user13544: The Berger tables for round-robin tournaments state:

Where there is an odd number of players, the highest number counts as a bye.

As far as I understand this statement correctly, this means that, for example, in an 8-player round-robin, the 8th seeded player will always be the bye player and hence will not play any game.
What else could this mean?

user17448: Its all documented here:
https://www.fide.com/fide/handbook.html?id=184&view=article
Example:
Where there is an odd number of players, the highest number counts as a bye.
9 or 10 players:
Rd 1: 1-10, 2-9, 3-8, 4-7, 5-6. 
Rd 2: 10-6, 7-5, 8-4, 9-3, 1-2. 
Rd 3: 2-10, 3-1, 4-9, 5-8, 6-7.
Rd 4: 10-7, 8-6, 9-5, 1-4, 2-3. 
Rd 5: 3-10, 4-2, 5-1, 6-9, 7-8. 
Rd 6: 10-8, 9-7, 1-6, 2-5, 3-4.
Rd 7: 4-10, 5-3, 6-2, 7-1, 8-9. 
Rd 8: 10-9, 1-8, 2-7, 3-6, 4-5. 
Rd 9: 5-10, 6-4, 7-3, 8-2, 9-1.

As result - who ever plays highest number - has bye, for example round 5 Nr3 gets bye as he plays against 10.

user15989: It means that in the pairings given in the tables, if there are an odd number of players (so not an 8-person round-robin for instance), the player playing against the highest number receives a bye.
For instance, for 5 players (use the 5-6 player table):

Round 1: #1 gets a bye
Round 2: #4 gets a bye
Round 3: #2 gets a bye
Round 4: #5 gets a bye
Round 5: #3 gets a bye


13544: <p>The <a href="https://www.fide.com/fide/handbook.html?id=184&amp;view=article" rel="nofollow noreferrer">Berger tables for round-robin tournaments</a> state:</p>

<blockquote>
  <p>Where there is an odd number of players, the highest number counts as a bye.</p>
</blockquote>

<p>As far as I understand this statement correctly, this means that, for example, in an 8-player round-robin, the 8th seeded player will always be the bye player and hence will not play any game.</p>

<p>What else could this mean?</p>
 17448: <p>Its all documented here:
<a href="https://www.fide.com/fide/handbook.html?id=184&amp;view=article" rel="nofollow noreferrer">https://www.fide.com/fide/handbook.html?id=184&amp;view=article</a></p>

<p>Example:
Where there is an odd number of players, the highest number counts as a bye.</p>

<pre><code>9 or 10 players:
Rd 1: 1-10, 2-9, 3-8, 4-7, 5-6. 
Rd 2: 10-6, 7-5, 8-4, 9-3, 1-2. 
Rd 3: 2-10, 3-1, 4-9, 5-8, 6-7.
Rd 4: 10-7, 8-6, 9-5, 1-4, 2-3. 
Rd 5: 3-10, 4-2, 5-1, 6-9, 7-8. 
Rd 6: 10-8, 9-7, 1-6, 2-5, 3-4.
Rd 7: 4-10, 5-3, 6-2, 7-1, 8-9. 
Rd 8: 10-9, 1-8, 2-7, 3-6, 4-5. 
Rd 9: 5-10, 6-4, 7-3, 8-2, 9-1.
</code></pre>

<p>As result - who ever plays highest number - has bye, for example round 5 Nr3 gets bye as he plays against 10.</p>
 15989: <p>It means that in the pairings given in the tables, if there are an odd number of players (so not an 8-person round-robin for instance), the player <em>playing against</em> the highest number receives a bye.</p>

<p>For instance, for 5 players (use the 5-6 player table):</p>

<ul>
<li>Round 1: #1 gets a bye</li>
<li>Round 2: #4 gets a bye</li>
<li>Round 3: #2 gets a bye</li>
<li>Round 4: #5 gets a bye</li>
<li>Round 5: #3 gets a bye</li>
</ul>
