# CGT path

PageType: Path     Keywords: EndGame, Theory, Index page

 Table of contentsTheory Application Notes Chat

CGT is an acronym for Combinatorial Game Theory, which is a mathematical theory of abstract games, i.e. two-player, alternate turn-taking games with perfect information, no element of chance and no infinite sequences of turns. CGT often analyses such games by reducing them to sums of simpler games, as happens in the endgame of go. A game of go, however, even when it separates into independent positions, is often not a sum of such games, because the positions may include kos and thus have the potential for an infinite sequence of moves.[1]

### Theory

• Introductions
• Basic elements of the theory
• Surreal Numbers  An introduction to a some special abstract games which behave like the members of many mathematical number systems such as integers, rationals reals, transfinite ordinals, infinitesimal numbers
• Negative of a Game  An abstract game with the roles of the players reversed
• Disjunctive Sums  How two games are combined to form a third, analogous to independent positions on a go board
• Ordering of Games  How games may be partially ordered in terms of how favourable they are to one side or the other, depending on the outcome class of their difference game.
• Equality of games  A special case of the ordering, when two games are equally favourable (or unfavourable) to a given player (and hence also to the other)
• Canonical form  An abstract game may be reduced to a canonical form by removing dominated options and eliding reversible options; short games in canonical form are only equal when they have the same structure
• Dominated Option  An option of a game which may be eliminated because another option for the same player is at least as favourable to them
• Reversible  A play or option is reversible if the opponents best answer leaves the position no better for the first player than it was originally; such a move should normally only be played if one also plays the follow-up, or because of a situation beyond the scope of basic CGT, such as a ko or to get another byo-yomi period
• Related topics
• Game theory  An overview of game theory in the broader sense, including probabilistic elements, imperfect information and simultaneous turn-taking.
• Minimax  A placeholder, probably intended to describe an algorithm? to find the best move allowing for all ones opponents possible reactions

## Notes

[1] Although the rules forbid repetitions, this applies at the level of the whole game, and cannot be formulated exclusively in terms of the sequence of moves in one part of the board.

## Chat

CGT path last edited by 2.87.228.112 on February 23, 2024 - 13:09