Some relevant information excerpted from pages 230-8 of
Nicholas & Alexandra: The Last Imperial Family of Tsarist Russia:
"Today, the State Archive of the Russian Federation holds the private collections of Emperor Nicholas II, Empress Alexandra Feodorovna and their children, Grand Duchesses Olga, Tatiana, Maria, and Anastasia, and the heir to the throne, Alexei. The Archive contains 4,509 items, of which more than a quarter are individual photographs or albums. In addition to these collections, the private archives of the grand dukes and courtiers contain correspondence and photographs of the last tsar and his family."
""Nicholas II obtained a camera in the year of his coronation; he took pictures throughout his life. [....] The first family album dates from this year [1896]... The album contains 508 photographs from the period 1896-7."
"Thirty-three albums for the period 1906-1917 with family photographs from the personal collections of the Grand Duchesses Olga, Tatiana, Maria, and Anastasia are kept in the State Archive of the Russian Federation."
"The last amateur photographs were taken by the youngest members of the family in the spring and summer of 1917 in Tsarskoye Selo at the time of their arrest...The photographs from the Tobolsk period of the family's incarceration are missing from the State Archive, but a few pictures survive in private collections and have been reproduced in various publications. There are no known photographs of the Romanovs in Ekaterinburg."
Private family albums belonging to NII survive for the following years:
1896
1897
1900-01
1905-1910
1910-11
1911-1913
1914
In Alexandra's private papers, there were 900 loose photographs dating from 1896 to 1916.
So by my count, there are a minimum of 40 private family albums (probably more, since I didn't find any mention of Aleksei's personal albums) which may contain up to 500 pictures each. When added to Alexandra's loose photos, that makes approximately 20,900 photos in the IF's private collection.
Incidentally, a court photographer named Yagelsky "was a master of the art of instant photography and left an enormous collection of photographs of the emperor and his family in moments of rest and relaxation.... Yagelsky accompanied the emperor and his family wherever they went, and took thousands of photographs." He even accompanied them to Livadia and on board the Standart. So we can't really know which of the informal shots were taken by Yagelsky, and which were captured by the IF themselves (except perhaps for those taken in the private apartments of the AP.)
