Big List of examples of recreational finite unbounded games What are some examples of mathematical games that can take an unbounded amount of time (a.k.a. there are starting positions such that for any number $n$, there is a line of play taking $>n$ times) but is finite (every line of play eventually ends.) Also, it would be nice if it were recreational in nature (by this I mean I basically mean its nontrivial, I could conceivably be enjoyed by humans theortically.) One answer per game please, but edit variants into the same answer.
This is a big-list question, so many answers would be appreciated.

The Hydra problem can be converted in a game with several players. The first player chooses the hydra. Players take turns cutting heads.
