Answers.Body: <pre><code>[FEN &quot;8/8/8/8/8/7p/8/5K1k w - - 0 1&quot;]
  </code></pre>
  <p>In this position, white's best is 1.Kf2 to force threefold repetition with 1...Kh2 2.Kf1 Kh1 etc.</p>
  <p>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).</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-13T17:33:52.783Z
Answers.LastActivityDate: 2024-08-13T17:33:52.783Z
Answers.UserDisplayName: RemcoGerlich
Answers.Body: <p>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:</p>
  <pre><code>[Title &quot;Draw by perpetual check or insufficient material&quot;]
  [FEN &quot;8/8/8/8/8/7q/4NK2/7k w - - 0 0&quot;]
  
  1. Ng3+ Kh2 2. Nf1+ Kh1 3. Ng3+ Kh2 4. Nf1+ Kh1 5. Ng3+
  </code></pre>
  <p>For material points, this 5-piece position has only 5 MP's, and the perpetual check is absolutely forced</p>
  <pre><code>[Title &quot;Draw by perpetual check&quot;]
  [FEN &quot;8/8/8/8/8/7p/p3NK2/7k w - - 0 0&quot;]
  
  1. Ng3+ Kh2 2. Nf1+ Kh1 3. Ng3+ Kh2 4. Nf1+ Kh1 5. Ng3+
   
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-12T00:18:37.087Z
Answers.Text: 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+ =
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-12T00:10:26.480Z
Answers.LastActivityDate: 2024-08-12T00:10:26.480Z
Answers.UserDisplayName: Noam D. Elkies
Body: <p>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:</p>
  <pre><code>[Title &quot;&quot;]
  [FEN &quot;q4rk1/5p1p/5Q2/8/8/6P1/p4P1P/6K1 w - - 0 1&quot;]
  [startflipped &quot;&quot;]
  
  1. Qg5 Kh8 2. Qf6 Kg8
  </code></pre>
  <p>This example uses <strong>11 pieces</strong> and <strong>29 material points</strong> (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.</p>
  
Tags: <problems><draw><puzzles><threefold-repetition>
Title: Threefold repetition: what's the minimum number of pieces and/or material points required?
ThreadText: # Threefold repetition: what's the minimum number of pieces and/or material points required?
  
  (Asked by: username_0 on 2024-08-11)
  
  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.
  
  **Tags:** problems, draw, puzzles, threefold-repetition
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2024-08-12. Score: 9 | Accepted answer
  
  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+
   
  
  ```
  
  > **Comments:**
  > **username_2**: 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+ =  
  
  ---
  
  ### Answer by username_1 on 2024-08-13. Score: 3
  
  ```
  [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).
  
  
  ---
  
  