According to trials in mice, the gene for alcohol dependence is thought to be nf1 (neurofibromatosis type 1).

This means that if a parent drinks and has a kid, the child is much more likely to drink, and be addicted to, alcohol.

Many environmental factors depend on whether or not the child will develop an addiction. Physical or sexual abuse, drug accessability, peer pressure, could influence this, and at a much higher risk than someone who's parent(s) did not drink.