The Hydra is a rooted tree. The object of the game is to chop off all its heads (the blue disks). At step n, when you cut a head, the Hydra will grow n new copies of the tree growing from the neck at which the head was cut.
A theorem by Paris and Kirby [1] states that you always win, no matter how you chop the heads, but it takes a rather long time to chop down a hydra. Paris and Kirby also showed that Peano arithmetic does not prove that hydra always loses.
The Hydra game was implemented by Andrej Bauer using a technology invented in the twentieth century known as "Java." The "applet" depended on NPAPI which was powered by a steam engine.
[1] Laurie Kirby and Jeff Paris: Accessible Independence Results for Peano Arithmetic. Bull. London Math. Soc. 1982; 14: 285-293.