I'm still looking for a name for this game. Everything else is there though. This was written as an exercise to limit the rules text to a maximum of 500 words. I'm well under, at around 350 or so, including the words used in the example.
Each player starts with six pieces of the same colour. They should place these pieces in the six closest black and white spaces to their own side (the board should be aligned so than there are four black and white spaces on the edges near the players).
Randomly decide which player moves first. In a turn, each player may move one piece. The piece may be moved to any empty adjacent space (adjacent spaces share an edge with the space the piece is currently in, spaces joined only at corners cannot be moved to).
You may only move into, out of or over a red space if there are an even number of pieces on the board. You can only move into, out of or over a blue space if there are an odd number of pieces on the board.
As well as moving pieces, you can capture pieces belonging to the opposing player. The winner of the game is the first to capture all of the opponent's pieces. To capture a piece, it must be in a space that is adjacent to your own piece, and also further onto the board than the space your piece is in. You must be able to move your piece into a space that adjacent and further onto the board than your opponent's piece. To execute the capture, move your piece to this space, and remove your opponent's piece.
If a player cannot move any of his pieces, he has lost.
E.g. In the example above, there are only 5 pieces remaining on the board (They are numbered for illustration purposes). The white player can move piece 3 to capture black piece 2, ending the move in the top black square. White piece 2 cannot capture black piece 2, as black's space is not further onto the board than the space occupied by the white piece. White piece 1 cannot capture black piece 1, as it cannot move over the blue space.