Allow either player to make the first move.

That is, by having the board be active even if we are not assigned to
a team yet. (Obviously, for this to work, this depends on the server
also permitting us to send a move before we've joined a team.)

When we send a first move this way we append an "assert_first_move"
property which tells the server to reject our move if someone else
beat us to it.

Finally, this commit rewords the message above the game to take into
account the team of the current player.