Sprouts just might be the world's best doodling game. It's simple (there are only six rules) easy to play (all you need is pencil and paper), and totally addictive. Most games are based on some field of mathematics. In the case of sprouts, it's topology.

In the family of math, you might call topology a cousin to geometry. Both involve lines and shapes, but in topology, the shapes can be bent and stretched any way you can think of.

Topologists (mathematicians who study topology) often try to find different ways to divide up a surface and since mathematicians love games, it is not too surprising that a couple of those topologists (Michael S. Paterson and the very clever John Horton Conway ) managed to make a game of dividing surfaces.

Here are the rules they came up with:

1. Start with some dots on the paper. The more dots you have the longer the game takes so you will probably just want to start with two or three.

2. Players take turns either connecting two of the dots with lines or drawing a line that loops back and connects a dot with itself.

3. The lines can be straight or curved but they can’t cross themselves or any other lines.

4. Each dot can have at most three lines connecting it.

5. When you draw a line put a new dot in the middle.

6. The first player who can’t draw a line loses.

You might think that a game of sprouts could just keep going but it turns out that each game has a limited number of moves. A game that starts with two dots can go at most five moves. A game that starts with three dots can only go at most eight moves.

Here's how a game that starts with two dots might go.

Player 1 wins this one, but the next time player 2 is a little bit smarter.