The list problem

I've been working on this algorithm since I learned how to write arrays in C, and I can't seem to see through what I'm missing. The algorithm is an attempt to make all the possible fixtures in a 20-teams League (EPL) if all teams are to play each other home and away once a week. That'll make 10 matches a week if all teams play, 38 games per team (38 weeks) that's 380 games total.

The challenge

A team can't play twice in a match week (20 teams can only make 10 matches),
No same fixture is to be repeated.

The problem

In other to avoid any repetition, I check if the fixture and both teams have not been previously selected, But then the result shows 10 games each for the first 6 weeks, 8 for the next 9, 10 for the next 3, to 4 games for the last 2 weeks, and a total of only 320 fixtures is selected.

Observation

Over the years I've tried different implementations in different languages, ranging from java, python, php, javascript, and c with no solution.
Then I decided to shuffle the fixtures and the selected fixtures were in a range of 360 to 369 in 10 different runs. Why the change of heart?

Is this a list problem or there is simply a better way?

teams = ["ARS", "AVL", "BRE", "BOU", "BRI",
        "BUR", "CHE", "CRY", "FUL",
        "EVE", "LEE", "LEI", "LIV", "MCI", "MUN",
        "NEW", "TOT", "WHU", "WOL", "WAT"]

#All 380 possible fixtures len(fixtures) prints 380
#Shuffle this to see the change
fixtures =  [f"{home} - {away}" for home in teams for away in teams if home != away]

#38 match weeks if 10 matches are played every week. Each team plays only once per week
match_weeks = []

#Fixtures played // no same fixture is to be played twice
#i.e ARS - CHE can appear only once per season, but CHE - ARS only
s_fixtures = []

#Making fixtures for all 38 weeks
for i in range(38):
    match_week = [] #should be exactly 10 unique games every week = 20/2
    s_teams = [] #teams already selected in the current week // 20 teams every week
    for fixture in fixtures:
        if len(match_week) == 10: #to save some iterations/time 
            break
        if fixture not in s_fixtures:
            home, away = fixture[:3], fixture[6:]
            if home not in s_teams and away not in s_teams:
                s_teams.extend([home, away]) # add teams to selected list
                print(len(s_teams))
                match_week.append(fixture)
                s_fixtures.append(fixture) #add fixture to selected list
    match_weeks.append(match_week)

Blog

JJenus

The challenge

The problem

Observation

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