I assume that your car rental will be in the United States. If it is not, the advice below may not apply.

I cannot comment on the PAI (personal accident insurance), but if by LIA you are referring to supplement liability insurance (sometimes referred to as "ALI" or "SLI"), that coverage has nothing to do with the value of the rental car. Supplemental liability insurance provides coverage (typically up to one million dollars) for injuries you cause to third parties or damages you cause to third-party property. If you own your own car, your own car rental insurance may extend your liability coverage to rental cars, and you should check with your auto insurer. If you do not own your own car, but have homeowner's insurance with an "umbrella" policy, you should check with your home insurer to see whether the umbrella covers you for injuries or damage you cause when driving a rental car. (Chubb's umbrella coverage does cover rental cars, even if the insured does not own an automobile; I'm not sure about umbrella coverage from other insurnace companies.)

If you have no personal insurance that would cover you for third-party injuries or damage you cause while driving a rental car, and if you have substantial assets (which is likely, since you are a Centurion card holder), you should definitely purchase the supplemental liability insurance.

Moderator: Since the OP's inquiry is really not specific to rentals from Avis, you might consider moving this thread to "Travel Buzz."