## The Game of Chessnot

My friend Zeb, aka Zarathustra Brady, invented a new game that uses chess pieces and a chessboard. Before the game, the players put all chess pieces on white squares of the board: white pieces are placed in odd-numbered rows and black pieces are in even-numbered rows. At the beginning all white squares are occupied and all black squares are empty. As usual white starts.

On your turn, you can move your piece from any square to any empty square as long as the number of enemy neighbors doesn’t decrease. The neighbors are defined as sharing a side of a square. Before the game starts each piece has zero enemy neighbors and each empty square has at least one white and one black neighbor. That means that on the first turn the white piece you move will increase the number of neighbors from zero to something. As usual, the player who doesn’t have a move loses.

As you can immediately see, that number of pairs of enemy neighbors is not decreasing through the game. I tried to play this game making a move which minimizes the increase of the pairs of neighbors. I lost, twice. I wonder if there is a simple strategy that is helpful.

It is important that this game is played with chess pieces in order to confuse your friends who pass by. You can see how much time it takes them to figure out that this game is not chess, but rather a Chessnot. Or you can enjoy yourself when they start giving you chess advice before realizing that this is not chess, but rather a Chessnot.

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## Jesse O.:

“As usual, the player who doesn’t have a move loses.”

Is “as usual” here meant to mean “as in chess”? In chess, not having a move is not a loss but a draw.

28 December 2019, 1:40 pm## tanyakh:

Jesse, I meant as usual in many games.

28 December 2019, 2:56 pm## Theodore M. ALPER:

I think you said both of these explicitly, but just to clarify, (A) a move need not be to an adjacent square, but to any empty square anywhere on the board [that meets the enemy neightbor requirement]? and (B) the requirement is that the total number of enemy pairs on the board doesn’t decrease (i.e. it’s ok if it doesn’t strictly increase)?

28 December 2019, 3:08 pm## tanyakh:

Theodore, Yes, a move need not be to an adjacent square. Yes, the number of enemy pairs on board doesn’t strictly increase.

28 December 2019, 3:17 pm