I am currently trying to better understand probabilistic skill ranking systems for games, but I find that I have trouble properly understanding the basic concept of how skill as a pairwise comparison can be generalized.

For instance, if all you know is that player C wins player B 80% of the time, while that same player B wins player A 80% of the time, would this be enough data to determine how often C would win against A? How would those calculations work?

Of course it might even be possible for a game to have different styles of play where A might win specifically against C, which would completely confuse the issue, but I am talking about general ranking systems such as [ELO][1] or [Trueskill][2] that only take winning into account.


  [1]: http://en.wikipedia.org/wiki/Elo_rating_system
  [2]: http://research.microsoft.com/en-us/projects/trueskill/faq.aspx