I have a persistent cervical hpv infection (4 years). what is the likelihood that this will cause cancer? and how often should i have smear tests?

Hard to say: The frequency of HPV positive college age women prior to the vaccine approached 70% in some studies. Some would eventually develop cervical cancer over the years or decades. Most would not. Pap smears were the most effective method of early detection long before the link to HPV was known. Your OBGYN keeps up with the current suggested frequency based on your specific case.