exploding statline

rule

to generate a standard six-stat line with each stat ranging from 0 to 5:

1. roll six d6; for each die that shows a 1, mark one stat down as 0 and set those dice aside.
2. re-roll the remaining dice; for each die that shows a 1 or a 2, mark a remaining stat down as 1 and set those dice aside.
3. re-roll the remaining dice; for each die that shows a 1, 2 or 3, mark a remaining stat down as 2 and set those dice aside.
4. ...and so on.

repeat, increasing the threshold, until either no dice remain or it is impossible to keep going (that is, if you would have to roll higher than a 6).

why?

if bonuses from skill range from 0 (unskilled) to 5 (expert) and bonuses from circumstance range from 8 (easiest task that could be failed) to 0 (hardest task that could succeed), then a Target-20-style core mechanic of d20 + stat + skill + circumstance such that a roll of 1 always fails and a roll of 20 alwasy succeeds.

to my mind this is a pretty good balance of character ability and circumstance. also, this kind of exploding roll is fun.

but...what are the probabilities?

the most likely stat values to be generated are 1 or 2, followed by 3, 0, 4 and distantly by 5. the exact frequencies are:

0	16.67%
1	27.78%
2	27.78%
3	18.52%
4	15.43%
5	3.09%

75.5% of six-stat lines rolled with this method will total 9 or more, and 72% will total 12 or less. the probability that the highest score rolled will be the given number is given in the following table

0	46,656 to 1 ≈ 0%
1	0.77%
2	13.42%
3	41.63%
4	35.27%
5	8.91%

3d6 down the lifepath

the system presented here builds on this statline

rule

A background is something you could be raised to, while a career is a way to seek your fortune. Backgrounds have longer skill lists and careers have short ones. There is also a skill list for unfortunate wretches. All adventurers start with some basic adventuring skills (2 body, 2 verbal).

1. Roll two distinct d6 three times. 
2. One die increases your Condition and the other increases your Presence.
3. Take verbal skills based on the CO die and body skills based on the PR one.
   

   Roll	1	2,3	4,5	6
   Skills	4	3	2	1

4. Until you roll doubles, take skills from the first background you rolled. After that, take skills from either the career matching that roll or from the wretched list.

Your Training is equal to your total number of body skills (2 + those you chose) and your Learning is equal to your total number of verbal skills (2 + those you chose).

build

To support this character creation system, one obviously has to provide setting-appropriate backgrounds and careers. How exactly a roll of two dice indicates one or the other is not specified. Here are some possibilities, given that indicate the fact that only non-doubles can be keyed to backgrounds.:

• Difference: 5 backgrounds of descending probability or 6 careers of varying probabilities (0: 1/6, 1: 5/18, 2: 2/9, 3: 1/6, 4: 1/9, 5: 1/18).
• Sum: 9 backgrounds or 11 careers with a curve:
  2. 1/36 career
  3. 1/15 background, 1/18 career
  4. 1/15 background, 1/12 career
  5. 2/15 background, 1/9 career
  6. 2/15 background, 5/36 career
  7. 1/5 background, 1/6 career
  8. 2/15 background, 5/36 career
  9. 2/15 background, 1/9 career
  10. 1/15 background, 1/12 career
  11. 1/15 background, 1/12 career
  12. 1/36 career
• Combination: 15 equiprobable backgrounds, or 15 careers of 1/18 probability and 6 of 1/36.
• Ordered pair: 30 equiprobable backgrounds or 36 equiprobable careers.

Regardless of how one orders the transitions, be aware that there's a 125/216 ~ 57.87% chance that a character will come through with no career. Of those that have a career, all of them will have rolled doubles for their first career, so doubles should be assigned to the sorts of careers that are commonly "open to all comers."

why?

I wanted something that was somewhat close to both 3d6 down the line and a lifepath system. This deviates from 3d6 down the line by having much more centrally-normalized TR and LE in the 5-14 range, but CO and PR are pure 3d6. The main thing I don't like about it is that it is fixed length. Ideally, I'd want a lifepath system that's purely random except for your choice to stay on for another round or get off. Well, one must compromise I suppose.

dice pools

Postulated: dice pools are fun. It is fun to adjust the number of dice you roll. It's scary to face a roll with fewer dice than usual, and feels great to roll a huge fistful.

Postulated: forgone conclusions are not fun. If you know before you roll the dice that there's no way to get a certain outcome, why roll?

Proposed: this is why people don't like taking sums of dice pools.

The fact that the floor of the sum of a dice pool shifts is problematic in a different way than that the peak of its bell curve shifts or than that its ceiling shifts. Look at the probability of rolling a certain sum or greater on 1-4 dice:

#	1D	2D	3D	4D
1	100.00%
2	83.30%	100.00%
3	66.70%	97.20%	100.00%
4	50.00%	91.70%	99.50%	100.00%
5	33.30%	83.30%	98.10%	99.90%
6	16.70%	72.20%	95.40%	99.60%
7		58.30%	90.70%	98.80%
8		41.70%	83.80%	97.30%
9		27.80%	74.10%	94.60%
10		16.70%	62.50%	90.30%
11		8.30%	50.00%	84.10%
12		2.80%	37.50%	76.10%
13			25.90%	66.40%
14			16.20%	55.60%
15			9.30%	44.40%
16			4.60%	33.60%
17			1.90%	23.90%
18			0.50%	15.90%
19				9.70%
20				5.40%
21				2.70%
22				1.20%
23				0.40%
24				0.10%

The floor moving is bad because it creates forgone conclusions by opening gaps in the outcome range of the smaller dice pools. It also creates them by shifting the 100% to outcomes that had previously not been 100%. We don't see either of those problems when we subtract the number of dice rolled from the sum:

#	1D	2D	3D	4D
0	100.00%	100.00%	100.00%	100.00%
1	83.30%	97.20%	99.50%	99.90%
2	66.70%	91.70%	98.10%	99.60%
3	50.00%	83.30%	95.40%	98.80%
4	33.30%	72.20%	90.70%	97.30%
5	16.70%	58.30%	83.80%	94.60%
6		41.70%	74.10%	90.30%
7		27.80%	62.50%	84.10%
8		16.70%	50.00%	76.10%
9		8.30%	37.50%	66.40%
10		2.80%	25.90%	55.60%
11			16.20%	44.40%
12			9.30%	33.60%
13			4.60%	23.90%
14			1.90%	15.90%
15			0.50%	9.70%
16				5.40%
17				2.70%
18				1.20%
19				0.40%
20				0.10%

This also makes the tiers of possible outcomes go up by 5s which is a lot easier to deal with mentally than going up by 6s (unless you're Count Rugen).

a modest proposal

Take the sixes off your dice and replace them with zeroes. Boom, done.