I tried completed a few games using my laptop to play myself and haven't had any problems, yet. As it turns out, it's actually faster for me to just play other random people, as my school's high speed connection almost auto-wins mini games, but I suggest this strategy to anyone suffering from a slower connection.
You can play with your primary computer and work on other projects while your secondary computer idles its turns away(as long as you don't miss two turns in a row).
Because of the idling, it is actually slower than playing against someone else, but if you have a slower connection and have problems winning because of it, it may be worth the extra time.
Be sure that you use two different internet connections.