Mathematical impact of sacrificing for prime requisites?

“Once a player has selected his character class, he may raise the
class’s prime requisite ability or abilities if desired by sacrificing
points in other abilities. 2 ability points may be sacrificed from
an ability to raise a prime requisite ability 1 point. This may be
done more than once, but no ability can be lowered below 9, and
no ability may be lowered if it is also a prime requisite for the
class, even if there are a few points to spare above the minimum
required score.” (ACKS p. 17)

For those more mathematically gifted than me, is it possible to calculate the impact of this rule on the otherwise random distribution of ability scores?

To simplify the problem, we could limit the analysis to the four core classes, and assume a player will seek to raise a character’s prime requisite as high as the rule allows.

I guess we would further need a specific measure of the impact? Perhaps highest ability score modifier plus, lowest minus, sum of +/-? So, possibly the impact of the rule is to move the expected +/- of 0 to something like -1, with a “stretched out” distribution of pluses and minuses toward the extremes?

But also, the rule doesn’t impact “middle” rolls (like 10, 9, 10, 9, 10, 9), so 1) the player has to have a little luck or more rolls to benefit, and 2) the rule reshapes only the high/positive edge of the normal distribution.

For comparison, if it helps any, without the rule you’re looking at a highest attribute of:

9: 0.25%

10: 1.28%

11: 4.40%

12: 10.56%

13: 18.10%

14: 21.20%

15: 19.42%

16: 14.15%

17: 7.86%

18: 2.75%

(Mean 14.23, deviation 1.77)

Numbers pulled from AnyDice using the command:

output [highest of [highest of [highest of 3d6 and 3d6] and [highest of 3d6 and 3d6]] and [highest of 3d6 and 3d6]]

It’ll take some heavier functioning than what’s easily presented in the documentation to do what you’re asking through that site (and it may even just time out on the request even if it ‘works’). Probably worth a try, though- Will report back if I get it figured out.

Edit: Should note that a simple “what’s the highest attribute going to be on average” obviously is making the assumption that the highest roll happened to line up with the prime requisite of one of the four classes, just because that’s easier.

Hi DrPete, you can't sacrifice two 10s, no. 



Hi DrPete, you can't sacrifice two 10s, no. 




welp... i've been doing that wrong for quite some time :-/




Hi DrPete, you can't sacrifice two 10s, no. 






welp... i've been doing that wrong for quite some time :-/


Nonsense. You  merely have a campaign-specific optional rule in play.