The Connect Game

Two friends are playing the following game:

They start with 10 dots and taking turns, connect any two of them which are not already connected. The player who first makes all dots connected to each other, loses.

Who will win the game?

The second player will win. First, he makes sure he gets 9 of the points connected to each other, leaving the tenth point isolated. After that, both players must keep connecting points among the connected 9, until exhaust all 36 edges between. Since 36 is an even number, the first player will be the one who will connect the tenth point to the first 9 and lose the game.