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How rare is a Remington Standard No. 2? I just picked up a rather rough, albeit complete example on eBay very cheaply to restore. I can’t find too much out about them online aside from the historical aspect of it being the first typewriter with a shift key etc.
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I think that depends on your definition of rare. It's a frequently used word in the typewriter world - mostly by sellers trying to convince people that the odds of winning a lottery are better than finding a 5-Series Smith-Corona.
Estimating actual versus perceived rarity is difficult. Using your No. 2 as an example, it appears that some 95,000 were produced - and no one can authoritatively say how many of those have survived. Based on the Database, which has thirteen examples of the No. 2, I would describe it as uncommon rather than rare. Others will undoubtedly disagree with me, but I say this because Database contributions are mostly made by collectors who are actually willing to make the effort of registering their machines (I know a couple of collectors who don't have their collections represented there). This representation doesn't account for all of those other owners, which I perceive to be the majority, who just consider typewriters to be decoration or a family heirloom being kept in the attic.
Some might describe it as rare, but I wouldn't be shocked if I spotted a No. 2 in a local antique shop.