It keeps our dogs in the pasture, but it is primarily a psychological barrier. Our young dog will slip under if she doesn't get zapped hard in a spot, and she will go through there again.
Put some bacon grease on a spot when you first put it up, as you want the first touch to be a memorable one. The charger only hits once per second and if the dogs learn they can slip under fast without a good hit, that's what they'll do.
Get a decent charger too, so it will work when its dry out, or kill off weeds and grass on it.
I don't know if you can get away with 1 strand, maybe with the grease trick?