Sprouts

Sprouts

This is a game for two players. All you need is paper and a pencil. The game starts by drawing three dots.

The first player has a turn by joining two of the dots and marking a new dot in the middle of the line. Or the line may start and end on the same dot.

When drawing a line, it cannot cross another line. (This is important to remember!)
A dot cannot have more than three lines branching to or from it. For example, in the game below, dots A and B cannot be used any more because they already have three lines.

The idea is to make it impossible for the other player to draw a line.
So the last person to draw a line is the winner. What are the winning tactics?
Does it matter who goes first?
Why must the game end after a limited number of moves? How many?
What happens when you start the game with four or five dots?