Ron Guth:
The 1802 "Reverse of 1800" is one of the rarest of all U.S. Half Cents. As the name indicates, the reverse of this variety is a holdover from 1800; in fact, it is the very same reverse that was used to strike 1800 Half Cents. Sometime in 1802, the old reverse was retired from use and a new reverse (Reverse of 1802) was utilized. At least one example of this rare variety shows the undertype of an error large cent that was cut down and re-used as a planchet. Most examples of the 1802 Reverse of 1800 Half Cents are in low grade and none are known in grades above Extremely Fine.