sided die and add four to the result -- DCC offers an alternative way to express modifications in terms of changing the die you use, either up or down the dice chain.  The dice chain is
which, if you're familiar with gaming dice or 3D geometry, you realize includes a lot of shapes that don't exist.

In the D20 system of games (such as D&D since 3.5 or Pathfinder), whenever your character attempts something they need to roll for, you most commonly roll a d20 -- a twenty-sided die -- and add whatever modifiers, and try to beat a Difficulty Class for the attempt.  The DCs are usually such that, for instance, a DC 15 is a fairly difficult check.  If you are rolling a check for something you character does well, you will get a positive modifer that you add to your result (like +2, or +6), and if rolling a check your character does poorly, a minus modifier (like -4).  DCC offers an alternative way to think of bonuses and penalties in terms of the dice chain.  Rather than subtracting a modifier, they may ask you to instead roll a d16 to represent low training; or instead of adding a modifier, to roll a d24 or a d30.  Rather than just making your result higher or lower, it actually changes the probabilities by decreasing of increasing the range of possible results.  If the check is DC 15 and you have to roll a d16, success becomes very rare.  If you get to roll a d30 instead, then what is normally a fairly difficult task suddenly seems to your character like no problem.

While it's a brilliant mechanic of the game, after some reading online, I've found that it's also the single most maligned mechanic of the game and represents a pretty big barrier to people joining the game.  Not because they dislike the dice chain in itself, but because where the heck do you get a 16-sided die???

While such dice do exist, they aren't usually available at the Friendly Local Gaming Store.  The standards -- d4, d6, d8, d10, d12, d20 -- can be found at pretty much any game store or online for very cheap, whereas these so-called funky dice are usually only available from small boutique stores online, and aren't cheap.  If you live in the UK or Australia or elsewhere outside the US, then just the shipping costs can be way more than $20.  This represents a pretty big barrier to a lot of people to starting the game.  If you can't get the tools, you can't play the game.

Goodman Games needs to consider offering at least just the crucial d14, d16, d24, d30 to come with the book (or perhaps in a starter set), but until they do, let me offer some ideas on how to simulate funky dice so you can still play the dice chain, at least until you decide to get the actual dice.

There are some ideas on how to do this in one of the earlier sectons of the DCC RPG book, but frankly it's kind of complicated, inelegant, and involves things like ignoring a roll of 8 on a d8 (sure to go over great with players -- especially when they then proceed to roll a 1).

Here are my ideas on how to get around this.  While your Friendly Local Game Shop may not have a 16-sided polyhedron, they almost definitely carry blank d6s (or can get them to you very cheaply).  My work-arounds will involve only modifying blank d6 dice to simulate the funky dice.

Note, there are also dozens of dice roll simulators out there that will simulate any dice roll for you.  These are for people who really want to maintain the "feel" of rolling at the table, without springing for expensive dice.

Reduce the Dice Chain

Firstly, use a "truncated" dice chain.  Part of the reason for the funky dice is to make the transition between dice more smooth.  The biggest offender is the jump from d12 to d20, since the rest go in increments of 2.  The smaller funky dice add some extra smoothness at low numbers, then the d14 and d16 give some transition steps before the d20.  Notice, the jump from d16 to d20, and then d20 to d24 on the dice chain is already a step of 4.  So one possibility is to drop d14 and d7 from the dice chain, while still retaining a bit of smoothness.  (The reason for this is that these are impossible - or very hard- to simulate effectively).

So the new, truncated dice chain is
which, you're noticing, still includes dice like d3 and d16.  I'll tell you how to simulate this next.

Make a d2

The d2 isn't part of the dice chain, and doesn't come up very much in gaming for some reason, but we're going to make some anyway.  This is basically just flipping a coin.  Say that heads is 2 and tails is 1, and you have a d2.  If you'd like, get a wooden or plastic chit and write each side.  While that's as good a d2 as any, flipping a coin doesn't "feel" the same as rolling a dice.  If you have a blank d6, then you can make a d2 by marking it with three 1's and three 2's.  Now you can roll it like a normal die and get the same distribution of results.  Another option is to paint one half green (as an example) and the other half red, and treat green as a 2 and red as a 1 -- this allows you to also use it as a d3 by marking each face with a number, but more on that later.

Make binary dice

A d2 offers two options, and with two options, your standard geek should be reminded of binary.  A binary die is basically a d2, but with 0 and 1 instead of 1 and 2.  I will be calling this a db.  You can make it in any of the ways you make a d2, just number differently.  More effectively, use the coloring option above.  Make the 1s green and the 0s red -- or make the 1s green circles and the 0s red Xs, or the 1s blue and the 0s yellow, or make the 1's a smiley face and the 0's a frowny face.  Using coloration instead of specific numbers will let you use this as either a d2 or a db as needed, and will also let you use this as a d3.

Make a d3

A d3 is actually pretty standard -- some game shops may already be selling these as a d6 numbered 1-3 twice.  If you look closely in the d6s, you will might find some.  If not, they can be created very easily by modifying a blank die.  They can also be coupled to serve as a d2/d3.  I have one that I bought in a store, where half is red and half green, with the numbers 1-3 on the red half and 1-3 on the green half, which serves double duty.  You can also do this simply without modifying a blank die by just rolling a regular d6 and splitting up the range.  Either take 4-6 to be 1-3, or divide the result by two, rounding up.  If taking 4-6 to be 1-3, consider marking those sides as a reminder.

Make a d5

The rule book suggests rolling a d6 and re-rolling on a 6.  Besides being fiddly, one major problem with that is that 6 on d6 is the highest roll.  So a player rolls high, but rather than getting to savor this lucky stroke, they instead have to roll again.  You could avoid this by rolling d6-1 and re-rolling on a 0.  It's the same thing, mathematically, but now they don't feel as bad re-rolling that 1.  But it's even more fiddly now.

This is actually pretty easy, though.  Roll a d10, and take 6-0 to be 1-5.  Or roll a d20 and take 6-10, 11-15, 16-20 as 1-5.  Consider marking those ranges in a different color as a reminder.  You can also roll d10, divide by 2, and round up; or roll d20, divide by 4, and round up.

Make a d7 and a d14

I have no idea how to get this one with dice.  The problem is that 7 is prime and 14 is just 2x7.  This is why I considered dropping them from the dice chain.  If you have a d14, then a d7 is the same procedure used to get d3 from d6, or d5 from d10.

While they can't be effectively simulated with dice (the DCC suggestion is quite fiddly) they can be simulated with other means that were used back in the heyday of RPG gaming during the Great Dice Shortage of '79.  These include spinners, or drawing numbered chits out of a bag.  Another possibility is to make a spinning top/dreidel/teetotum numbered 1-14.  You can get a normal top and -- as evenly as possible -- square off the top edge into 14 notches.  If you go with chits, a spinner, or a top, then the d14 is the only one you need to make, as d7 is then just 1/2 of d14, and the rest can be made with d6s.

Or just consider dropping d7 and d14 from the dice chain.

If you follow the rule book's suggestion for the d7 to use a d8 and re-roll on an 8, then take my suggestion and instead roll d8-1 and re-roll on a 0.  There still isn't any non-fiddly way to get a d14 without rolling d16 or d20 and dropping lots of rolls.

Make a d16

This one requires the binary dice.  Make four dbs.  You will need to make all four visually distinct.  You might have four different base colors, or use four different coloration schemes (viz. one is red numbered 0,1, another is yellow numbered 0,1; or, one is red/green, the other is yellow/blue; or more clear, one is labeled 1000, 0000, the other 0100, 0000, the other 0010, 0000, then 0001,0000).  With these, we are going to create a binary number between 0 and 15.

The logic is similar to the d% by rolling 2d10.  If you understand rolling a tens place with one d10 and the ones place with another d10 to get up to 100, then you should be able to understand rolling four db to get up to 16. When you roll d% from 2d10, then you usually specify, say, the red die is tens, the blue ones.  Or, nowadays, a lot of d10s are numbered 10,20,30,...90,00 to specify they are for the tens place in a d% roll.

The distinction in the four dbs is the same here, except we're distinguishing binary digits.  So the red dice is the 1's place, the blue dice is the 2's place, the green dice the 4's place, and the yellow dice the 8's place (for example).  In this way, you can get d16 by rolling four db, interpretting as binary, and taking 0000 as 16 (similarly to how 0,0 with d% is takn as 100).  Line them up in order, and then the conversion from binary to decimal is as follows:
0001 -  1
0010 -  2
0011 -  3
0100 -  4
0101 -  5
0110 -  6
0111 -  7
1000 -  8
1001 -  9
1010 - 10
1011 - 11
1100 - 12
1101 - 13
1110 - 14
1111 - 15
0000 - 16
Now you have a d16.  (Many of your players will already know this conversion table cold, this being a game by and for nerds).  Consider writing the correct order of the dice down on paper in clear view (e.g. yellow, green, blue, red), perhaps with a visual aid showing their correct order by color, so debates of which is which don't break out; draw squares of the appropriate color on paper in order and have players place the appropriatly colored die on each square.  Numbering with all the zeros (as in 0100, 0010, etc.) also works.

You could also just roll one db four times, starting at 8's digit and going down.  imagine the tension when three 0s come up before the final roll... will it be 0 and give a crit, or a 1 and give a fumble...?

Make a d24

This one is probably the most complicated of the suggestions.  There are two standard shapes for d24, one of which is basically a d6 with square-based pyramids glued onto each side.  That's the one we are going to simulate using a marked d6 and a d4.

Get a blank d6 (preferably a larger one), and divide each face into trangular quarters.  In the central corner of each triangle on each face, write a number 1-4.  Now fill in the numbers 1-24 in each triangle.  The d24 is simulated by rolling the marked d6, then rolling a d4 to determine which of the triangles from the shown face is the result.

The trick here is *how* you put the numbers on the faces.  You want to spread them out as evenly as possible, preferably so that the sum of the numbers on each face is as close to equal as possible.  Might take some thinking to get right.  One possibility I worked out is shown here, so that each face sums to 50 and each opposing triange sums to 25.  The pips are used to indicate the d4 roll for that face.  Since each number 1-24 has only one possibile roll, this gives the same distribution as rolling a d24.
If necessary, cut out and fold over d6 t o see how this fits together

Another obscure option, using the same dice, is to work in heximal notation.  This will probably be way more conceptually confusing to your players, but would work.  Roll d4-1 to represent the 6s place, and a standard d6 as the 1s place.  While binary gets used frequently in computer science, so that the binary d16 not much of a stretch, heximal notation is pretty much useless, and mostly just a neat footnote after learning binary and hexadecimal -- so even most big-time nerds will still get tripped up on heximal notation.  Marking a blank d6 is probably the easier route.

Make a d30

If you get how two d10s can be a d%, then you can understand that a d30 only needs a d3 and a d10.  Consider making a special d3 numbered 0-2 instead of 1-3, and take a result of 0,0 as 10, 0,1 as 1, 1,0 as 20, 1,1 as 11, 2,0 as 30 (and the rest in the obvious way).  This isn't very different from the suggestion in the rule book, except that by labeling the d6 0-2, you make it a bit more obvious.


That's it.  Using only blank d6s from the Friendly Local Game Shop, you can make d2s, d3s, and dbs, and most of a d24, which, together with the "usual" polyhedral dice, can simulate the same rolls as the real thing.  The d14 remains more elusive still, but its place can be dropped from the dice chain without too much shock to the system, if absolutly necessary -- if a d14 is called for, go down to d12 or up to d16 instead.

I think these rolls are a bit less fiddly than the suggestions in the DCC rules book.  The binary dice for d16 probably isn't conceptually simpler, but it involves a lot less rerolling on high rolls, and has the benefit that the result is your result (just in a different number base system).

I should note again at this point, that every one of these can be simulated on a computer without needing to mark any dice at all.

They can also all be simulated with numbered spinners, bags of numbered chits, or with a numbered spinning top/teetotum (a d10, for instance, is just a sort of two-sided top, and the standard 14 and d16 in most DCC dice sets are likewise two-sided tops).  If you have access to wood- or metal-working equipment, you may find the numbered top method to be a more effective method for all of these; just divide the top circle into the proper number of sections and file it down.

All of these are methods for generating uniformly distributed results in the desired ranges.  The numbers generated will have equal probability for each number, as though they were rolled with a fair dice with the desired number of sides.

This should at least help get you started in DCC, at least until you decide if you'd like to shell out the extra money for the funky dice.

If you decide to buy the funky dice, note that d14, d16, d24, and d30 are the only ones you really need, with the lower funky dice being readily generated from these and the standard polyhedra by halving the result.

Hope it helps potential DCC gamers get over that hurdle.


reid said...

I think for d8, it's quicker to roll a d8 and db and compute the answer. But you will have to choose before rolling (I prefer the former): d16 = (db8 * 2) + db OR d16 = (db2 * 8) + d8

reid said...

I meant to start that sentence "I think for rolling d16..."

Reece said...

That would also work. It'd just be an octal representation as opposed to a binary representation. Octal isn't as common as binary of hexadecimal, though.

reid said...

I don't think the representation matters as much as ease or speed, but I just realized it's not as easy/quick as I thought (there is one extra subtraction required). Correction to the formula above: d16 = ((db8 - 1) * 2) + db OR d16 = ((db2 - 1) * 8) + d8

Alas, dice aren't 0 based... it would make my suggestion simpler and get rid of the pesky subtraction I erroneously omitted on my first post. It would also fundamentally change the mechanics for a 1d6 to return 0..5

Also, using a d4 and d6 to make a d24 wouldn't require the use of a blank die. d24 = ((d6 - 1) * 4) + d4

reid said...

Check this out:

Blohggehr said...

There's an easier way to do the d24. You roll a d12 and a d6.
1-3 = +0
4-6 = +12
and then add the result of the d12.

Reece said...

That's true. But it's not nearly as cool ;)

You can get all of the funky ones using tricks like that. I just wanted to show everything except the d7 and d14 can be done only using d6s, and without any "if 1-X add Y" kinds of things. For some people the funky dice is a deal-breaker, and the "fiddly" mechanics are a no-go.

formixian said...

Mathematically, to have the same chance to hit a number there is a simple way to make the funky dices:

d2 : d4 where 1-2 = 1; 3-4 = 2 (divide by 2 round up)
d3 : d6 where 1-2 = 1; 2-4 = 2; 5-6 = 3 (divide by 2 round up)
d5 : d10 where 1-2 = 1; 3-4 = 2; ...; 9-0 = 5 (divide by 2 round up)
d7 : d8 reroll if you obtain 8
d14: d2 + d7 if the d2 == 2 add 7 to the d7 result
d16: d2 + d8 if the d2 == 2 add 8 to the d8 result
d24: d2 + d12 if the d2 == 2 add 12 to the d12 result

About the d7 and obtaining an 8: do not assign an importance to the number obtained, especially if it's an 8. Statistically, the value 7 is as good as the value 1. Getting 8 is equivalent to getting NULL or 0. It is just the face of the dice. The same happens with the D10: we assign the value 10 to the face numbered 0... that's the same idea.

formixian said...
This comment has been removed by the author.
formixian said...

I forgot about the D30:

d30: d3 + d10; if d3 == 2, add 10 to the d10; if d3 == 3 add 20 to the d10