Loopy

The term loopy in combinatorial game theory refers to a game in which a position may be repeated. Such a game no longer satisfies the usual definition of an abstract game.

In go, a ko rule (depending on the rule set) forbids such repetitions, which means that go can be treated as an abstract game. A problem arises when we try to apply the usual methods of CGT to go: this involves separating a game into a sum of smaller games. As long as no ko can arise this works for go, especially in the endgame, when the position reduces to regions in which a move has no direct effect on the score in other regions.

When a region does contain a ko, we need to describe that region in a way which permits repetition after a move elsewhere.

References

• David Moews' article onLoopy Games and Go pp. 259-272 in Richard Nowakowski's Games of no Chance Berkeley/CUP MR 98d:90152. http://library.msri.org/books/Book29/files/moloopy.pdf