Does each NFL team get an equal number of Monday/Night games? If not how are teams chosen?
The year Monday night football started each team played exactly once. There were then 26 teams and a 14 week schedule. There was no Monday night game the the last week of the season though at some early point ABC got a Saturday night game the last week. This was at least in part due to TV contracts. ABC didn’t want the dregs and NBC and CBS didn’t want to give up too much. The original contract was negotiated just as teh merger was taking place.
I don’t know how long the practice lasted, but certainly Monday night moved to more marque games after a while.
Monday and Thursday are scheduled before the season starts, usually big games (or games they expect to be big) get those slots. As far as I know there’s no rule that all teams are guaranteed a prime time slot. Sunday night games can be flex scheduled as the season plays out-- surprise teams can make their way into primetime.
Under the current NFL policy, each team gets a Thursday night game at some point during the season. They’re trying to make more of these division games to make them more “meaningful”.
No team is guaranteed a Monday night or Sunday night game but no team is going to have too many such games in a season, either.
There’s also a couple Saturday games this year in week 16, which is the week before Christmas.
Detroit and Dallas always play at home on Thanksgiving, so they’re always going to have a Thursday game, even before Thursday night football became a thing.
With a full Thursday night schedule, each team gets stuck with a Thursday game. Monday and Sunday night games are different. The networks try to pick games that will guarantee good ratings and sometimes competitive games. Bad ratings teams will rarely have a Sunday or Thursday night game unless they’re playing a powerhouse team. You’ll almost never see a Buffalo Bills, Jacksonville Jaguars, or Tennessee Titans game on a Monday or Sunday night unless they’re playing a team known to draw good ratings.
What they’ve done is taken already terrible games (where the first team to score wins, or at least that’s been the pattern this season) and make them more important by putting divisional games on a short week. It winds up being terrible, yet important football.
The Rams didn’t play in a single MNF football game from November 1991 (when they were still in Los Angeles) until September 2000 (after they won the Super Bowl.)
The longest current streak is the Buffalo Bills, whose last MNF appearance was the opening game in 2009.