The first really strong argument for some randomization that I remember learning went like this:
1. Suppose you have a game which is a perfect indicator of skill. Whenever two people play, the one with more skill wins.
2. We can now give everyone an ordinal number representing their skill in the game. But ordinal numbers are a little unsatisfying. What we really want are cardinal numbers (the answer to the question "how good am I at this, anyway?").
3. We can get much closer to that goal by adding noise to the game. Now, instead of the better player winning 100% of the time, the better player will win with some probability (> 50%) related to his skill. Instead of being doomed to label three people as first, second, and third, we can say "A wins against C 75% of the time, and B wins against C 72% of the time; A is better than B, but the gap is not so large".
Randomization isn't necessary though. Just give one player a deterministic advantage and see how high the handicap has to be for the other player to win. It's essentially the same thing.
