Answers.Body: <blockquote>
  <p>It would be nice to see an example where this rule is applied. Just to be sure.</p>
  </blockquote>
  <p>Here's a small 5 round Swiss.</p>
  <pre><code> Pair | Player Name         |Total|Round|Round|Round|Round|Round| Tie 
   Num  |                     | Pts |  1  |  2  |  3  |  4  |  5  |Break 
   ---------------------------------------------------------------------
      1 | A                   |4.0  |W   5|W   4|D   3|D   2|W   6| 12.5 
  ----------------------------------------------------------------------
      2 | B                   |4.0  |W   7|D   3|W   6|D   1|W   4| 12.5 
  ----------------------------------------------------------------------
      3 | C                   |3.0  |W   8|D   2|D   1|L   4|W   9| 12.5
  ----------------------------------------------------------------------
      4 | D                   |3.0  |W   9|L   1|W   7|W   3|L   2| 12.5
  ----------------------------------------------------------------------
      5 | E                   |3.0  |L   1|L   6|W   9|B    |W   8| 8.5
  ----------------------------------------------------------------------
      6 | F                   |2.5  |H    |W   5|L   2|W   7|L   1| 8
  ----------------------------------------------------------------------
      7 | G                   |2.0  |L   2|W   8|L   4|L   6|B    | 7
  ----------------------------------------------------------------------
      8 | H                   |2.0  |L   3|L   7|B    |W   9|L   5| 4.5
  ----------------------------------------------------------------------
      9 | I                   |1.0  |L   4|B    |L   5|L   8|L   3| 7
  ----------------------------------------------------------------------
  </code></pre>
  <p>For player A, the opponents' scores (after adjusting for the byes) are 2.5, 3, 3, 4, and 2.5. Because player A has a plus score, the lowest score (2.5) is excluded. The modified median tiebreaker score is 12.5.</p>
  <p>For player B, the opponents' scores are 1.5, 3, 2.5, 4, and 3. The lowest score (1.5) is excluded. The modified median tiebreaker score is 12.5. This is the same tiebreaker score as Player A.</p>
  <p>For player G, the opponents' scores are 4, 1.5, 3, 2.5, and 0. Because this player had a minus score, the highest score (4) is excluded. The modified median tiebreaker score is 7.</p>
  <p>For player H, the opponents' scores are 3, 1.5, 0, 0.5, and 2.5. The highest score (3) is excluded. The modified median tiebreaker score is 4.5. Player G would win this tiebreak over Player H.</p>
  <p>Player F is not tied with anyone, but their opponents' scores are 0, 2.5, 4, 1.5, and 4. This player has an exactly even score of 2.5/5, so to calculate the tiebreak we would exclude both the lowest score (0) and the highest score (4). The modified median tiebreaker score would be 8.</p>
  <blockquote>
  <p>What is unclear to me is the term: the least significant opponents’ scores.</p>
  </blockquote>
  <p>The &quot;least significant&quot; opponent's score is the highest opponent's score for a low-scoring player, or the lowest one for a high-scoring player.</p>
  <blockquote>
  <p>Does this include a Bye, which is a score without an actual opponent. Or is the Bye excluded from the modification procedure?</p>
  </blockquote>
  <p>&quot;If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.&quot; The bye is not excluded from the modification procedure; it is treated like any other 0 score. In Player F's case, the 0 from the bye was the lowest score, and we threw out the lowest score, so this score was thrown out. But in the case of Player G and Player H, the <em>highest</em> score was thrown out, so the 0 for the bye stayed in the calculations.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-31T07:49:37.097Z
Answers.Text: I meant an example of a real US Chess tournament. I have clarified my question. Was this example created with a US Chess approved tournament manager?
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-31T11:08:28.200Z
Answers.Text: It is an actual tournament from several years ago with names removed. Tiebreak calculations were done manually by me since those aren't shown in the official crosstable, though.
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-31T11:20:19.507Z
Answers.Text: These triebreak calculations should be shown somewhere (?), if only for the participants to check.
  
  I understand how to do the calculations. But how do I know that they comply with the rules of the tournament?
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-31T11:50:46.830Z
Answers.Text: There's an example here: https://midwestchess.com/pdf/USCF_ChessTie-Break_%20Systems.pdf
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-31T15:41:06.350Z
Answers.Text: I have seen that example. Unfortunately it does not includes byes (X, H, F, -).
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-08T06:51:32.757Z
Answers.Text: Where and how to find the small 5 round Swiss tournament, or similar tournaments?
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-08T11:41:08.373Z
Answers.Text: You can search for completed tournaments at https://www.uschess.org/datapage/events-rated.php but it doesn't show tiebreakers and the results aren't in tiebreaker order.
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-08T12:00:10.820Z
Answers.Text: Or : http://www.uschess.org/msa/.
  I have come to the conclusion that the calculation, as seen by the USCF, is a well-kept secret. I have not found any example of a calculation. Perhaps to be found in antique publications by Kennett  Harkness.
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-08T12:03:47.620Z
Answers.Text: For clarity, you could update your answer by including your calculation of the modified median as the last column. After round 5.
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-24T20:58:13.217Z
Answers.Text: @clp I finally got around to adding a column for it. Only took me a year...
Answers.UserDisplayName: D M
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-27T20:23:34.560Z
Answers.Text: Very nice indeed.
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-30T22:38:01.610Z
Answers.LastActivityDate: 2024-08-24T20:56:44.300Z
Answers.LastEditDate: 2024-08-24T20:56:44.300Z
Answers.UserDisplayName: D M
Answers.Body: <blockquote>
  <p>What is unclear to me is the term: the least significant opponents’ scores</p>
  </blockquote>
  <p>As described in the text:</p>
  <ol>
  <li>If the tied players have a plus score then for each tied player their lowest scoring opponent is excluded from the calculation</li>
  <li>If they have a minus score then each player's highest scoring opponent is excluded.</li>
  </ol>
  <blockquote>
  <p>Does this include a Bye</p>
  </blockquote>
  <p>As you say, a bye does not involve an opponent with a score. Byes don't take part in the exclusion process.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-30T17:30:12.020Z
Answers.Text: Can you show me a tournament where this rule is applied ? Just to be sure.
Answers.UserDisplayName: clp
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-07-30T16:48:52.463Z
Answers.LastActivityDate: 2023-07-30T16:48:52.463Z
Answers.UserDisplayName: Brian Towers
Body: <p>The calculation is described in the &quot;<a href="https:////https://new.uschess.org/sites/default/files/media/documents/us-chess-rule-book-online-only-edition-7-chp-2-8-24-20.pdf" rel="nofollow noreferrer">USCF Chess Rule Book</a>&quot;, chapter 34E1,</p>
  <blockquote>
  <p>34E1. Modified Median</p>
  <p>The Median system, also known as the Harkness system for inventor Kenneth Harkness, evaluates the strength of a player’s opposition by summing the final scores of his or her opponents and then discarding the highest and lowest of these scores.</p>
  <p>In the Modified Median system, players who tie with even scores (an even score is equal to exactly one half of the maximum possible score), have the highest- and lowest-scoring opponents’ scores excluded. <em>The system is modified for players with non-even scores to disregard only <strong>the least significant opponents’ scores</strong></em>: the lowest-scoring opponent’s score is discarded for tied players with plus scores and the highest-scoring for tied players with minus scores.</p>
  <p>For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties.</p>
  <p>These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed.</p>
  <p>If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.</p>
  </blockquote>
  <p>What is unclear to me is the term: <strong>the least significant opponents’ scores</strong>.
  Does this include a Bye, which is a score without an actual opponent.
  Or is the Bye excluded from the modification procedure?</p>
  <blockquote>
  <p>I find the text ambiguous and open to multiple interpretations, as in the answers below. Therefore, I would like to see how the calculations are performed in actual USCF tournaments.</p>
  </blockquote>
  <p><strong>Update-2</strong></p>
  <p>A cross table including the four USCF tie-breaks can be found here <a href="http://www.chesstour.com/nysc07r.htm" rel="nofollow noreferrer">2007, 128th (=129th) Annual New York State Championship</a>. From this cross table one can conclude the unplayed games are part of the deletion process.</p>
  <p><strong>Update-1</strong></p>
  <p>Consider the <a href="https://www.uschess.org/results/2022/usopen/" rel="nofollow noreferrer">2022 US Open Championship</a>, 30 July - 7 August, 2022· Rancho Mirage CA.</p>
  <p>Are the default US Chess tiebreakers applied? Why is Aleksey Sorokin champion?</p>
  <pre><code>No.  Name                       St  Rate  Pts Rnd1  Rnd2  Rnd3  Rnd4  Rnd5  Rnd6  Rnd7  Rnd8  Rnd9  
     1  SOROKIN, ALEKSEY          TX  2648  8.0 W193  W125  W 65  W 36  W  3  D 15  D 17  W  7  W  9  
     2  MORADIABADI, ELSHAN       NC  2614  8.0 W370  W269  W 78  W 46  W 81  W 14  D  5  D  9  W 15  
     3  JACOBSON, BRANDON         NJ  2626  7.5 W281  W124  W 68  W 37  L  1  W157  W 39  D  5  W 17  
     4  EIDELMAN, GABRIEL         CA  2249  7.5 W272  W 84  W 85  L 10  W112  D 12  W 81  W 35  W 32  
     5  NARODITSKY, DANIEL A      NC  2699  7.0 W135  W 73  W 41  W 19  W 33  D 17  D  2  D  3  D 10  
     6  AKOBIAN, VARUZHAN         MO  2655  7.0 W277  W123  W 64  D 18  D  8  W 37  W 38  D 17  D 12  
     7  SHABALOV, ALEXANDER       PA  2607  7.0 W138  W 51  W 42  W 22  D 16  D 39  W 61  L  1  W 38  
     8  Hong, Andrew              CA  2604  7.0 W235  W 31  W216  W212  D  6  L  9  W108  W 24   -H-  
     9  MATVIISHEN, VIKTOR        TX  2558  7.0 W152  W126  W 70  D 15  W 72  W  8  W 16  D  2  L  1  
    10  SHENG, JOSHUA             CA  2558  7.0 W 97  W217  W 27  W  4  L 17  D 16  W 44  W 25  D  5  
    11  SCHMAKEL, SAMUEL ARTHUR   IL  2504  7.0 W140  D 76  W175  D 39  W 45  W 22  W 46  L 15  W 42  
    12  COSTELLO, ALEXANDER JOHN  CA  2379  7.0 W271  W 83  W 28  L 17  W213  D  4  W 48  W 52  D  6  
    13  MELIKIAN, GNEL            CA  2338  7.0 W 99  W167  D317  D213  W214  D 26  D 28  W 46  W 57  
    14  MEI, AUSTIN R             CA  2265  7.0  -X-  W 57  W218  D 47  W 50  L  2  W 76  D 33  W 34  
  </code></pre>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-07-31T23:05:48.287Z
Comments.Text: In that event, they used a playoff. Pre-event publicity said "If tie for first, top two on tiebreak play Armageddon game for bonus and title." Since there were only 2 tied for first they didn't need to use the tiebreaker to see who got to qualify for the playoff; they just played the Armageddon game.
Comments.UserDisplayName: D M
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-01T08:01:11.373Z
Comments.Text: Thanks.
  
   The order for the places 5 to 14 remains a puzzle (as well as the colors).
Comments.UserDisplayName: clp
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-08-01T11:25:09.830Z
Comments.Text: The order shown for 5 to 14 (and everything else, if you look at the entire results on that page) is sorted by rating. Everything except first place was just cash prizes which were split between the tied players. So tiebreakers weren't used for them. Colors are shown at https://www.uschess.org/msa/XtblMain.php?202208071492.0
Comments.UserDisplayName: D M
Tags: <rules><tournament><uscf><tie-breaks>
Title: How to calculate USCF's Modified Median (with or without byes)?
ThreadText: # How to calculate USCF's Modified Median (with or without byes)?
  
  (Asked by: username_0 on 2023-07-30)
  
  The calculation is described in the "[USCF Chess Rule Book](https:////https://new.uschess.org/sites/default/files/media/documents/us-chess-rule-book-online-only-edition-7-chp-2-8-24-20.pdf)", chapter 34E1,
  
  > 34E1. Modified Median
  >
  > The Median system, also known as the Harkness system for inventor Kenneth Harkness, evaluates the strength of a player’s opposition by summing the final scores of his or her opponents and then discarding the highest and lowest of these scores.
  >
  > In the Modified Median system, players who tie with even scores (an even score is equal to exactly one half of the maximum possible score), have the highest- and lowest-scoring opponents’ scores excluded. *The system is modified for players with non-even scores to disregard only **the least significant opponents’ scores***: the lowest-scoring opponent’s score is discarded for tied players with plus scores and the highest-scoring for tied players with minus scores.
  >
  > For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties.
  >
  > These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed.
  >
  > If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.
  
  What is unclear to me is the term: **the least significant opponents’ scores**.
  Does this include a Bye, which is a score without an actual opponent.
  Or is the Bye excluded from the modification procedure?
  
  > I find the text ambiguous and open to multiple interpretations, as in the answers below. Therefore, I would like to see how the calculations are performed in actual USCF tournaments.
  
  **Update-2**
  
  A cross table including the four USCF tie-breaks can be found here [2007, 128th (=129th) Annual New York State Championship](http://www.chesstour.com/nysc07r.htm). From this cross table one can conclude the unplayed games are part of the deletion process.
  
  **Update-1**
  
  Consider the [2022 US Open Championship](https://www.uschess.org/results/2022/usopen/), 30 July - 7 August, 2022· Rancho Mirage CA.
  
  Are the default US Chess tiebreakers applied? Why is Aleksey Sorokin champion?
  
  ```
  No.  Name                       St  Rate  Pts Rnd1  Rnd2  Rnd3  Rnd4  Rnd5  Rnd6  Rnd7  Rnd8  Rnd9  
     1  SOROKIN, ALEKSEY          TX  2648  8.0 W193  W125  W 65  W 36  W  3  D 15  D 17  W  7  W  9  
     2  MORADIABADI, ELSHAN       NC  2614  8.0 W370  W269  W 78  W 46  W 81  W 14  D  5  D  9  W 15  
     3  JACOBSON, BRANDON         NJ  2626  7.5 W281  W124  W 68  W 37  L  1  W157  W 39  D  5  W 17  
     4  EIDELMAN, GABRIEL         CA  2249  7.5 W272  W 84  W 85  L 10  W112  D 12  W 81  W 35  W 32  
     5  NARODITSKY, DANIEL A      NC  2699  7.0 W135  W 73  W 41  W 19  W 33  D 17  D  2  D  3  D 10  
     6  AKOBIAN, VARUZHAN         MO  2655  7.0 W277  W123  W 64  D 18  D  8  W 37  W 38  D 17  D 12  
     7  SHABALOV, ALEXANDER       PA  2607  7.0 W138  W 51  W 42  W 22  D 16  D 39  W 61  L  1  W 38  
     8  Hong, Andrew              CA  2604  7.0 W235  W 31  W216  W212  D  6  L  9  W108  W 24   -H-  
     9  MATVIISHEN, VIKTOR        TX  2558  7.0 W152  W126  W 70  D 15  W 72  W  8  W 16  D  2  L  1  
    10  SHENG, JOSHUA             CA  2558  7.0 W 97  W217  W 27  W  4  L 17  D 16  W 44  W 25  D  5  
    11  SCHMAKEL, SAMUEL ARTHUR   IL  2504  7.0 W140  D 76  W175  D 39  W 45  W 22  W 46  L 15  W 42  
    12  COSTELLO, ALEXANDER JOHN  CA  2379  7.0 W271  W 83  W 28  L 17  W213  D  4  W 48  W 52  D  6  
    13  MELIKIAN, GNEL            CA  2338  7.0 W 99  W167  D317  D213  W214  D 26  D 28  W 46  W 57  
    14  MEI, AUSTIN R             CA  2265  7.0  -X-  W 57  W218  D 47  W 50  L  2  W 76  D 33  W 34  
  
  ```
  
  **Tags:** rules, tournament, uscf, tie-breaks
  
  > **Comments:**
  > **username_1**: In that event, they used a playoff. Pre-event publicity said "If tie for first, top two on tiebreak play Armageddon game for bonus and title." Since there were only 2 tied for first they didn't need to use the tiebreaker to see who got to qualify for the playoff; they just played the Armageddon game.  
  > **username_0**: Thanks.   The order for the places 5 to 14 remains a puzzle (as well as the colors).  
  > **username_1**: The order shown for 5 to 14 (and everything else, if you look at the entire results on that page) is sorted by rating. Everything except first place was just cash prizes which were split between the tied players. So tiebreakers weren't used for them. Colors are shown at https://www.uschess.org/msa/XtblMain.php?202208071492.0  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2023-07-30. Score: 2 | Accepted answer
  
  > It would be nice to see an example where this rule is applied. Just to be sure.
  
  Here's a small 5 round Swiss.
  
  ```
   Pair | Player Name         |Total|Round|Round|Round|Round|Round| Tie 
   Num  |                     | Pts |  1  |  2  |  3  |  4  |  5  |Break 
   ---------------------------------------------------------------------
      1 | A                   |4.0  |W   5|W   4|D   3|D   2|W   6| 12.5 
  ----------------------------------------------------------------------
      2 | B                   |4.0  |W   7|D   3|W   6|D   1|W   4| 12.5 
  ----------------------------------------------------------------------
      3 | C                   |3.0  |W   8|D   2|D   1|L   4|W   9| 12.5
  ----------------------------------------------------------------------
      4 | D                   |3.0  |W   9|L   1|W   7|W   3|L   2| 12.5
  ----------------------------------------------------------------------
      5 | E                   |3.0  |L   1|L   6|W   9|B    |W   8| 8.5
  ----------------------------------------------------------------------
      6 | F                   |2.5  |H    |W   5|L   2|W   7|L   1| 8
  ----------------------------------------------------------------------
      7 | G                   |2.0  |L   2|W   8|L   4|L   6|B    | 7
  ----------------------------------------------------------------------
      8 | H                   |2.0  |L   3|L   7|B    |W   9|L   5| 4.5
  ----------------------------------------------------------------------
      9 | I                   |1.0  |L   4|B    |L   5|L   8|L   3| 7
  ----------------------------------------------------------------------
  
  ```
  
  For player A, the opponents' scores (after adjusting for the byes) are 2.5, 3, 3, 4, and 2.5. Because player A has a plus score, the lowest score (2.5) is excluded. The modified median tiebreaker score is 12.5.
  
  For player B, the opponents' scores are 1.5, 3, 2.5, 4, and 3. The lowest score (1.5) is excluded. The modified median tiebreaker score is 12.5. This is the same tiebreaker score as Player A.
  
  For player G, the opponents' scores are 4, 1.5, 3, 2.5, and 0. Because this player had a minus score, the highest score (4) is excluded. The modified median tiebreaker score is 7.
  
  For player H, the opponents' scores are 3, 1.5, 0, 0.5, and 2.5. The highest score (3) is excluded. The modified median tiebreaker score is 4.5. Player G would win this tiebreak over Player H.
  
  Player F is not tied with anyone, but their opponents' scores are 0, 2.5, 4, 1.5, and 4. This player has an exactly even score of 2.5/5, so to calculate the tiebreak we would exclude both the lowest score (0) and the highest score (4). The modified median tiebreaker score would be 8.
  
  > What is unclear to me is the term: the least significant opponents’ scores.
  
  The "least significant" opponent's score is the highest opponent's score for a low-scoring player, or the lowest one for a high-scoring player.
  
  > Does this include a Bye, which is a score without an actual opponent. Or is the Bye excluded from the modification procedure?
  
  "If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0." The bye is not excluded from the modification procedure; it is treated like any other 0 score. In Player F's case, the 0 from the bye was the lowest score, and we threw out the lowest score, so this score was thrown out. But in the case of Player G and Player H, the *highest* score was thrown out, so the 0 for the bye stayed in the calculations.
  
  > **Comments:**
  > **username_0**: I meant an example of a real US Chess tournament. I have clarified my question. Was this example created with a US Chess approved tournament manager?  
  > **username_1**: It is an actual tournament from several years ago with names removed. Tiebreak calculations were done manually by me since those aren't shown in the official crosstable, though.  
  > **username_0**: These triebreak calculations should be shown somewhere (?), if only for the participants to check.  I understand how to do the calculations. But how do I know that they comply with the rules of the tournament?  
  > **username_1**: There's an example here: https://midwestchess.com/pdf/USCF_ChessTie-Break_%20Systems.pdf  
  > **username_0**: I have seen that example. Unfortunately it does not includes byes (X, H, F, -).  
  > **username_0**: Where and how to find the small 5 round Swiss tournament, or similar tournaments?  
  > **username_1**: You can search for completed tournaments at https://www.uschess.org/datapage/events-rated.php but it doesn't show tiebreakers and the results aren't in tiebreaker order.  
  > **username_0**: Or : http://www.uschess.org/msa/. I have come to the conclusion that the calculation, as seen by the USCF, is a well-kept secret. I have not found any example of a calculation. Perhaps to be found in antique publications by Kennett  Harkness.  
  > **username_0**: For clarity, you could update your answer by including your calculation of the modified median as the last column. After round 5.  
  > **username_1**: @username_0 I finally got around to adding a column for it. Only took me a year...  
  > **username_0**: Very nice indeed.  
  
  ---
  
  ### Answer by username_2 on 2023-07-30. Score: 2
  
  > What is unclear to me is the term: the least significant opponents’ scores
  
  As described in the text:
  
  1. If the tied players have a plus score then for each tied player their lowest scoring opponent is excluded from the calculation
  2. If they have a minus score then each player's highest scoring opponent is excluded.
  
  > Does this include a Bye
  
  As you say, a bye does not involve an opponent with a score. Byes don't take part in the exclusion process.
  
  > **Comments:**
  > **username_0**: Can you show me a tournament where this rule is applied ? Just to be sure.  
  
  ---
  
  