Round Robin Tournament Scheduling

Recent Posts

Requests / Re: Bridge marathon
« Last post by Ian Wakeling on Today at 11:42:25 AM »
Hi Janice,

I don't think it is possible to change the schedule above to suit.  If I understand correctly then what you want is part of round-robin where teams are assigned home or away for each match.  The Excel generator here made the following:

you may need to be logged in to see he image above.
Requests / Re: Getting around ghost entries in odd-numbered bridge games!
« Last post by McBruceWX5 on September 26, 2021, 08:00:11 PM »
Wow, very interesting solution.  I especially admire the way you have taken your familiarity with a schedule type where each round is run in rows and realized that running it in columns would work for my problem!  Bravo!

The original scenario was for a summer league which was going to go for six consecutive weeks, but I am already seeing possible applications for two or three session team events where a complete round robin is better than a swiss when there are 11 or 13 or 15 teams.  The one drawback is the requirement that one team play the 3-ways throughout (many teams don’t like these), but I think in most events a volunteer team could be found for this role.

The other application for PBTD’s in bridge scheduling may be in our local league of bi-monthly matches, where I have used the “circle” method of producing a schedule.  A few times the top teams have complained that the sequence of teams played sometimes gives them a run of lower-ranked teams (apparently they lose interest or something unless they have a tough match fairly often!), and PBTD’s may be a better solution.
Requests / Re: Bridge marathon
« Last post by sunshinehappy2 on September 26, 2021, 07:16:48 PM »
Hello - I'm trying to set up a marathon bridge playing schedule for 14 pairs to play over a 7 month time period. Games are played between 2 teams at time in individual homes with each pair taking a turn hosting the games. Would you be able to help? I saw the schedule for the 16 pair - can I just eliminate 2 pairs and use that schedule?
Thank you very much for your help, Janice
Requests / Re: 13 person Doubles Platform Tennis League / 13 Weeks
« Last post by Ian Wakeling on September 26, 2021, 10:45:19 AM »
What you want is a 'Whist' schedule for 13 players, which gives all partners once, and all opponents twice.  Here is an example:

[(B M):(I F)] [(C L):(D K)] [(E J):(G H)]
[(C A):(J G)] [(D M):(E L)] [(F K):(H I)]
[(D B):(K H)] [(E A):(F M)] [(G L):(I J)]
[(E C):(L I)] [(F B):(G A)] [(H M):(J K)]
[(F D):(M J)] [(G C):(H B)] [(I A):(K L)]
[(G E):(A K)] [(H D):(I C)] [(J B):(L M)]
[(H F):(B L)] [(I E):(J D)] [(K C):(M A)]
[(I G):(C M)] [(J F):(K E)] [(L D):(A B)]
[(J H):(D A)] [(K G):(L F)] [(M E):(B C)]
[(K I):(E B)] [(L H):(M G)] [(A F):(C D)]
[(L J):(F C)] [(M I):(A H)] [(B G):(D E)]
[(M K):(G D)] [(A J):(B I)] [(C H):(E F)]
[(A L):(H E)] [(B K):(C J)] [(D I):(F G)]

for even numbers of players (4n) you can click on "Visit the pages that inspired the forum", at the top of this page, and then look for 'Whist' link.  Both even (4n) and odd (4n+1) numbers of players are covered here at Durango Bill web site.
Requests / 13 person Doubles Platform Tennis League / 13 Weeks
« Last post by lunkerhunter on September 26, 2021, 09:54:31 AM »
Can anyone help us (PLEASE)?

We have a 13 person doubles platform tennis league and are trying to figure out a 13 week scheduler that allows every person to partner up with each other once).  

Yes we will have a bye week but is this possible?  

Thanks very much to anyone that can help!!!!!  Really appreciate it!!!
Requests / Re: Getting around ghost entries in odd-numbered bridge games!
« Last post by Ian Wakeling on September 26, 2021, 06:59:52 AM »
There is a way to do what you want, however it is not going to be possible to express it in a simple set of a rules that can be used to build the schedule from scratch.  Of course that is not a big problem,  all it means is that you will need to prepare a collection of schedules for 2t + 1 teams, and have them to hand when the tournament starts.

The key to a solution is knowing about Partitioned Balanced Tournament Designs - which I discuss here and give examples in replies #1 and #5.

Given a PBTD for 2t teams, then it is possible to construct your bridge schedule for 2t+1 teams. As an example I will use the 10 team PBTD to make an 11 team bridge schedule. Here is the PBTD

(I E) (H J) (G B) (F C) (D A)
(J F) (G I) (H A) (E D) (B C)
(H C) (E B) (D I) (A J) (G F)
(G D) (F A) (C J) (B I) (E H)
(A B) (C D) (E F) (G H) (I J)
(F H) (J E) (B D) (I A) (C G)
(E G) (I F) (A C) (J B) (H D)
(D J) (A G) (I H) (C E) (F B)
(C I) (B H) (J G) (D F) (A E)

The first two sessions of the bridge schedule are made from the 1st column above as follows.  Add the 11th team K to the middle pair from round 5, to make the sub-group of 3 teams. The ordinary pairings for the two sessions are then the games taken from above and below the middle pair respectively.

Session 1: (A B K) (I E) (J F) (H C) (G D)
Session 2:  -----  (F H) (E G) (D J) (C I)

continue in the same way for all 5 of the columns, so sessions 3 and 4 are:

Session 3: (C D K) (H J) (G I) (E B) (F A)
Session 4:  -----  (J E) (I F) (A G) (B H)


A PBTD for 18 teams was discovered relatively recently and can be found here on  In summary using PBTDs will give you a way to make the 2t+1 bridge schedules for  t >= 5, excepting t=11 which is still unknown.

Hope that helps.
Requests / Getting around ghost entries in odd-numbered bridge games!
« Last post by McBruceWX5 on September 25, 2021, 05:00:53 PM »
At the beginning of the pandemic I decided to try a round-robin problem that had eluded me since it came up in the 1990s: a bridge league expecting 12 teams that gets a 13th.  The interesting catch is that in tournament bridge we have a way to make three teams play a round-robin amongst themselves over two rounds, avoiding byes.  So the question became: can we make a schedule of six two-round gamedates where three of the 13 teams play a round-robin (AvB BvC CvA) and the other ten play two matches against different opponents, and have it all work out so all 13 teams play each other once after six matchdays and twelve rounds?

I've posted at

a statement of the problem in pdf, along with a LibreOffice spreadsheet you can use to try fitting the 13 teams into the 12 rounds, and a second LibreOffice spreadsheet with the solution that I stumbled upon after a few days tinkering.  The spreadsheets check as you tinker with the schedule and turn cells red when a problem is discovered.

What I'm really after is some generic rule that dictates what to do with ANY odd number of teams, 2t + 1, playing t rounds of two matches, with three teams each week in a round-robin to make a complete schedule.  The solution I found is random and was arrived at by tinkering.  Most bridge schedules have simple rules that allow Directors like me to improvise solutions when an unexpected number of people arrive.  When this problem came up in the 1990s, we were stumped and ended up convincing two teams to merge and get us back down to 12!
Mathematics / Re: Permutations and combinations with SRRT scheduling
« Last post by jlasdf on September 20, 2021, 02:08:22 PM »

Belated thanks for your reply.  I had no idea what branch of mathematics I was dealing with, nor did I know the academic or formal disciplines that the papers and OEIS refer to.    

Thanks also for your feedback on watching the video.  As you might have interpreted from the video, I don't necessarily have any formal training on this subject.  I also don't really know 100% if my video is even 100% correct in its thinking.  For the 8 team league with 7 rounds in the season, I do not 100% know if the valid weekly rounds are complete.  I also do not know if the way I "calculated" possible seasons is 100% valid either.  It was mathematics / analysis via intuition, not necessarily mastery.  Still always learning!!! 

Thanks again!! Justin 
Requests / Re: 10 teams on 4 courts in 11 games?
« Last post by Ian Wakeling on September 15, 2021, 08:15:52 AM »
I have found the 12 round schedule below by computer search and I think it should work.  You have the option of shortening the tournament by playing (9 v 10) on the 5th court in round 11.

  C1      C2      C3      C4       byes
 (1  9)  (2  6)  (3 10)  (4  5)    (7  8)
 (1  5)  (2  3)  (6 10)  (7  8)    (4  9)
 (1 10)  (2  5)  (3  8)  (4  9)    (6  7)
 (1  8)  (2  4)  (5 10)  (6  7)    (3  9)
 (1  7)  (2  8)  (3  9)  (4 10)    (5  6)
 (1  3)  (2  9)  (4  7)  (5  6)    (8 10)
 (3  4)  (5  7)  (6  9)  (8 10)    (1  2)
 (1  2)  (4  6)  (7 10)  (8  9)    (3  5)
 (1  6)  (3  5)  (4  8)  (7  9)    (2 10)
 (2 10)  (3  7)  (5  9)  (6  8)    (1  4)
 (1  4)  (2  7)  (3  6)  (5  8)    (9 10)
 (9 10)

Requests / 10 teams on 4 courts in 11 games?
« Last post by Paulepin on September 11, 2021, 08:04:16 AM »
I am trying to setup a round-robin for 10 teams on only 4 (not 5) courts. This means two teams will not play in each round (due to the lack of a fifth court).  I need these two teams to play each other in the next round so that a cold team (one that sits out) doesn't play a hot team (one that's just played) in any round.  There will be 45 games in total, which means 11 rounds of 4 games and 1 round of 1 game.  We can fit the one game into a fifth court once but otherwise that court is needed for other competitions.  The cold versus cold requirement is making this more complicated to work out.  Can anyone help?  This is the best I've been able to manage: