Random Tables - Linear Tables and Bell Curves

Continuing the series on Random Table Theory looking at bell curve tables against linear tables.

Linear / Simple Tables

A linear table uses a d10, a d6, a d20, or a d1000.

Each single number has the same chance as happening as the others.

1d10 What's in the Bag?
1 Coins
2 Books
3 Jelly
4 Clothes
5 Tools
6 Bones
7 Shells
8 A nest of wasps
9 Food
10 Kittens

There is the same chance of the bag having books, jelly or kittens.

That doesn't mean each item has to have the same chance.

1d6 Number of Treasures
1 None
2-4 1
5 2
6 1d4+2

Each number has a 1 in 6 chance of happening but there is a 50% chance of getting just 1 treasure.

The same table could be written

1d6 Number of Treasures
1 None
2 1
3 1
4 1
5 2
6 1d4+2

Giving more clarity at the expense of a little space. Not a problem for a d6 table but it would be for a d100 table with 10 results.

Linear tables are easily recognised and simple to make and use. Within a regular set of polyhedral dice we can linear tables for 1-4, 1-6, 1-8, 1-10, 1-12, 1-20 and 1-100.

If the temptation to use a d3, d5 or d50 comes along, kill it and use a d6, d10 or d100 instead, doubling the numbers.

Bell Curve Tables

A bell curve random table is one using 2 or more dice. The name comes from the bell-curve distribution, meaning some results have far more likelihood of occurring than others.

The 2d6 is a simple example

2d6 Chance of Occurring
2 1 in 36
3 2 in 36
4 3 in 36
5 4 in 36
6 5 in 36
7 6 in 36
8 5 in 36
9 4 in 36
10 3 in 36
11 2 in 36
12 1 in 36

So they are useful for times where we want some results to happen more often than others. They are useful for modelling more complex structures.

3d6 Original D&D Modifier
3 -3
4-5 -2
6-8 -1
9-12 0
13-15 +1
16-17 +2
18 +3

Or the 5th Edition version would look like.. But you're hopefully using 4d6 drop the lowest.

3d6 5th Edition
3 -3
4-5 -2
6-7 -2
8-9 -1
10-11 0
12-13 +1
14-15 +2
16-17 +3
18 +4

I use these in encounter tables, using 1d8+1d12 to give a familiar spread of numbers but a non-linear spread.

1d8+1d12Mountain Non-Combat Encounters
2 A hairy troll (Speaks Goblin, Dwarvish) tends a herd of goats and has named them all. Challenges people to a game of jumping off cliffs.
3 A galeb duhr is in a longstanding and slow-moving argument with a mountain, about a cave. They try to explain this to the group.
4 An old gladiator is enjoying the view. Has retired here after a successful fighting career. Talks of local legend and past glories.
5 An outcast sahuagin priestess (Speaks Common) is the guardian of a waterfall. Friendly with local druids and seek news of wider world.
6 A wounded manticore has been chained to a rock as a sacrifice for giants. Beg for help and promises non-existent treasure as reward.
7 A group of acolytes seek a famed lake said to have healing waters. Some of them bear a magical curse or disease.
8 A gargoyle is trying to hire themselves out as an artist's model. Has written references and keen to show off own stone carving work.
9 An awakened hawk (Int 10) offers its services as a scout and guide.
10 Several commoners are searching for signs of their livestock. Another hour of searching reveals recent tracks of giants.
11 A group of guards (Athletics +3) are training for upcoming games. A variety of physical challenges which strangers are welcome to join.
12 An orog (Armor Class 11, Religion +3) has replaced its plate with brown robes and is preaching about one of the dwarven gods.
13 A goblin boss on a wolf is a trader in cute animals, furs and puppets.
14 A dryad can't leave her grove of trees and asks travelers to deliver a lost set of bagpipes to a nearby settlement. Left by an admirer.
15 A wight is searching for its tomb in the surrounding valleys. Wants to return its sword and helm there before someone else destroys it.
16 Two cloud giants know of a local renowned silversmith and want a go-between as they don't want to scare the locals.
17 A winged kobold (or kobold inventor - VGtM) has several modified hunting traps they want help in trying out.
18 A group of flying killer whales (fly 60 ft.) follow the clouds. One of them is curious about the group and follows them for a day or so.
19 A thug from nearest city is bruised and battered, left to starve by locals. Depserate to change course of the life and get out of debt.
20 A friendly bulette adorned with bangles thinks it is a dog. Plays with local children and digs tunnels around the nearby village.

You can do more funky things using one of the dice for a tables. 3d6 but with one d6 determining the colour of the item.

Hybrid Tables

Some tables can be made both with a little work

One example is the range 3-12, which can use both the linear 1d10+2 or 3d4

Using our "What's in the Bag" from earlier we get... (with chances of results using 3d4)

3-12 (3d4 or 1d10+2) What's in the Bag
3 Jelly [1 in 64]
4 Books [3 in 64]
5 Shells [6 in 64]
6 Clothes [10 in 64]
7 Tools [12 in 64]
8 Food [12 in 64]
9 Coins [10 in 64]
10 Bones [6 in 64]
11 A nest of wasps [3 in 64]
12 Kittens [1 in 64]

I've moved the items around a little. Using 3d4 we have more chance of getting tools than shells. and more chance of shells than jelly.

Another choice is to use something like a d20 and 2d10, or 2d6 and 1d0 +1. On the results that can't be reached. we can place special types. or have particular results such as roll twice or roll on another table.

I do this in my encounter tables

So What Should I Use?

Linear tables have the advantage of simplicity. They are easier for readers to understand and work out what is going on.

A list is very easy to turn into a linear table.

Bell curve tables are as easy to use but harder to work out what is going on. There are rarities and nuances which require some numbers work to understand what is going on.

Modifiers are a topic unto themselves. But have very different applications on a linear tables... vs a bell curve table. Because the numbers change

Also there are still other things to be done with linear tables. It could have the option of using different dice sizes to access subgroups within a table, for example.

Then there are d66 (which is really a d36 linear table disguised as something else) groups of tables and sub tables. Best left for another day.

All the Tables

I have a discord for discussing random tools and tables and I'm also on instagram as rpg_generators with random tables and gens.