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Tom L.Jay is obviously the expert.
Let me answer your question with a different approach:
It is quite difficult to find a specific player's pose from a particular year with a particular name/position/team variation. Even for a common player with multiple poses from every year, it is tough to locate that one particular card. Not necessarily because of rarity - I think Jay estimated that there are somewhere around 10-20 of the more common individual cards(with a specific pose/year/variation), and as few as 1 of the rarest ones - but just because of the abundance of possibiities: hundreds of players, thousands of poses, and tens of thousands of combined variations. With the exception of the California League cards, the 1890 Player's League and NL cards, possibly a few of the early 1887 cards (e.g. the toughest of the script/spotted tie), and possibly some of the more obscure 1888 cards (e.g. a few of the Chicago Maroons), it seems that just about every catalogued card comes to market at least once over a several year period (and possibly more frequently). I'm sure Jay can name a number of unique exceptions, but that is my general perception.
As an example, I collect Baltimore OJs, and have been able to pick up about 70 different variations over the last 4 years. (There are 24 different players, plus two 2-player cards, adding up to over 140 different possible variations just listing Baltimore as the team; many more if you consider the same poses in subsequent years with different teams, or the same player from earlier years with different teams.) Additionally, I have seen most of the variations that I don't have, but it doesn't seem that they were particularly difficult; I couldn't get them either because they were already sold, they went for high prices, or they were part of a large OJ lot.
Just my two cents,
Tom