Odd-Y

Odd-Y is a connection game played on a hexagonal grid containing an odd number of sides of equal length (thus, an equilateral triangular board, or an equilateral pentagonal board, or an equilateral heptagonal board, etc.). RulesOn each turn a player plays a single stone to an empty cell on the board; once placed, stones do not move. Corner cells belong to both of the sides that they join. The Pie Rule applies: after the first stone is placed on the board, the second player can choose either to play a stone of his/her color, or swap colors with the first player. A player wins by connecting a set of three sides of which the following is true: a triangle drawn of straight lines connecting the mid-points of each of the three sides contains the gameboard's midpoint (i.e., has the gameboard's midpoint inside its borders). (That is the fully general statement of the win condition. For the 5-sided board in particular, there is a very simple statement of the win condition: The winner is the player who connects three sides, not all of which are adjacent.) Draws are impossible in Odd-Y. For each way of completely filling an Odd-Y board with stones, there will always be one -- and only one -- winning group of stones. CommentsWhen played on a triangular board, Odd-Y is also known as 3-Y. Likewise: 5-Y on a pentagonal board, 7-Y on a heptagonal board, etc. Note too that 3-Y is equivalent to The Game of Y designed by Ea Ea. Thus, Odd-Y is a generalization of The Game of Y. Ea Ea himself discovered 5-Y on a pentagonal board, which he called "Star Y" (stating the win condition as described above). Odd-Y generalizes 3-Y and 5-Y further, to any hexagonal grid board with an odd numbered of sides.