There are ways to extend the significance of the ideas forwarded in the preceding post (on Bridge Whist and Bridge), but for the most part, our knowledge is too limited. But if you were to collect Professor Hoffmann’s rule-booklets for (say) ten years, you might find that you have collected twenty copies of Selected Patience Games and ten copies of Bridge. From that you would have a pretty good idea that Selected Patience Games (leaving aside the question of editions) is probably roughly twice as common as Bridge. It might only be 1.5 times as common. Or it might be 3 times as common. Or it might be something else. But it is highly unlikely that, with those numbers, Bridge is more common!
And that brings us to Poe’s Tamerlane and Other Poems (first edition). The most common estimate of the number printed is 50. For a long time after Poe’s death, the work was basically unknown. But copies began appearing, and the work got publicity, and now, twelve or so copies of the first edition are known. (And that, given the circumstances, is a high percentage of the number of copies that are generally thought to have been printed.)
A 2009 Christie’s auction catalog-entry on the internet states details in connection with a copy that Christie’s sold at that time. Specifically, the work was first published in 1827. Copies of the first edition, however, were basically unknown until 1876. At that time a copy was discovered at the British Museum. In 1890 another copy was discovered. In 1925, the Saturday Evening Post published a Vincent Starrett article about the book, and “five or so” copies were found because of that article. At the time of the auction in 2009, twelve copies were known (in varying condition; several completely lack the covers), and only two of those were outside of institutional collections. (The book sold for $662,500, including buyer’s premium.) Again, this information is from the Christie’s website. Note: Wikipedia indicates 1859 as the time a copy was first discovered.
There are several interesting points mixed into the Tamerlane story. First, when people don’t know what to look for (or otherwise are not motivated to look), there can be quite a number of copies of a book that are completely hidden from people’s knowledge. Secondly, when people have sufficient motive to find and sell copies of a rare book, additional copies will (probably) be discovered and sold. Also, I think that there is a suggestion that, even when we think that there may be only a handful of copies of something in existence, there may be many more. In the case of Tamerlane, we thought there were zero copies of the first edition, but twelve copies have appeared. Of course, these points are not immutable truths, but they do provide ideas to think about.
But there is another dimension to all of this. Different types of collectibles tend to be preserved at different rates. If you look at old comic books, I would guess that as to certain semi-early comic books, the number of copies known probably approximates the number of copies in existence. In any event, for some items it seems that the known quantity is not going to increase much in the course of a decade or so.
An example would be the original printing of Action Comics, No. 1, which introduced Superman. It is widely (though not universally) known that certain old comic books are worth a lot of money, and I am guessing that nearly all existing copies of Action Comics, No. 1, have now surfaced. Wikipedia states that 200,000 copies were printed, and I have seen it stated in more than one place that approximately 100 copies are known. So, only one out of every 2000 copies printed is known to exist–and I imagine that most of them are not in the greatest shape. (Needless to say, these remarks apply to the first printing only.)