Crossline

Crossline is a simple game that can be played in a few minutes with minimal setup. To begin, draw a circle and then draw 10 dots evenly spaced around the perimeter of the circle. The first move is to draw a line between any two non-adjacent dots. Players then take turns drawing lines between any two dots such that the new line crosses exactly one other line. The player who draws the last line is the winner.

Example Crossline game showing the setup on the left, a game with the first three moves annotated in the middle, and a completed game on the right.

Strategy

Because the goal is to draw the last legal line, it is important to keep track of how many legal lines are still possible to draw, and how each line limits the moves going forwards. If you can place your line such that there are an even number of remaining legal lines, then you can guarantee a win. If you cannot force the game to end in an even number of moves, try to find a line that provides more even endings than odd endings. This will tilt the game in your favor. It's very difficult to do this until the very end of the game because there are so many possible moves to keep track of, but if you practice, you'll get better looking ahead. The player that can look ahead the furthest will have the advantage.