![]() StartingPoints Paths Referenced by
|
Game Theory Interface
Path: CGTPath · Prev: CombinatorialGameTheory · Next: TreeRepresentation
Difficulty: Advanced
Keywords: Theory
This is a page trying to smooth the path of go players who would like access to the combinatorial game theory (rather than those coming in the opposite direction). Minimax playThis corresponds to what go players would recognise as proper or honest play (effectively honte). Both sides do the best not to make mistakes that can be punished by the other side (as measured by the final score): so no overplays. This is taken for granted in game theory in general, unless players are consciously applying random strategies. This connects with one attitude for handicap play in go: White may assume that Black is (unconsciously) applying a random strategy rather than best play.
Minimax play corresponds therefore to seeking 'saddle points' or 'pivots' in pay-offs. It also corresponds to the logicians' idea that games in general model alternation of existential and universal quantifiers ("whatever she played I had a move such that whatever she played I had a move such that ..."). Given a tree-representation of a finite game with numbers as leaves, it is routine to calculate the minimax result. One works from the leaves towards the root, simply choosing the maximum (resp. minimum) of the leaf numbers at each level and making that a new leaf. EndingIn CGT the ending condition at foundational level is ''if you can't play you lose". For example, this apples to the normal version of Nim. This sorts out finite games, but allows infinite games where no one wins. For go players that's like not having a superko rule in operation to force the end of the game.
One should be aware, however, that in the translation into CGT terms of go positions, that ending condition is masked. It hasn't gone away: scoring comes down to adding up numbers and within the translation of numbers the same ending condition still operates. If one pushes too hard on that door, though, one finds one is talking about go with a group tax. This is slightly murky, and, more to the point, not required.
Path: CGTPath · Prev: CombinatorialGameTheory · Next: TreeRepresentation This is a copy of the living page "Game Theory Interface" at Sensei's Library. ![]() |