I am totally totally totally TOTALLY stealing these.
OK.
So, over 100,000 characters, rolling straight 3d6 obvs. gets you a character with (ignoring rounding) 10.5 in every attribute.
If we roll those 100k characters, then always try to reroll the lowest attribute 14 times, we get:
12.7
12.6
13.2
13.8
14.6
15.7
which isn’t necessarily a good model in practice, but kind of shows how it skews averages.
I believe on this forum in another post someone said the best of 3d6 (six scores) five times was roughly equivalent to 4d6 (six scores) one time. I, too, very much like “organic” characters and was dissatisfied with ACKS’ raising of primes producing same-y characters.
I returned to Len Lakofka’s generation method (from Dragon #39):
“Roll 4d6 seven times. Record the sum of the three highest six-sided dice. If that sum is six or less, reroll at once. The sums must be recorded in order. The player is allowed two chances to alter the numbers as recorded. She may switch the positions of two of the numbers and she may discard one number – not necessarily the lowest one.”
Adapted to ACKS, the “discarded” number becomes the character’s starting wealth/template number, and of course there’s no raising of primes.
Alas, I have no attribute improving mini-game …
The nittiest of picks: 1d8+1d6+1d4 will also generate a non-skewed, bell-curved distribution between 3 and 18, as will 1d10+2d4. They’re still bell-curves centered on 10.5, just with higher variance.
I’m trying to understand what those scores represent. Are they the scores average guy has at level 14 using the rule? Technically, you get 13 opportunities, since you don’t roll at 1st level.
Whoops. Rerunning at 13 rerolls, it doesn’t materially change - losing about .1-.15 on each value or so.
And that average is their state at 14th, taking 100,000 characters, rolling 3d6 in order, and for 13 levels picking the lowest stat at each level and attempting to improve.
But it’s not really representative of the system. One would want to delineate different Prime Reqs, roll the original character, swap two scores, then start rerolling each level based on some weighting of your prime reqs vs. attributes where you have penalties, and then come back and say “Characters with one Prime Req may look like this on avg.; etc”.
Something must be off then. Best case scenario, if a character with all 6 scores being 10.5 succeeded all 13 times and you always applied the bonus to a lowest score, then the scores would look like:
13.5
12.5
12.5
12.5
12.5
12.5
They’re not 10.5 in the model; they’re rolled randomly (they average out to 10.5 amongst the 100k characters modelled). So like this:
Original:
6
7
8
10
15
16
New
13
14
14
15
16
18
(this guy was lucky!)
Then the “New” stats, all 100k of them, are averaged.
No, something’s wrong here. Are you rolling for every stat at every level?
The original post had successful rolls increase the stat by 1. So you can’t have a stat total more than 13 points higher than what you started with.
Hah, wow - I derped that up back and forth. Bad week for coding apparently. Wasn’t rerolling multiple stats, but I was just assigning the roll to the stat.
With a simple +1:
STAT: 10.85529
STAT: 10.67734
STAT: 10.98565
STAT: 11.53343
STAT: 12.54543
STAT: 14.24921