Zillions of Gamesboard games in the Zillions format (only available for Microsoft Windows, currently). After coding the rules to define a new game, the system's artificial intelligence can automatically play one (or more) players. Generally, it is rated at appr. 1900-2000 ELO for chess and most chess variants. Zillions games are programmed using ZRF - a domain-specific language.
Nearly 1000 freeware board games (with appr. 5000 variants total) have been written in the Zillions language. This includes classic, popular games as well as many newly-invented games. Although the vast majority of the entries, to date, are two-dimensional, the program also supports three-dimensional games competitively. [It currently lacks three-dimensional graphics support, however.] The authors all work for free and anybody can contribute games. On the Zillions download page, games are grouped into four categories- 'Chess Variants', 'Puzzles', 'Educational Games', 'Other Games' (a miscellaneous category).
Some of these games are educational and can be used in school classes to teach mathematics (esp. geometry) and other subjects. Zillions Development claims that the power of playful learning is underestimated by some educators.
Note that the Zillions game engine itself is not freeware, although a free demo version with reduced functionality is available.