Collectible items, such as stamps, coins, paintings, and trading cards, are often valued for their rarity. A side effect of rarer items being more highly valued is that they are also more often traded, discussed, and displayed. A new collector's experience of the category defined by a set collectible items is thus heavily biased towards the rare items. Theories of category learning predict that these conditions make for a uniquely challenging environment in which to learn a category because rarity-based sampling can invert the distribution of associated attribute frequencies. Here, we show that under these conditions, the demand for rarity is self-defeating: when newcomers do not correct for the sampling bias present in their experience, they will have a distorted sense of the category and misunderstand which items are in fact rare, causing rarity to become devalued over time. We find evidence for this dynamic in the context of The Bored Ape Yacht Club (BAYC), a collection of 10,000 non-fungible tokens (NFTs), each with a set of attributes that vary in rarity. We demonstrate that, in line with our theory, over time the influx of newcomers learning about BAYC has been associated with a decrease in the demand for tokens with rare attributes.