I hate to tell you this, but this is a correspondence site. It doesn't matter if they have 1 or 500 games. If they decide not to move, they don't have to for the time frame the each game is set for, and that can be up to 21 days with a 28 day time bank. So you are looking at the possibility of over a month between moves if this is the time out time bank set.
I would recomend subscribing, this way you can get more than just 6 games that will make you wait for a move.