Right, so a bit behind on following up on things. However, I do want to clarify the Shadowrun / dice pool chart presented in the linked articles. I looked over my old tabulations from the outdated forums – check out the p = 1/3 chart (meaning that 5 and 6 on a d6 will work; these are two of the six faces, hence 1/3). You will note that if you compare the die rolls column (n = 8) with the success rows (k), you get the same data as the chap in the linked article got:
https://www.dropbox.com/s/ydmjo7jgxrxkq1d/D6-P13Prbs.PNG?dl=0
Compare this with the other graph:
k = x = 0, 3.90%
k = x = 1, 15.61%
k = x = 2, 27.31%
k = x = 3, 27.31%
k = x = 4, 17.07%
k = x = 5, 6.83%
k = x = 6, 1.71%
k = x = 7, 0.24%
k = x = 8, 0.02%
…Note that it’s really important to understand data in context. The graph he generated for Shadowrun’s dice pool requires that all eight dice be rolled to get that data. If you require a certain percentage (p = ?) to meet a target number with a given number of dice (n = ?), you need to have numbers available for those situations, and you need to understand how to use that information once you have it.
One thing to consider with Codex is that the target number can change depending on the scenario, rather than being a fixed percentage. The dice can also change in terms of quantity used. So, you will have similar charts generated to the one for Shadowrun in that particular case, but they will all be very different.