I am writing a script that creates a tournament fixtures using round robin algorithm with first team fixed. And it works well.
Problem is that when I create those fixtures I have to distribute home and away as close as possible to HAHAHA... pattern where H - is home and A - is away. Where limit is that team cannot play 3 home(or away) matches in a row.
What I tried is preserving how many home and away matches each team played and then team with lowest home or away number will play where it should.
For example
Team 1 (2 H and 1 A) VS Team 2 (with 2 H and 2 A)
Result would be :
Team 2(H) vs Team 1(A) // because Team 1 played least number away of games
Question: Is there other way to implement such home away distribution, and if is what would be the idea behind it?
The equal distribution pattern that you seek is not readily available. The suggestion to do a 'random shuffle' does not solve the problem. Distributing teams equally with opponents, equally as home & visitor, and equally to play in the time/location slots can be done. There are different requirements that must be met for an even number of teams and an odd number of teams. Add to this that the math to create each schedule is totally different (for example a 7 team league schedule is different than an 8 team league).
Checkout the information provided on this link about "equal distribution".
Equal distribution of; teams, time slots, & home & visitor is possible only if you have the correct number of time slots available for the number of teams you are scheduling. Understanding the structure of schedules is very important. Your question above about equal Home & Away (H & A) is answered in the link above. The best you can do is no more than two H or two A games in a row in each round robin. There is a minor exception where a team could have 3 Home or 3 Away games in a row when a round robin is ending and starting the next round robin. This only happens to a few teams, is unavoidable, but H & A is balanced at the end of each 2 round robins.
When scheduling teams for round robin play, in the simplest of terms you are looking to create a round robin of teams, a round robin of home & visitor status, and a round robin of time/location slots... all at the same time.
To further complicate the subject it takes a different number of round robins (one) to satisfy equal 'team' distribution, a different number of round robins (two) to satisfy 'home & visitor' balance, and a different number of round robins to satisfy 'time slot' balance. The number of round robins needed to balance all teams playing equally in all the time slots, for an even number of teams, is equal to half the number of teams being scheduled. This changes when scheduling an odd number of teams.