Definition: At-fault accident means you caused the accident to take place. If the insurance company deems you 51% or more at-fault, then you are considered to have caused the accident. A ticket from a police officer is not required to be at-fault according to the insurance company. If you are in a single vehicle accident, more than likely you are at-fault.
If you hit ice, slide off the road, and hit a tree, you are considered to be at-fault because you did not have control of your vehicle at all times. If you hit a pot hole
it is also considered at-fault, because it is a single vehicle accident that is avoidable. The only time you are not at fault is if another vehicle hits you while you are following all the rules of the road.