Hydra game

In mathematics, specifically in graph theory and number theory, a hydra game is a single-player iterative mathematical game played on a mathematical tree called a hydra where, usually, the goal is to cut off the hydra's "heads" while the hydra simultaneously expands itself. Hydra games can be used to generate large numbers or infinite ordinals or prove the strength of certain mathematical theories.

Unlike their combinatorial counterparts like TREE and SCG, no search is required to compute these fast-growing function values – one must simply keep applying the transformation rule to the tree until the game says to stop.