Obviously inspired by the analogous [selfmate](https://chess.stackexchange.com/questions/33168/the-quickest-selfmate-in-1) question. (Helpmate would also be possible in principle, but looks a bit silly.)

Thus, 1.f3 e5 2.g4 allows Black a #1, and 1.f3 e5 2.h3 a #2. 1.f4 e5 2.Nf3 Be7 3.h3 is a #3. This should be the quickest games.

Find a shortest helpplay to a position where one side has a forced #4 (and of course it must be unique and not be shortenable), for starters.