My family was in town last weekend (new baby--very exciting) and my brother Sam and I got to talking about board games, and what makes a good game. One reasonable standard comes from Othello's tagline: "a minute to learn, a lifetime to master." For strategy games, at least, we like the idea of complex gameplay emerging from simple rules.
Following that idea, we pulled up a list of ~30 well-known games and rated them for "game complexity" (How complicated are the rules?) and "strategy complexity" (How complicated are strategies for winning?). We came up with our ratings separately, but they were strongly correlated (R-squared values of .68 and .73, respectively).
The strength of this correlation surprised me at first. In retrospect, board games have been such an important part of brotherly bonding that I shouldn't have been taken aback. Case in point: we had agreed to use 1 to 10 scales, but we both independently decided that War and Candyland should score zero for strategy complexity, because neither game ever presents players with a choice.
With data in hand, I averaged our scores and then plotted game complexity against strategy complexity. The two dimensions of complexity are correlated (R2 = .494). Note that both my favorite game (Go), and his favorite game (Texas holdem) are strong positive outliers.
Apologies for the ugly graph. If I had the time, I'd have plugged in logos for all the games. Still, the picture mostly comes through.