[jnqlnxts] classification of extensive-form games by computational requirements

game length:

1. infinite-length games possible.  (if finite game state, then game must be loopy.)
2. games are guaranteed to be finite length but finite games of arbitrary length possible.  (e.g., players alternate naming smaller positive integers.)
3. maximum game length known at start.

this classification is practically fuzzy: maximum game length could be finite but so large as to effectively be infinite (future post hxfdvhup).  (e.g., loopy games with special rules prohibiting repetition.)  or, infinite or extremely long games are theoretically possible but require both players to be silly.

game state:

bounded or unbounded amount of information needed to describe game state.

common case of unbounded: loopy game has special rules regarding repeating a previous position (e.g., chess 3-fold repetition, go 囲碁 super-ko) so, as the game progresses, game state includes a growing list of positions already seen (in practice, a hash table).

this classification is practically fuzzy: theoretically bounded but so huge as to effectively be infinite.  chess and go 囲碁 have finite numbers of possible positions so keeping track of all of them classifying each as already seen or not requires only a finite bounded (but huge) amount of information.

the above classifications matter for computer implementations of games: how many bits wide should the move counter be to avoid overflow?

other famous classifications: perfect vs. imperfect information (players hide information).  complete vs. incomplete information (randomness or chance).