However, the duo does make the scene hilarious (or more so than it would be without their reactions and dialogue).
[Max trying to locate his boss in all the mess] "Hey Professor...!?" [Fate, standing next to him, forcefully throwing a pie in his face] "I'm right here you idiot!"
and of course:
[Splat! of pie in his face, Fate, as his king double, tastes pie] "...Brandy! Throw more brandy!" [Splat! of a second pie, then tasting it] "Hmm, Rum!. I never mix my pies!"
HappyCamper said: Yes, a great scene. But, I wish there was more than one woman involved. Peter Falk and Jack Lemmon do nothing for my libido!
Quite so. Only now do I think back at Natalie Wood's light attire and then to the Prince's undergarments. If all were fair, he wouldn't be wearing a union suit. He could be in a long john, and as the Prince might do, proudly exhibit his confidence. Perhaps then those with a male attraction may have enjoyed the scene more.
Alas, on the topic of more female cast members, 1908 is limiting. Miss Dubios's whole movement of suffragist is significant. In America, their contribution was around 10% to the workforce, and even then it was teachers, nurses, and dressmakers. Maybe some factory workers but not the high end production of baked goods.
We could blame the choice of the producers for picking that era although they based the race on a real racing event.
"The Great Race" is also on Max (formerly HBO Max) in the TCM section, which includes practically the entire Warner Brothers catalogue. I don't think those films rotate in and out. Unfortunately the only "extra" is the trailer. I keep hoping someone will find some outtakes footage. From photos posted here, we know that Natalie's first pie hit was shot more than once. The film must be at Warners somewhere.