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Message:: [QUOTE="Numbers, post: 508184, member: 11668"]Maybe not long at all, especially if it was a dealer rather than a collector. Keep in mind that there are only 9999 different radar serials possible, from 00011000 up to 99999999.  So a dealer specializing in fancy serials doesn't need to have very many radars in his inventory before it becomes quite likely that a match will turn up.  For example, if he's got 100 random radar notes, there's a 39% chance that two of them will have identical serials; and if he's got 200 radars, it's an 87% chance.  Even with only 50 radars, there's almost a one-in-eight chance of two of them matching. The formula here is exactly the same one used for the (in)famous "birthday problem", in which you only need to have 23 people in a room to get a better-than-even chance of two of them having the same birthday.  Just replace the 365 in that formula by 9999, and you get the results above. This is why, whenever you see matched-serial pairs, they nearly always have fancy serials: radars, repeaters, low numbers, or something else that a dealer would've been keeping in inventory anyway.  It's a lot less common to see a pair of matching serials that aren't individually special at all....[/QUOTE]