Lattices in Game Theory: should partially ordered sets be left to the experts

The games born on day n form a bounded partially ordered set. The Hasse diagram of day 3 games was given in the book "Winning Ways" 1982 (first edition). It took 17 years before anyone noticed that the diagram was wrong! The proper diagram is a distributive lattice. Several natural classes of games also form distributive latices. I'll present a survey of these results and the first example of a class that forms a planar but non-distributive lattice.