Forgive the late reply (this is my first post, by the way -- hi everybody!), but I'd like to chime in on this one. Kubrick actually did shoot the pie fight scene. It was to be the big climax of the whole war room sequence. As I understand it, it was supposed to be a standard Kubrick black comedy type sequence, in keeping with the tone of the rest of the film -- absurd, but ultimately dark and grim, a mirror to the very real war that was about to happen right outside... just with cakes and pies instead of nukes and tanks. Unfortunately, Kubrick either didn't convey that idea to the cast, or they just plain got too much "into" the moment, because they were gaily throwing pies at each other and having a grand old time -- it can clearly be seen in photographs taken during the sequence, of the cast members smiling and laughing. Kubrick would later call it a disaster of "Homeric proportions."
The studio had been against the whole idea from the start, and gave him the time and resources to shoot only one take. So unfortunately, the sequence was lost from the film forever. Shame. I think it would have been great.
Cheers,
Tofu
