The Voronoi game

Questions
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1

Voronoi (the game)

  1. Ten random points in a grid make Voronoi cells.
  2. Players R and B alternate placing points on the grid for red and blue Voronoi cells. (Alt+click)
  3. First to connect three sides wins.

Here’s some code I came up with for it.

DynamicModule[{p=RandomReal[{-1,1},{10,2}]},LocatorPane[Dynamic@p,Dynamic@Show[VoronoiMesh[p, 
ImageSize-> {500,500}, MeshCellStyle->Table[{2,n}-> If [n>10,If[OddQ[n],Red,Blue], Gray],{n,1,Length[p]}]],
 Graphics[Table[{If [n>10,If[OddQ[n],Red,Blue], White],Text[n,p[[n]]]},{n,1,Length[p]}],ImageSize-> {500,500}]],
LocatorAutoCreate->True, Appearance-> None]]

voronoi.gif
voronoi.gif436×491 23.5 KB

It doesn’t quite work, though – the cell order doesn’t correspond to the Point order. That makes the game a lot more random.

So… some questions.

  1. Is there a good strategy for the current random game?
  2. Is there a fix for the code? Can it be made shorter?
  3. Is there a strategy for the fixed game?
  4. Can an AI be made for one or both of the colors?
  5. If the game is too easy with 10 initial points, how many points make the game interesting?
2

Cool concept! But “three sides” of what? - Do you mean “three sides” of the square field?

3

Yes, three sides of the square field. A similar game is Y, where the winner connects three sides of a triangle. In Hex and games like it, there is a pair of opposing red sides and a pair of opposing blue sides.

A search on “Voronoi game” shows some implementations. In one version, the winner is the person with the greatest total area after some given number of turns.