The way I try to use the most is to have the player roll under the appropriate attribute number on 1D20. This works well; pick the most relevant attribute and roll. It works pretty well for opposed rolls, too, so long as the winner is based on the character's attribute and not the opposed roll unless the attribute numbers are equal (in which case things might just have to cancel and something else has to be done). Although sometimes I do make use of the "beat my roll" technique even when I probably should have the player roll against an attribute.
Anyway, whenever I think about these things sometimes questions pop in my head. Questions like....
Suppose the CS SAMAS programme has a special forces unit. How might we determine whether our SAMAS pilot succeeds in joining it?
Say that any current SAMAS pilot seeking to join the unit must complete a number of qualifying trials in sequential order and do so in 15 days or less. Say that CS number crunchers have determined that the average number of successes is given by
σ = 30 - I.Q. attribute number.
"Time to event" random variables are usually distributed exponentially. The probability function for such variables is
f(x) = m * exp(-mx)
here m = 1/σ = 1/(30 - I.Q.) and the interval is [0, 15] days.
So for pilots with I.Q. attribute number 10 the probability is obtained by integrating
(1/20) * exp(-x/20) dx over [0,15]
which is 1 - (1 / exp(3/4)) = 52.763%. The integrations for several I.Q. attribute numbers are summarised in the following table.
Code: Select all
I.Q. P, %
---- ----
10 52.764
12 56.54
14 60.839
16 65.748
18 71.35
20 77.687
22 84.665
24 91.792
26 97.648
28 99.945
29 100
I don't think the choice to use I.Q. attribute number gives bad results. But factoring in the other required attribute and the character's experience level (or points) might be fairer. In any case, this killed the time I needed it to...
