Yeah, that's why the algorithm was implemented. It used to not be that way. But that algorithm helped the balance a lot, and makes the expected value level out very quickly as opposed to taking hundreds of games to do so.

Ah, but there are algorithms for assigning players when using the physical board game. Take a look at this 1998 article from The Diplomatic Pouch. Scroll down for methods of assigning powers using maximin, minimax, or other optimization based on players making ranked preference lists.

Edited for clarity to replace the word "actual" with "physical".