There are of course people who have looked into these things, game designers who want to know how to best please the game playing crowd. And it can be very interesting to hear what they have to say. Some time ago I came across an article which talked about randomness and how it affects the popularity of a game. Even if you only have the slightest interest for these kinds of things I can recommend that you read the article. It really goes into some depth as to when randomness is perceived as something positive and when it has a negative influence on game play. Any attempt from my part to summaries what he's trying to say would do it injustice so I won't comment on it any further. Just read the article.
Also, make sure to read the extra section on Randomness in Chess which has some interesting nuggets such as this one:
All good games have a "rock, paper, scissors" metagame. By "rock, paper, scissors," I mean to imply three or more strategies that work to defeat one another without any one being dominant. How do I know this? Because if one strategy could dominate, it would, and the game would collapse in on itself. Thus by the knowledge that a game has lasted the test of time, I know it has an inherent "rock, paper, scissors" metagame.