The 2-player, 2-strategy, strictly ordinal, normal form games were originally studied by Anotol Rapoport and Melvyn Guyer in a paper entitled A Taxonomy of 2x2 Games. Their paper appeared in 1966 and included an exact count, an enumeration (that is, a complete listing), and a taxonomy of such games. Since then it has been known that there are 78 such games. If we allow each player access to one additional strategy, however, the number of games explodes to nearly two billion. In this paper we compute the exact number of 2-player, 3-strategy, strictly ordinal, normal form games.
"On the Number of 2-Player, 3-Strategy, Strictly Ordinal, Normal Form Games,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 9.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss1/9