We use the concept of entropy maximisation to calculate the influence on a GO board. We provide a Mathematica code and a document explaining the code. We are able to arrive at a simple formula, which can be used to write efficient algorithms. To calculate the influence of, say, the white stones on an empty space V, we calculate how many, how long, and how strong are the paths that link V to the other white stones. See doc/README.md for some illustrating videos.
It has been suggested that maximising entropy is an "intelligent" move in any game. See Link between Intelligence and Entropy for a light discussion on the topic.
Needs["EntropyGO`", NotebookDirectory[] <> "src/EntropyGO.m"]
Board = {{0, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0},
{0, 0, 0, 1, 0, 0},
{0, 0,-1, 0, 0, 0},
{0, 0, 0, 0, 0, 0}};
LoadBoard[board] (*loads global varibles such as BoardInfluence*)
Draw[]
To draw the influence of the paths from the top white piece:
options = {"boardPaths" -> True};
{boardInf, boardPaths} = BoardInfluenceFromGroup[Groups[1][[1]], 1, options];
(*use Group[-1] to access black groups*)
influenceSize = 3
DrawTentacles[boardInf, influenceSize] (*influenceSize inversely specifies how big influence balls should be. *)
To draw the balance of influence between white and black
DrawTentacles[BoardInfluence, influenceSize]
The size of the red (blue) balls indicate the influence of the white (black) stone.
GenerateRandomBoard[19]
Draw[]
DrawTentacles[BoardInfluence, 3]
