I collect game dice as a hobby. What is a word for someone who collects dice?
If you mean what is the word that has the same relation to game dice collection as philately to stamp collection?
Then, I don't think there is already one (also note: while dictionaries define philately as collection and study of stamps, according to encyclopedias stamp collecting is not the same as philately, which is the study of stamps, see here and here).
If you want to be inventive you could attempt to coin:
phil- "loving" + astragaloi "knucklebones"
EDIT: This form was chosen due to etymology of philately
The word "philately" is the English version of the French word "philatélie", coined by Georges Herpin in 1864. Herpin stated that stamps had been collected and studied for the previous six or seven years and a better name was required for the new hobby than timbromanie, which was disliked. He took the Greek root word phil or philo, meaning an attraction or affinity for something, and ateleia, meaning "exempt from duties and taxes" to form "philatelie". The introduction of postage stamps meant that the receipt of letters was now free of charge, whereas before stamps it was normal for postal charges to be paid by the recipient of a letter.
The alternative terms "timbromania", "timbrophily" and "timbrology" gradually fell out of use as philately gained acceptance during the 1860s.
Following "coin collector", "stamp collector", and so on, the collector of dice should be known as a "die collector".
The Romans had actual dice, rather than the Greek knucklebones: the word was alea, as in Caesar's "Alea iacta est". Wouldn't aleaphile be easier to pronounce?
going with Unreason may I propose astragaloiphile
and as psmears suggested (going by the "anthromorphoi" precedent) - astragalophile
A tongue-in-cheek term:
Someone who collects dice is a cubist.
Philocubist is a person who loves dice games but not specifically a collector, and tesserarian is "of, like or pertaining to dice games" but even though dice games pre-date historical records, there is not a known term used by present-day collectors
You collect dice with a rake at a craps table (and other less popular games). A more invented term for a die collector would be a raker.