Threefold repetition: what's the minimum number of pieces and/or material points required?

I found the following position online where White's best course is to force a threefold repetition with the sequence Qg5-Kh8-Qf6-Kg8 because all other moves lose:

``````[Title ""]
[FEN "q4rk1/5p1p/5Q2/8/8/6P1/p4P1P/6K1 w - - 0 1"]
[startflipped ""]

1. Qg5 Kh8 2. Qf6 Kg8
``````

This example uses 11 pieces and 29 material points (i.e., Queen = 9, Rook = 5, Bishop = 3, Knight = 3, Pawn = 1). I'm wondering if a position can be found with fewer pieces and/or fewer material points.

4 pieces is the minimum, and is attained by this position though Black has the option of trading Q for N to a bare-king draw:

``````[Title "Draw by perpetual check or insufficient material"]
[FEN "8/8/8/8/8/7q/4NK2/7k w - - 0 0"]

1. Ng3+ Kh2 2. Nf1+ Kh1 3. Ng3+ Kh2 4. Nf1+ Kh1 5. Ng3+
``````

For material points, this 5-piece position has only 5 MP's, and the perpetual check is absolutely forced

``````[Title "Draw by perpetual check"]
[FEN "8/8/8/8/8/7p/p3NK2/7k w - - 0 0"]

1. Ng3+ Kh2 2. Nf1+ Kh1 3. Ng3+ Kh2 4. Nf1+ Kh1 5. Ng3+

``````
• One can also make a 4-piece, 4-point position that leads to a position equivalent to the first diagram after promotion, e.g. Kg3,Nh7/Kg1,f2: 1 Ng5! f1Q 2 Nh3+ Kh1 3 Nf2+ = Commented Aug 12 at 0:18
``````[FEN "8/8/8/8/8/7p/8/5K1k w - - 0 1"]
``````

In this position, white's best is 1.Kf2 to force threefold repetition with 1...Kh2 2.Kf1 Kh1 etc.

Of course black can deviate, but that's also a draw (1...h2 2.Kf1 stalemate, or 2...Kg3 3.Kg1 h2+ 4.Kh1 Kh3 stalemate).