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.