Is the argument of perihelion random? I am currently designing star and planet systems in the RPG framework GURPS. This game system has a very elaborate set of rules to set up a star system, complete with planets and the like. However, one (for me at least) critical issue is not addressed in the book: The argument of perihelion.

Now, since I am writing a program to generate these systems for me, I would like to know what steps I can take to make a planet system as realistic as possible. Looking at data from our own planet system, the argument of perihelion looks to be pretty evenly distributed over all angles $[0, 2\pi)$. 

Is there scientific evidence that this is actually the case, or are there any good suggestions on how I could proceed with my program?

(The related question on RPG.SE can be found here.)
Argument of perihelion or most planets/bodies changes very slowly over time due to higher order perturbations from other planets' motions (mostly Jupiter and Saturn for the solar system). General relativistic effects also cause the perihelion to advance over time, though this effect is smaller than the others for most purposes.

So given enough time, the arguments of the planets' perihelia would likely end up being fairly randomly distributed at any given time. Also, the planets' orbits are often dynamic on such timescales due to the effects of higher order perturbations showing up, which can cause eccentricity changes, which also affect the positions of perihelia.

So, my guess would be that it is okay to have the arguments of perihelia randomly distributed, since it is inconceivable (at least for me) that any sort of resonances would be visible at this level in order for the distributions to be non-random.