Infinite Chess

Ahh, grasshopper. Your knowledge of standard openings and board positions is useless here.

It takes a few plays just to get used to seeing all the potential moves, what with rooks wrapping around, bishops curving along their course, and some knight-paths that look almost straight - the pattern-matching is different. And as with regular chess, until you can read what moves are possible fairly easily, trying to chain together coherent strategies is very hard... but still a lot of fun, so long as you're playing against someone of roughly comparable skill.

2 players; abstract game