Ron Guth:
Proof 1865 Three-Cent Nickels are generally considered to be the rarest of the series, though the margin between the rarest and the second rarest is not large. The low mintage of only 500 Proofs adds to the allure of this date.
In grades up through PR66, the 1865 Three-Cent Nickel is available for a price. In PR67, this date becomes a real condition-rarity. Cameo Proofs represent approximately half of the total population, but only ten percent of the population are Deep Cameos.
The best advice for this date is to seek out fully struck examples as free as possible of minor planchet flaws and copper spots. The rare coin with colorful toning should command a premium.