8 golfers -21 rounds of paired 4ball competition.

[Dave_Mack]

We have 8 golfers playing 21 rounds in paired four-ball competition.
 
OBJECTIVE:  Each golfer to 1.) partner everyone else 2.) oppose every other team and 3.) play in the same four ball the same number of times.
 
Could this be achieved by taking the "Balanced Round Robin Schedule for 8 players" and having Match 1 pairs v Match 2 pairs and Match 3 pairs v Match 4 pairs for the first 7 rounds; then Match 1 v Match 3 and Match 2 v Match 4 for rounds 8 to 14 and then Match 1 v Match 4 and Match 2 v Match 3 for the final 7 rounds?
 
If so how many time will each pair achieve each of the 3 stated objectives. Many thanks for any and all responses!

[Ian Wakeling]

Yes, this will work very well.  The schedule will have the following properties:

all pairs partner exactly 3 times.
all pairs oppose exactly 6 times.
all 42 four-balls will be different.
consider the 3 four-balls that involve a particular partnership, then the 6 opponents will all be different.

[Dave_Mack]

Excellent!

Thank you for such a speedy and clear response. We're actually planning to play these rounds on a golf tour in Ireland over a 2 week period! The 3rd objective is focused on camaraderie. Each of us want to try to play an equal amount in the company of everyone else on tour.

Your expertise is greatly appreciated and adds to the fun of friendly competition. Thanks again.  

[Dave_Mack]

On the "camaraderie" objective, I was just wondering how many times will an individual golfing tourist play in the same four ball with each of the other 7 tourists? 

[Ian Wakeling]

The camaraderie count is simply the sum of the partner and opposition frequency, so 3 + 6 = 9 times.

[Dave_Mack]

Perfect! Thanks again.

[Dave_Mack]

See below. Covid killed the trip I was planning in 2019 but we're now embarking on a shorter golf trip of 14 rounds!  When I use the "Balanced Round Robin Schedule 8 players" and have Match 1 pairs play Match 2 pairs and Match 3 pairs play Match 4 pairs for the first 7 rounds; then Match 1 play Match 3 and Match 2 play Match 4 for rounds 8 to 14, I believe all pairs partner exactly twice and all pairs oppose different opponents exactly four times, which is great.

My concern is what I referred to below as the "camaraderie objective" whereby ideally everyone would play in a fourball with everyone else the same number of times, either as a partner or an opponent. Using the Schedule as I describe above some players will play with other members of the touring party as little as 4 times over the 14 rounds while they will play with others as many as 8 times.   

My question is is it possible for this to be balanced out so everyone would play in the company of everyone else exactly 6 times or are my thee objectives as described below not mutually achievable? If so, what would be the implication of prioritizing the "camaraderie objective"?

Many thanks in advance for any guidance others can offer.  

[Ian Wakeling]

I think you will need to use two copies of the whist schedule for 8 players.  So when you use the viewer here, instead of using the 'balanced' option, click on 'whist'.  You will get a 7 round schedule for 8 items which you need to use twice, where the two tables become the two foursomes.  In order to avoid playing the exact same foursomes in rounds 8 to 14 as you did in rounds 1 to 7, you should make a different random assignment of the 8 players to the numbers 1 to 8 for each half.

[Dave_Mack]

Of course! The whist schedule being for pairs of pairs makes prefect sense. We have been doing these golf trips for coming up to 20 years and I now recall that was what we used so successfully in the past. Randomly reassigning the players numbers for rounds 8-14 is such a simple solution. Thanks so much. I'll provide further feedback when I've completed the draw. 

[Dave_Mack]

Just wondering whether I would achieve the same result as reassigning the players if in rounds 1 to 7 whist pairs 1 opposed pairs 2 and pairs 3 opposed pairs 4. Then for rounds 8 to 14 we went 1 v3 and 2 v 4? 

[Ian Wakeling]

Yes, this does work and also guarantees different foursomes.  Be careful as I am not sure every re-arrangement of the pairs will work for larger whist schedules with 12 or more players.