Last semester, I stumbled on the game Yavalath while browsing reddit. This game is especially exciting because the rules are very similar to tic-tac-toe type games... except for an excellent twist!
Yavalath is played on a hexagonal board. Each turn a player paints an empty hexagon their color. So far, no twist.
If you get four hexagons in a contiguous line, you win. No more moves are played. Still no twist.
However, you are not allowed to play in such a way that you get exactly three hexagons in a row. More than three is fine (and you win) but exactly three is not allowed. Twist! :)
One problem keeps this from being strictly combinatorial: the board can fill up so that neither player wins. In this case, you could just announce that the last player is the winner since no more moves exist. The site gives an example of such a case:
Notice that this position would probably be the result of a sum, as there are an even number of white and black pieces. Cool!
This is a game Cameron Browne generated with the program Ludi. I know nothing about
automatically generating rulesets, except that it seems to have worked out here. Yavalath is very fun to play. I challenged many of my students to quick games before class, and also over lunch.