People talk a lot about"how much luck" a game has, without a lot of specificity as to what that means. Sure, most people are talking in general terms anyway, so there's not a lot of need to deconstruct it, but where would be the fun in that?
I think a decent model for deconstructing "luck in games" as follows: Each player has a "skill" (S) which we'll treat as constant over the span of a single game. Over time this may improve or degrade. Second, each game has a distribution of "luck" (L) or "random factors". Finally, each play of a game, there is a distribution of "performance" (P) or "how well you played". Then to determine the winner, we take S+L+P for each player (where L and P are random variables) and whoever is higher ends up winning. For some games, such as chess, L is essentially 0.
Additionally, the absolute values of these don't really matter, so we can just put some stakes in the ground. Let's just define a "typical novice" as having S=0. Of course, this means some people have negative skill, but that's fine. I also believe that while there are variations in P, from game to game, that it's actually relatively constant. So, let's define P as being a gaussian with variance of 1. When talking about a game, we regularly talk about its "depth" and learning curve, and let's call the difference between S for a "world-class" player and a novice "D", for depth. The units for D are defined by the fact that we've defined P as variance 1. Tic-Tac-Toe has a D well under 1, while something like Chess or Go could easily have D of dozens or higher. Another way to think of D (for games with no luck) is "how many distinct levels of play does the game have?". So, if Joe is a novice at a no-luck game and he is always beat by Fred, and Fred is always beat by Mark and Mark is usually, but not always beat by the best players in the world, then that game is D=2.5. For games with luck, the number of distinct levels of play is roughly D/(L+1). The notion that P is fixed variance of 1 breaks down for games with no choices, like Bingo, because it leads to L being infinite, but I'll ignore that problem for now.
Now, this model has some issues. It doesn't represent atypically non-linear skill curves well. It doesn't handle cases where the performance variation is strongly skill-dependent, or where there are other cross terms. It doesn't model "style" differences well, where you might get circular skill relationships. But, I think it does alright at representing the relationships.
Other than being a fun toy model, I think this actually is a useful, if arcane, way to talk about games. Further, it highlights a category of game I suspect I like more than most people. What I really want in a game is one where L>1 and D>2*L. Further, I mostly don't want D to get too high though, as that makes it too likely that opponents will be badly mismatched. That is, I want a game where luck is more important than how well you play in a particular game, but long term experience trumps both of these, but not by a huge factor. In this kind of game, there's enough luck and variation depending on the players' performance that a novice has a chance, albeit a very small one, against an expert.
Some concrete examples, of my opinions:
The most useful thing this illuminates for me is that I like high-luck, high-depth games. Unfortunately, there's not a ton of them. Heroscape, Race for the Galaxy, Battle Line, Lord of the Rings, and Funny Friends (sort of) are decent examples though. Further, I often find myself arguing that these games are not "high-luck" (contrary to what I just said), because I think a lot of people when they say high-luck mean (L/D) and these all have reasonably low values for L/D. But, maybe I'm misinterpreting, and people mean L/R, in which case they're right, the game is high-luck, but that can be more than made up for with experience. What other high-luck, high-depth games would you recommend?
A lot of people clearly have strong biases toward the left edge of the plot, or the upper left, or even the center. Where on the plot do you tend to prefer? Or, is the plot even a useful breakdown to anyone other than me?