King of Pearls

Players simultaneously choose how many stones, up to four, they wish to play each turn. Then they sow them along a diagonal line of empty spaces on an 8x8 board, each picking up where the other player left off. When either player reaches the edge of the board, he chooses any empty diagonal line of spaces to continue sowing his stones. After the board has been filled, the players count the number and size of the strings of stones they have created along an orthogonal axis of the board. Players earn points for sets of strings that contain one of each of the four allowable sizes of strings and lose points for strings that can't fit in a sequence.