From what I understand there are no records of the actual mintage's of the 1937 Specimen sets. There were two different sets available in 1937, a red presentation set, and a cardboard set. There also was two different finishes available, matte and mirror. The estimated mintage's for these sets is that approx. 1000 sets were issued to collectors in 1937. Complete sets with there original cases are quite rare as many sets were broken up to get the different dollars. My guess would be the survival rate of these sets would be less than 500 known.
From an old book (1957) in my library here is a copy of a article referring to these 1937 Specimen sets.
