In general, I'm a HUGE fan of variability. I don't think winning is that important, but it is important as a gauge to determine everyone's performance. Now if a game has so much variation that it doesn't seem like anything you do will change the course of the game then it's probably too random, and of course, that threshold varies per player.
BUT.. I don't want a game full of scripted responses and memorization. (tic-tac-toe anyone?) What I really really want is to assert my will against or with players who are doing the same and the phrase that I want to use is from fighting games. I want to play board game footsies.
A little bit about footsies (fighting games). At its foundation, it basically comes down to game theory (economic). If you're unfamiliar with either of those concepts, I'm sorry. I highly doubt I can explain either of those concepts well without embarrassing both of us.
But my interest essentially boils down to this question "do you know, that I know, that you know etc?" and the decisions that we make from there. For instance, if someone in Catan starts laying roads down aggressively, other players have to guess if the road-guy is rushing to a location or is trying to control area. The only problem in that game is that you either 1. can't do anything about it or 2. it doesn't really matter. HOWEVER.. in that rare case where you can do something, it's interesting to watch players either challenge the road, run away or feign a challenge. Most area control games have this in some shape or form but a lot of the times it's very clunky or the encounters are random or something.
The concept that I want to explore is whether or not player agency can drive events instead of semi-artificial randomness. Next, the choose your adventure mechanic for multiple players in either cooperative or competitive format.