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%