Which legal position has the smallest number of moves in a "forced loop"? Consider this (illegal) position.
[FEN &quot;5n1k/3p1p1p/3PpPpP/4P1P1/1p1p4/pPpPp3/P1P1P3/K1N5 w - - 0 1&quot;]

If we do not consider the position's illegality, and the fact that it is clearly unwinnable by eiter player (and therefore an automatic draw even if either of the players resgined, ran out of time, etc), then this position has an interesting property. Regardless of what move every player does (which is obvious in this case, since there is always only one legal move), the position results in forced threefold repetition in 4 moves.
Now here arises a question, basically a problem creation: Which legal position has the least amount of moves to make threefold repetition, assuming no player wants to repeat the positions?
This legal postion should fit the bill for the least amount of units needed and the least amount of moves. There is one king, one bishop, and four pawns for each side-a total 12 pieces. The threefold repetition is forced no matter what moves the players make since they only have one legal move each time. It's basically your idea in a legal and lighter setting.
[FEN &quot;5b1k/4p1p1/4P1P1/8/8/1p1p4/1P1P4/K1B5 w - - 0 1&quot;]