Stat Generation: Random but fair - this time for D&D

Previously I gave a random (but balanced) method for generating stats for my game Explore. This was a random method of generating three pairs of bonuses for Strength/Con, Agility/Reflexes, and Memory/Intuition where the total bonus is 0, and no pair differs by more than 2.

Unfortunately this method cannot easily be adapted to D&D stats because there are too many possibilities to list them all in a table!

So here's a method for generating random stats for D&D where the sum of all the stats is always the same:

Rolling Stats

Draw out a 3*3 table as follows:

3	4	5	2	5	2	13
4	3	3	4	5	2	12
1	6	6	1	5	2	12
	13		7		6

Roll one d6 nine times and fill in the table in order (left to right starting at the top):

3		5		5		13
4		3		5		12
1		6		5		12
	13		7		6

Then sum each row and write the sum at the end:

3		5		5		13
4		3		5		12
1		6		5		12
	13		7		6

Then for each of your 9 rolls fill in 7 minus your roll:

3	4	5	2	5	2	13
4	3	3	4	5	2	12
1	6	6	1	5	2	12
	13		7		6

Then sum these new columns:

3	4	5	2	5	2	13
4	3	3	4	5	2	12
1	6	6	1	5	2	12
	13		7		6

Your 6 stats are these column and row sums: 13, 13, 12, 12, 7, 6.

Add them up and check that they add up to 63!

Stats of Stats
So what's the chance of rolling an 18 with this system? You need to roll all 6s in a row, so 1 in 216 chance for these, or all 1s in a column, so again 1 in 216 chance. So the distribution of stats is almost identical to that of the normal 3d6 system.

It isn't as balanced as my system for Explore - using the bonus tables from B/X it is possible (just) to get as much as a total bonus of +3 or -3 (e.g. 18, 18, 9, 6, 6, 6). It works much better for the 3rd edition stat bonuses, in which case the total bonus is always between +1 and -1. Either way I would allow anyone with a total negative bonus to increase their lowest stat until the bonus is zero. For example 15, 15, 15, 12, 3, 3 is -3 total so you increase the 3 to 9 and get 15, 15, 15, 12, 3, 9.

Stat Generation: Random but fair

Generating stats has always been problematic. Rolling 3d6 often leads to under-powered characters, but although many solutions attempt to fix that (e.g. 4d6 discard the lowest), you still end up with some characters much better than others. "Point buy" systems are fair, but lose that random element.

After several iterations I came up with the following random method for Explore, though the method can be easily altered for any other system.

For Explore it generates three sets of pairs, each with a bonus +3 to -3, where the sum of the bonuses is 0, and each pair cannot differ by more than 2.

Method

To generate your stats roll on the table below.

Roll 2d%. Write down one followed by the other to give you a result 1-10000.

This gives you a row on the table.

This gives you three pairs, allocate these pairs to STR/CON, AG/REF, IN/MEM. You decide the order in each pair.

You can swap the order of the two d% to give you an alternative row on the table.

You may also choose to have the inverse of your stats (swap all + and – signs). For the rows where this is different, this is given as an extra column.

Example

For example if you roll 32 and 73 you can have 3273 or 7332. For 3273 that give you [2,0],[0,0],[-1,-1] or[ 1,1],[0,0],[0,-2]. For 7332 it only gives you [2,2],[1,-1],[-2,-2], since the inverse of this is the same. You can choose any of these three sets of stats, and allocate them as you see fit. For example

  STR 0, CON 2, AG -1, REF -1, IN 0, MEM 0

or

  STR 2, CON 0, AG 0, REF 0, IN -1, MEM -1

but not

  STR 2, CON -1, AG 0, REF 0, IN 0, MEM -1

(as you have to keep them in pairs).

The distribution of stats is almost exactly the same as rolling 3d3-3:

Note this system gives you 1575 different sets of stats (given the different ways you can assign them), which is a reasonable amount - 1.3% of the possible sets you could get by rolling 3d6.

Stats

In Explore there are three pairs of stats:

STRENGTH / CONSTITUTION
AGILITY / REFLEXES
INTUITION / MEMORY

Each is a bonus +3 to -3. (There is no 18 Strength gives +3, a strong character simply has Strength +3), the total bonus is 0, and stats in a pair cannot differ by more than 2.

Why these six?

I liked the idea of linking pairs of stats so that a high Strength character is also likely to have a high Constitution. (It has to be Constitution as Stamina sounds too SciFi). That means an even number of stats, 4 stats is too few, and 10 is too many, hence it's got to be 6 or 8 stats.

It's common to have a pair of stats for Agility / Dexterity / Quickness / Reactions / Reflexes. I've gone for Agility and Reflexes.

For the mental stats it's a bit tricky - do you have two or four?

I dislike using a roll on Intelligence / Logic / Reasoning  to solve problems - it's always more fun to set players a puzzle to solve themselves. Similarly Charisma / Personality / Presence / Charm is generally superfluous as players usually attempt to persuade NPCs through Role Play. Hence I've settled on two mental stats: Intuition and Memory.