The players start with a certain number of dots scattered across a sheet of paper. A move consists of drawing either a line between two dots or a loop starting and ending at the same dot. The player then places an additional dot somewhere along the new line or loop. Furthermore, no dot may have more than three lines emanating from it. Hence, a new dot placed on a line actually has two connections already made.
Players take turns drawing curves.
The winner is the last person able to play. At first glance, it may seem that a game could keep sprouting forever. However, because each turn makes two connections and opens up only one, the number of moves has a definite limit. Indeed, one can prove that a game starting with n dots must end after a maximum of 3 n - 1 moves. Initially, there are no lines, so the dots have a total of 3 n possible links.