I also sensed that I had a killer excuse to call a special phone number that puts you through to a room deep in the British Museum where, if you speak the hallowed words, "Can I talk to the duty curator?" a brilliant academic will come to the phone and then has to try and find out the answer to your stupid question. (I should add that I only know about this phone number because of a fantastic lady I used to chat to while dropping my daughter off at nursery in Rottingdean.) Anyway, I dialled Greece and Rome. I requested the duty curator. Then, I asked him: What is it, IIII or IV? And he said he would get back to me.
And he did. And get this: IIII and IV are both legit, by the looks of it. Romans did apparently use both, and sometimes they even used both in the course of a single document. (I almost ended that sentence with an exclamation mark, such is the scandalous frisson of merely typing such a thought.)
Also, if you are boring like me, this stuff is actually quite interesting. Roman numerals are created by addition, subtraction and multiplication, I have been told by the British Museum duty curator for Greece and Rome. Often addition (IIII = 4) was preferred to subtraction (IV = 4). The subtraction notation - also called the subtractive notation, which is moderately cooler to say but I'll admit it's a squeaker - was not used exclusively until the 13th century, in fact - and it was not universally adopted in the Roman period. ('Exclusively' is not quite right either, of course - modern watchmakers in particular remain fond of IIII.)