I personally (having never been drunk but having dated a lot of alcoholics) would define the number of drinks in a binge to be enough, and rapidly enough, to result in throwing up or passing out. If the person can still walk enough to make it to the door unaided I'm not sure it's a binge.
A bender, however, is when there's not enough drinking for passing out, but enough to prevent the person making it to the door unaided, that goes on for more than half a day.