How to create a perfect round-robin tournament

 
Important in a perfect schedule is that 1 first must play versus an
even number, but not the smallest or the largest number.
In the schedule below with 5 or 6, it's only 1-4 that's possible, but
in the schedule below with 7 or 8, it's possible both with 1-4 and 1-6
in round 1. With 9 or 10, it will be 3 possibilities, and possibilities
will increase with 1 for every larger schedule below, as you will see.
 

Schedule for 5 or 6:
Round 1
1-4
2-3
6-5
Round 2
5-1
4-2
3-6
Round 3
1-6
2-5
3-4
Round 4
1-2
5-3
6-4
Round 5
3-1
4-5
2-6
Round 6 is opposite of round 1, 7 of 2 etc.

 

Schedule for 7 or 8:
Runde 1
1-4
2-3
7-5
8-6
Round 2
5-1
4-2
6-7
3-8
Round 3
1-6
2-5
3-4
8-7
Round 4
7-1
6-2
5-3
4-8
Round 5
1-8
2-7
3-6
4-5
Round 6
1-2
7-3
6-4
8-5
Round 7
3-1
4-7
5-6
2-8
Round 8 is opposite of round 1, 9 opposite of 2 etc.

or

Schedule for 7 or 8:
Round 1
1-6
2-5
3-4
8-7
Round 2
7-1
6-2
5-3
4-8
Round 3
1-8
2-7
3-6
4-5
Round 4
1-2
7-3
6-4
8-5
Round 5
3-1
4-7
5-6
2-8
Round 6
1-4
2-3
7-5
8-6
Round 7
5-1
4-2
6-7
3-8
Round 8 is opposite of round 1, 9 opposite of 2 etc.


Notice following rule which applies for all schedules:
x and (x + largest number in the schedule divided with 2),
will never play white/black or home/away at the
same time in the same round. In the schedule above
with 7 or 8: 1 and (1+(8:2)), 2 and (2+(8:2)) etc.
meaning 1 and 5, 2 and 6 etc. will never play white/black
or home/away at the same time in the same round.
You can check it out in the schedule above!
 

schedule for 9 or 10:
Round 1
1-4
2-3
9-5
8-6
10-7
Round 2
5-1
4-2
6-9
7-8
3-10
Round 3
1-6
2-5
3-4
9-7
10-8
Round 4
7-1
6-2
5-3
8-9
4-10
Round 5
1-8
2-7
3-6
4-5
10-9
Round 6
9-1
8-2
7-3
6-4
5-10
Round 7
1-10
2-9
3-8
4-7
5-6
Round 8
1-2
9-3
8-4
7-5
10-6
Runde 9
3-1
4-9
5-8
6-7
2-10
Round 10 is opposite of round 1, 11 opposite of 2 etc.


You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1. That's
because 1-6 and 1-8 is not 1 versus smallest or biggest even number.

Notice if an odd number, then opponent for the largest number, will
have bye. For example if 9 participants in the schedule above, then
the opponent for 10 will have bye in all rounds.

The schedules is general in the set-ups on this site, so to get a meaning
with a schedule, you must replace the numbers with names or teams.
 

Schedule for 11 or 12:
Round 1
1-4
2-3
11-5
10-6
9-7
12-8
Round 2
5-1
4-2
6-11
7-10
8-9
3-12
Round 3
1-6
2-5
3-4
11-7
10-8
12-9
Round 4
 7-1
6-2
5-3
8-11
9-10
4-12
Round 5
1-8
2-7
3-6
4-5
11-9
12-10
Round 6
9-1
8-2
7-3
6-4
10-11
5-12
Round 7
1-10
2-9
3-8
4-7
5-6
12-11
Round 8
11-1
10-2
9-3
8-4
7-5
6-12
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
Round 10
1-2
11-3
10-4
9-5
8-6
12-7
Round 11
3-1
4-11
5-10
6-9
7-8
2-12
Round 12 is opposite of round 1, 13 opposite of 2 etc.


 You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1. That's because 1-6, 1-8 and 1-10
is not 1 versus smallest or biggest even number.
 

Schedule for 13 or 14:
Round 1
1-4
2-3
13-5
12-6
11-7
10-8
14-9
Round 2
5-1
4-2
6-13
7-12
8-11
9-10
3-14
Round 3
1-6
2-5
3-4
13-7
12-8
11-9
14-10
Round 4
7-1
6-2
5-3
8-13
9-12
10-11
4-14
Round 5
1-8
2-7
3-6
4-5
13-9
12-10
14-11
Round 6
9-1
8-2
7-3
6-4
10-13
11-12
5-14
Round 7
1-10
2-9
3-8
4-7
5-6
13-11
14-12
Round 8
11-1
10-2
9-3
8-4
7-5
12-13
6-14
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
14-13
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
7-14
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
Round 12
1-2
13-3
12-4
11-5
10-6
9-7
14-8
Round 13
3-1
4-13
5-12
6-11
7-10
8-9
2-14
Round 14 is opposite of round 1, 15 opposite of 2 etc.


 You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1. That's because 1-6, 1-8, 1-10
and 1-12 is not 1 versus smallest or biggest even number.
 

Schedule for 15 or 16:
Round 1
1-4
2-3
15-5
14-6
13-7
12-8
11-9
16-10
Round 2
5-1
4-2
6-15
7-14
8-13
9-12
10-11
3-16
Round 3
1-6
2-5
3-4
15-7
14-8
13-9
12-10
16-11
Round 4
7-1
6-2
5-3
8-15
9-14
10-13
11-12
4-16
Round 5
1-8
2-7
3-6
4-5
15-9
14-10
13-11
16-12
Round 6
9-1
8-2
7-3
6-4
10-15
11-14
12-13
5-16
Round 7
1-10
2-9
3-8
4-7
5-6
15-11
14-12
16-13
Round 8
11-1
10-2
9-3
8-4
7-5
12-15
13-14
6-16
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
15-13
16-14
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
14-15
7-16
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
16-15
Round 12
15-1
14-2
13-3
12-4
11-5
10-6
9-7
8-16
Round 13
1-16
2-15
3-14
4-13
5-12
6-11
7-10
8-9
Round 14
1-2
15-3
14-4
13-5
12-6
11-7
10-8
16-9
Round 15
3-1
4-15
5-14
6-13
7-12
8-11
9-10
2-16
Round 16 is opposite of round 1, 17 opposite of 2 etc.


You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1, or you can begin with row 1-14
and end with the row 13-1. That's because 1-6, 1-8, 1-10
1-12 and 1-14 is not 1 versus smallest or biggest even number.
 

Schedule for 17 or 18:
Round 1
1-4
2-3
17-5
16-6
15-7
14-8
13-9
12-10
18-11
Round 2
5-1
4-2
6-17
7-16
8-15
9-14
10-13
11-12
3-18
Round 3
1-6
2-5
3-4
17-7
16-8
15-9
14-10
13-11
18-12
Round 4
7-1
6-2
5-3
8-17
9-16
10-15
11-14
12-13
4-18
Round 5
1-8
2-7
3-6
4-5
17-9
16-10
15-11
14-12
18-13
Round 6
9-1
8-2
7-3
6-4
10-17
11-16
12-15
13-14
5-18
Round 7
1-10
2-9
3-8
4-7
5-6
17-11
16-12
15-13
18-14
Round 8
11-1
10-2
9-3
8-4
7-5
12-17
13-16
14-15
6-18
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
17-13
16-14
18-15
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
14-17
15-16
7-18
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
17-15
18-16
Round 12
15-1
14-2
13-3
12-4
11-5
10-6
9-7
16-17
8-18
Round 13
1-16
2-15
3-14
4-13
5-12
6-11
7-10
8-9
18-17
Round 14
17-1
16-2
15-3
14-4
13-5
12-6
11-7
10-8
9-18
Round 15
1-18
2-17
3-16
4-15
5-14
6-13
7-12
8-11
9-10
Round 16
1-2
17-3
16-4
15-5
14-6
13-7
12-8
11-9
18-10
Round 17
3-1
4-17
5-16
6-15
7-14
8-13
9-12
10-11
2-18
Round 18 is opposite of round 1, 19 opposite of 2 etc.


You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1, or you can begin with row 1-14
and end with the row 13-1, or you can begin with the row 1-16
and end with the row 15-1. That's because 1-6, 1-8, 1-10, 1-12
1-14 and 1-16 is not 1 versus smallest or biggest even number.
 

Schedule for 19 or 20:
Round 1
1-4
2-3
19-5
18-6
17-7
16-8
15-9
14-10
13-11
20-12
Round 2
5-1
4-2
6-19
7-18
8-17
9-16
10-15
11-14
12-13
3-20
Round 3
1-6
2-5
3-4
19-7
18-8
17-9
16-10
15-11
14-12
20-13
Round 4
7-1
6-2
5-3
8-19
9-18
10-17
11-16
12-15
13-14
4-20
Round 5
1-8
2-7
3-6
4-5
19-9
18-10
17-11
16-12
15-13
20-14
Round 6
9-1
8-2
7-3
6-4
10-19
11-18
12-17
13-16
14-15
5-20
Round 7
1-10
2-9
3-8
4-7
5-6
19-11
18-12
17-13
16-14
20-15
Round 8
11-1
10-2
9-3
8-4
7-5
12-19
13-18
14-17
15-16
6-20
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
19-13
18-14
17-15
20-16
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
14-19
15-18
16-17
7-20
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
19-15
18-16
20-17
Round 12
15-1
14-2
13-3
12-4
11-5
10-6
9-7
16-19
17-18
8-20
Round 13
1-16
2-15
3-14
4-13
5-12
6-11
7-10
8-9
19-17
20-18
Round 14
17-1
16-2
15-3
14-4
13-5
12-6
11-7
10-8
18-19
9-20
Round 15
1-18
2-17
3-16
4-15
5-14
6-13
7-12
8-11
9-10
20-19
Round 16
19-1
18-2
17-3
16-4
15-5
14-6
13-7
12-8
11-9
10-20
Round 17
1-20
2-19
3-18
4-17
5-16
6-15
7-14
8-13
9-12
10-11
Round 18
1-2
19-3
18-4
17-5
16-6
15-7
14-8
13-9
12-10
20-11
Round 19
3-1
4-19
5-18
6-17
7-16
8-15
9-14
10-13
11-12
2-20
Round 20 is opposite of round 1, 21 opposite of 2 etc.

 
 You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1, or you can begin with row 1-14
and end with the row 13-1, or you can begin with the row 1-16
and end with the row 15-1, or you can begin with the row 1-18
and end with the row 17-1. That's because 1-6, 1-8, 1-10, 1-12
1-14, 1-16 and 1-18 is not 1 versus smallest or biggest even number.
 

Schedule for 21 or 22:
Round 1
1-4
2-3
21-5
20-6
19-7
18-8
17-9
16-10
15-11
14-12
22-13
Round 2
5-1
4-2
6-21
7-20
8-19
9-18
10-17
11-16
12-15
13-14
3-22
Round 3
1-6
2-5
3-4
21-7
20-8
19-9
18-10
17-11
16-12
15-13
22-14
Round 4
7-1
6-2
5-3
8-21
9-20
10-19
11-18
12-17
13-16
14-15
4-22
Round 5
1-8
2-7
3-6
4-5
21-9
20-10
19-11
18-12
17-13
16-14
22-15
Round 6
9-1
8-2
7-3
6-4
10-21
11-20
12-19
13-18
14-17
15-16
5-22
Round 7
1-10
2-9
3-8
4-7
5-6
21-11
20-12
19-13
18-14
17-15
22-16
Round 8
11-1
10-2
9-3
8-4
7-5
12-21
13-20
14-19
15-18
16-17
6-22
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
21-13
20-14
19-15
18-16
22-17
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
14-21
15-20
16-19
17-18
7-22
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
21-15
20-16
19-17
22-18
Round 12
15-1
14-2
13-3
12-4
11-5
10-6
9-7
16-21
17-20
18-19
8-22
Round 13
1-16
2-15
3-14
4-13
5-12
6-11
7-10
8-9
21-17
20-18
22-19
Round 14
17-1
16-2
15-3
14-4
13-5
12-6
11-7
10-8
18-21
19-20
9-22
Round 15
1-18
2-17
3-16
4-15
5-14
6-13
7-12
8-11
9-10
21-19
22-20
Round 16
19-1
18-2
17-3
16-4
15-5
14-6
13-7
12-8
11-9
20-21
10-22
Round 17
1-20
2-19
3-18
4-17
5-16
6-15
7-14
8-13
9-12
10-11
22-21
Round 18
21-1
20-2
19-3
18-4
17-5
16-6
15-7
14-8
13-9
12-10
11-22
Round 19
1-22
2-21
3-20
4-19
5-18
6-17
7-16
8-15
9-14
10-13
11-12
Round 20
1-2
21-3
20-4
19-5
18-6
17-7
16-8
15-9
14-10
13-11
22-12
Round 21
3-1
4-21
5-20
6-19
7-18
8-17
9-16
10-15
11-14
12-13
2-22
Round 22 is opposite of round 1, 23 opposite of 2 etc.


You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1, or you can begin with row 1-14
and end with the row 13-1, or you can begin with the row 1-16
and end with the row 15-1, or you can begin with the row 1-18
and end with the row 17-1, or you can begin with the row 1-20
and end with the row 19-1. That's because 1-6, 1-8, 1-10, 1-12,
1-14, 1-16, 1-18 and 1-20 is not 1 versus smallest or biggest even number.
 

Schedule for 23 or 24:
Round 1
1-4
2-3
23-5
22-6
21-7
20-8
19-9
18-10
17-11
16-12
15-13
24-14
Round 2
5-1
4-2
6-23
7-22
8-21
9-20
10-19
11-18
12-17
13-16
14-15
3-24
Round 3
1-6
2-5
3-4
23-7
22-8
21-9
20-10
19-11
18-12
17-13
16-14
24-15
Round 4
7-1
6-2
5-3
8-23
9-22
10-21
11-20
12-19
13-18
14-17
15-16
4-24
Round 5
1-8
2-7
3-6
4-5
23-9
22-10
21-11
20-12
19-13
18-14
17-15
24-16
Round 6
9-1
8-2
7-3
6-4
10-23
11-22
12-21
13-20
14-19
15-18
16-17
5-24
Round 7
1-10
2-9
3-8
4-7
5-6
23-11
22-12
21-13
20-14
19-15
18-16
24-17
Round 8
11-1
10-2
9-3
8-4
7-5
12-23
13-22
14-21
15-20
16-19
17-18
6-24
Round 9
1-12
2-11
3-10
4-9
5-8
6-7
23-13
22-14
21-15
20-16
19-17
24-18
Round 10
13-1
12-2
11-3
10-4
9-5
8-6
14-23
15-22
16-21
17-20
18-19
7-24
Round 11
1-14
2-13
3-12
4-11
5-10
6-9
7-8
23-15
22-16
21-17
20-18
24-19
Round 12
15-1
14-2
13-3
12-4
11-5
10-6
9-7
16-23
17-22
18-21
19-20
8-24
Round 13
1-16
2-15
3-14
4-13
5-12
6-11
7-10
8-9
23-17
22-18
21-19
24-20
Round 14
17-1
16-2
15-3
14-4
13-5
12-6
11-7
10-8
18-23
19-22
20-21
9-24
Round 15
1-18
2-17
3-16
4-15
5-14
6-13
7-12
8-11
9-10
23-19
22-20
24-21
Round 16
19-1
18-2
17-3
16-4
15-5
14-6
13-7
12-8
11-9
20-23
21-22
10-24
Round 17
1-20
2-19
3-18
4-17
5-16
6-15
7-14
8-13
9-12
10-11
23-21
24-22
Round 18
21-1
20-2
19-3
18-4
17-5
16-6
15-7
14-8
13-9
12-10
22-23
11-24
Round 19
1-22
2-21
3-20
4-19
5-18
6-17
7-16
8-15
9-14
10-13
11-12
24-23
Round 20
23-1
22-2
21-3
20-4
19-5
18-6
17-7
16-8
15-9
14-10
13-11
12-24
Round 21
1-24
2-23
3-22
4-21
5-20
6-19
7-18
8-17
9-16
10-15
11-14
12-13
Round 22
1-2
23-3
22-4
21-5
20-6
19-7
18-8
17-9
16-10
15-11
14-12
24-13
Round 23
3-1
4-23
5-22
6-21
7-20
8-19
9-18
10-17
11-16
12-15
13-14
2-24
Round 24 is opposite of round 1, 25 opposite of 2 etc.


You can also begin with the row 1-6 and end with the row 5-1, or
you can begin with the row 1-8 and end with the row 7-1, or you can begin
with the row 1-10 and end with the row 9-1, or you can begin
with the row 1-12 and end with the row 11-1, or you can begin with row 1-14
and end with the row 13-1, or you can begin with the row 1-16
and end with the row 15-1, or you can begin with the row 1-18
and end with the row 17-1, or you can begin with the row 1-20
and end with the row 19-1, or you can begin with the row 1-22
and end with the row 21-1. That's because 1-6, 1-8, 1-10, 1-12, 1-14
1-16, 1-18, 1-20 and 1-22 is not 1 versus smallest or biggest even number.

The build-up of a schedule is quite logical: Always Round 1 with 1 versus even number
which is not the smallest or largest. The opponent of 1 increases with 1 for each round.
At the same round, for example home team number, increases with 1 and away team number
decreases with 1, until it's impossible. Then second largest number in the schedule plays
at home versus number for the opponent to 1 added with 1. If round 1 is 1-4, then
second largest number, for example in the schedule for 24, will be 23-5. The opponent of
the second largest number, as well as the opponent of 1, increases with 1 for each round.
The largest number in the schedule plays at home versus number not used so far in round 1.
The opponent of the largest number increases with 1 for every second round.
If a team plays at home in round 1, then it plays away in round 2.
If a team plays at home in round 3, then it plays away in round 4.
If a team plays at home in round 5, then it plays away in round 6 etc.
until 1 plays at home versus 2. If a team plays at home in the second last round,
then it plays away in the last round. Two teams will alternate between playing
home and away each round. It will always be 2 and (2 + largest largest number
in the schedule divided with 2). For example in the schedule with 24, it will be
2 and 14 (2+(24:2)=14). If round 1 is 1-4, then 3 plays at home in both round 2 and 3,
4 plays at home in both round 4 and 5, 5 plays at home in both round 6 and 7 etc.
It's not so easy to explain it, so you easily understand. You must carefully study
the schedules to understand the logical build-up. And when you can say eureka,
voila or aha or which language you use, and have understand it; then you
can create a schedule manually, automatically, without thinking so much.

In the examples above I used home team, but it could also be white in chess.
Copyright © The perfect schedule invented by Lars Asbjørn Stensen in 1991,
 whom developed and perfected the round-robin system, they are using in chess.
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Updating finished 13 October 2013, and became English as well.
Copyright © Lars Asbjørn Stensen
You can use my perfect round-robin tables, but don't take credit for the tables!