Parasol

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Parasol is a two-player game played on a hexagonal grid of any size, initially empty. The two players, Red and Blue, take turns placing their own stones onto unoccupied cells in the grid, one stone per turn, starting with Red. Parasol uses the pie rule. A "parasol" here is a hexagonal, size 2 (side length 2) grid. Any hexagonal grid can be thought of as being comprised of densely packed, overlapping parasols. For example, a size 3 grid is comprised of 7 overlapping parasols. A size 4 grid is comprised of 19 overlapping parasols. When the grid is completely filled, if you have the majority of stones in the majority of parasols, you win. Design notesI began the design process by studying random patterns in a parasol to see if I could deduce a means of determining a winner, which determinant could then be generalized to larger grids. Of course, the simplest determinant is who has claimed the majority of the 7 cells in the parasol. At one point, it occurred to me that grids of every size are comprised of an odd number of overlapping parasols. Thus Parasol was born.

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