Answers.Body: <p><strong>TLDR:</strong> Your shown position is probably the deepest depth half point zugzwang known till date. But that might change as we move to higher-piece tablebases or as more research goes into the existing 7-piece tablebase.</p>
  <h2>Terms I'll be using (for those unfamiliar with them):</h2>
  <ul>
  <li><p><strong>half point zugzwang</strong> - (WTM draws, BTM black loses) or (WTM white loses, BTM draws)</p>
  </li>
  <li><p><strong>full point zugzwang</strong> - (WTM white loses, BTM black loses)</p>
  </li>
  <li><p><strong>DTC, DTM, DTZ</strong> - <a href="https://en.wikipedia.org/wiki/Endgame_tablebase#Metrics" rel="nofollow noreferrer">link</a> (<em>Note</em> - the papers referenced below and this answer considers a full move (1 move by each) as 1 depth but lichess and Syzygy tablebase consider a half move as 1 depth)</p>
  </li>
  </ul>
  <h2>Greatest depth 6-piece zugzwang</h2>
  <p>Latest data I could find regarding zugzwangs was of 6-piece tablebase.</p>
  <p>According to <a href="https://centaur.reading.ac.uk/4561/1/2001c_ICGA_J_TH_Ken_Thompson%27s_6-man_Tables.pdf" rel="nofollow noreferrer">this paper</a>, the <strong>maximum possible zugzwang DTC of a 6-piece tablebase is 226</strong>. And the pieces involved are <code>KNN, KRN</code>. Unfortunately, they do not provide the fen notation of this position and instead direct towards <a href="http://chess.jaet.org/endings/" rel="nofollow noreferrer">this</a> website which no longer seems to host their data. Hence I could not verify if the position provided in the paper is the same as that of this question. But <strong>it does seem likely that both are the same</strong> since the pieces involved are the same and I verified that the question's position is shown as DTZ 450 by Lichess (meaning the no. of moves after which the game can be won by a checkmate is the same for both).</p>
  <p>Interestingly, the same paper also mentions that there is unique zugswang position with the pieces <code>KNN, KRB</code> with a <strong>max DTC of 213</strong>. While trying to search for this position, in <a href="https://centaur.reading.ac.uk/23047/1/ICGA_J_34_2_HHB_Zugzwangs_in_Chess_Studies.pdf" rel="nofollow noreferrer">another paper</a>, I came across the following 2 positions:</p>
  <pre><code>[title &quot;BTM draws, WTM Mated in 225&quot;]
  [fen &quot;k4b2/3K4/1r1N4/5N2/8/8/8/8 b - - 0 1&quot;]
  </code></pre>
  <pre><code>[title &quot;BTM draws, WTM Mated in 225&quot;]
  [fen &quot;k2r1b2/8/3NK3/5N2/8/8/8/8 b - - 0 1&quot;]
  </code></pre>
  <p>Issue is, both of them are mate in 225 and have the same DTZ of 419 according  to Lichess. Since, the original paper mentions that the position with DTC 213 is unique and 419 &lt; 2 * 213, I believe that a <strong>better mate than 225 should be possible with <code>KNN, KRB</code></strong>. Though it seems unlikely that this better mate would be better than OP's 245.</p>
  <p>Hence, we could safely assume that <strong>your position is the best we can do with 6 pieces</strong>.</p>
  <h2>Greatest depth 5 or lesser pieces zugzwang</h2>
  <p>If we go to 5 pieces or less, the maximum possible depth of zugzwang seems to be decreasing (<a href="https://centaur.reading.ac.uk/4581/1/2001j_ICGA_J_HKTW_3-5-man_Chess_Maximals_&amp;_Mzugs.pdf" rel="nofollow noreferrer">paper</a>). The best we can do with 5 pieces is this mate in 105 zugzwang:</p>
  <pre><code>[title &quot;WTM draws, BTM Mated in 105&quot;]
  [fen &quot;8/8/8/p7/K7/4k3/8/6NN w - - 0 1&quot;]
  </code></pre>
  <h2>Greatest depth 7 or more pieces zugzwang</h2>
  <p>Since we don't have any such data available for 7-piece zugzwangs, <strong>for now, your mate in 245 zugzwang is the best we have</strong>. Though, we can't say for certain if the 7-piece solution is going to be larger or smaller than the current one since after a threshold, the probability of zugzwang decreases as the no. of pieces increase.</p>
  <h2>Some interesting facts indirectly connected to the question (sources - above mentioned papers + <a href="https://centaur.reading.ac.uk/4518/1/ACG12_6-man_Chess_and_Zugzwangs_v9.19.pdf" rel="nofollow noreferrer">this</a> one):</h2>
  <ul>
  <li>full point zugzwangs are rarer than half point ones and are more focused upon due to their chess study aesthetic</li>
  <li>currently known <strong>max. depth full point zugzwang</strong>:</li>
  </ul>
  <pre><code>[title &quot;WTM Mated in 17, BTM Mated in 103&quot;]
  [fen &quot;8/8/8/8/p4p2/k1P5/2K1P3/8 w - - 0 1&quot;]
  </code></pre>
  <ul>
  <li>5 or lesser pieces full-point zugzwangs aren't possible without a pawn</li>
  <li><strong>Pawnless zugzwangs</strong> are just 5.26% of the total. Presence of at least one pawn increases the density of zugzwangs by a factor of 4</li>
  <li>Zugzwangs are also more frequent when <strong>Knights</strong> are present (always the tricky piece)</li>
  <li>Finally, all of the above data is subject to the condition that we aren't checking a subclass of zugzwangs. Tablebases assume that <strong>castling</strong> is not possible (<a href="https://en.wikipedia.org/wiki/Endgame_tablebase#Captures,_pawn_promotion,_and_special_moves" rel="nofollow noreferrer">source</a>). However, a zugzwang may become a non zugzwang and vice versa depending on castling. A case where castling makes a difference:</li>
  </ul>
  <pre><code>[title &quot;WTM draws, BTM w/o castling: Mate in 54, BTM with castling: draws&quot;]
  [fen &quot;1KQNk2r/7r/8/8/8/8/8/8 w - - 0 1&quot;]
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-07-26T08:29:20.420Z
Answers.LastActivityDate: 2024-07-26T14:07:25.460Z
Answers.LastEditDate: 2024-07-26T14:07:25.460Z
Answers.UserDisplayName: Rishav Raj
Body: <p>What is the maximum depth of a half-point zugzwang? Depth is defined as the number of fullmoves it takes for the winning side to win. I know 245 is possible. (Ignore 50-move, 75-move rules).</p>
  <pre><code>[Title &quot;WTM draws, BTM loses in 245 fullmoves&quot;]
  [FEN &quot;4n3/2n5/8/8/8/3K4/5k2/2R1N3 w - - 0 1&quot;]
  </code></pre>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-25T19:21:33.777Z
Comments.Text: you should link the source of this problem so that interested people can have a look.
Comments.UserDisplayName: Rishav Raj
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-27T06:10:58.610Z
Comments.Text: John Beasley's database of 6-unit zugzwangs has two of equal greatest depth: I can confirm that that depth is 245 and the one in the OP is one of them; the other is 2N5/6k1/4R3/3K4/6nn/8/8/8 w.
Comments.UserDisplayName: Rosie F
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-27T12:30:38.040Z
Comments.Text: Interesting. I saw the count 2 for deepest zug using KRNKNN and assumed the 2nd one to be the mirror of this one. I guess mirrors aren't considered in these analyses.
Comments.UserDisplayName: Rishav Raj
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-28T11:19:10.787Z
Comments.Text: @RishavRaj mirror images are usually considered equivalent.
Comments.UserDisplayName: Lucenaposition
Tags: <records><mathematics><zugzwang>
Title: Longest depth for a half-point zugzwang
ThreadText: # Longest depth for a half-point zugzwang
  
  (Asked by: username_0 on 2024-07-25)
  
  What is the maximum depth of a half-point zugzwang? Depth is defined as the number of fullmoves it takes for the winning side to win. I know 245 is possible. (Ignore 50-move, 75-move rules).
  
  ```
  [Title "WTM draws, BTM loses in 245 fullmoves"]
  [FEN "4n3/2n5/8/8/8/3K4/5k2/2R1N3 w - - 0 1"]
  
  ```
  
  **Tags:** records, mathematics, zugzwang
  
  > **Comments:**
  > **username_1**: you should link the source of this problem so that interested people can have a look.  
  > **username_2**: John Beasley's database of 6-unit zugzwangs has two of equal greatest depth: I can confirm that that depth is 245 and the one in the OP is one of them; the other is 2N5/6k1/4R3/3K4/6nn/8/8/8 w.  
  > **username_1**: Interesting. I saw the count 2 for deepest zug using KRNKNN and assumed the 2nd one to be the mirror of this one. I guess mirrors aren't considered in these analyses.  
  > **username_0**: @username_1 mirror images are usually considered equivalent.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2024-07-26. Score: 3
  
  **TLDR:** Your shown position is probably the deepest depth half point zugzwang known till date. But that might change as we move to higher-piece tablebases or as more research goes into the existing 7-piece tablebase.
  
  ## Terms I'll be using (for those unfamiliar with them):
  
  * **half point zugzwang** - (WTM draws, BTM black loses) or (WTM white loses, BTM draws)
  * **full point zugzwang** - (WTM white loses, BTM black loses)
  * **DTC, DTM, DTZ** - [link](https://en.wikipedia.org/wiki/Endgame_tablebase#Metrics) (*Note* - the papers referenced below and this answer considers a full move (1 move by each) as 1 depth but lichess and Syzygy tablebase consider a half move as 1 depth)
  
  ## Greatest depth 6-piece zugzwang
  
  Latest data I could find regarding zugzwangs was of 6-piece tablebase.
  
  According to [this paper](https://centaur.reading.ac.uk/4561/1/2001c_ICGA_J_TH_Ken_Thompson%27s_6-man_Tables.pdf), the **maximum possible zugzwang DTC of a 6-piece tablebase is 226**. And the pieces involved are `KNN, KRN`. Unfortunately, they do not provide the fen notation of this position and instead direct towards [this](http://chess.jaet.org/endings/) website which no longer seems to host their data. Hence I could not verify if the position provided in the paper is the same as that of this question. But **it does seem likely that both are the same** since the pieces involved are the same and I verified that the question's position is shown as DTZ 450 by Lichess (meaning the no. of moves after which the game can be won by a checkmate is the same for both).
  
  Interestingly, the same paper also mentions that there is unique zugswang position with the pieces `KNN, KRB` with a **max DTC of 213**. While trying to search for this position, in [another paper](https://centaur.reading.ac.uk/23047/1/ICGA_J_34_2_HHB_Zugzwangs_in_Chess_Studies.pdf), I came across the following 2 positions:
  
  ```
  [title "BTM draws, WTM Mated in 225"]
  [fen "k4b2/3K4/1r1N4/5N2/8/8/8/8 b - - 0 1"]
  
  ```
  
  ```
  [title "BTM draws, WTM Mated in 225"]
  [fen "k2r1b2/8/3NK3/5N2/8/8/8/8 b - - 0 1"]
  
  ```
  
  Issue is, both of them are mate in 225 and have the same DTZ of 419 according to Lichess. Since, the original paper mentions that the position with DTC 213 is unique and 419 < 2 \* 213, I believe that a **better mate than 225 should be possible with `KNN, KRB`**. Though it seems unlikely that this better mate would be better than OP's 245.
  
  Hence, we could safely assume that **your position is the best we can do with 6 pieces**.
  
  ## Greatest depth 5 or lesser pieces zugzwang
  
  If we go to 5 pieces or less, the maximum possible depth of zugzwang seems to be decreasing ([paper](https://centaur.reading.ac.uk/4581/1/2001j_ICGA_J_HKTW_3-5-man_Chess_Maximals_&_Mzugs.pdf)). The best we can do with 5 pieces is this mate in 105 zugzwang:
  
  ```
  [title "WTM draws, BTM Mated in 105"]
  [fen "8/8/8/p7/K7/4k3/8/6NN w - - 0 1"]
  
  ```
  
  ## Greatest depth 7 or more pieces zugzwang
  
  Since we don't have any such data available for 7-piece zugzwangs, **for now, your mate in 245 zugzwang is the best we have**. Though, we can't say for certain if the 7-piece solution is going to be larger or smaller than the current one since after a threshold, the probability of zugzwang decreases as the no. of pieces increase.
  
  ## Some interesting facts indirectly connected to the question (sources - above mentioned papers + [this](https://centaur.reading.ac.uk/4518/1/ACG12_6-man_Chess_and_Zugzwangs_v9.19.pdf) one):
  
  * full point zugzwangs are rarer than half point ones and are more focused upon due to their chess study aesthetic
  * currently known **max. depth full point zugzwang**:
  
  ```
  [title "WTM Mated in 17, BTM Mated in 103"]
  [fen "8/8/8/8/p4p2/k1P5/2K1P3/8 w - - 0 1"]
  
  ```
  
  * 5 or lesser pieces full-point zugzwangs aren't possible without a pawn
  * **Pawnless zugzwangs** are just 5.26% of the total. Presence of at least one pawn increases the density of zugzwangs by a factor of 4
  * Zugzwangs are also more frequent when **Knights** are present (always the tricky piece)
  * Finally, all of the above data is subject to the condition that we aren't checking a subclass of zugzwangs. Tablebases assume that **castling** is not possible ([source](https://en.wikipedia.org/wiki/Endgame_tablebase#Captures,_pawn_promotion,_and_special_moves)). However, a zugzwang may become a non zugzwang and vice versa depending on castling. A case where castling makes a difference:
  
  ```
  [title "WTM draws, BTM w/o castling: Mate in 54, BTM with castling: draws"]
  [fen "1KQNk2r/7r/8/8/8/8/8/8 w - - 0 1"]
  
  ```
  
  
  ---
  
  