Be it TTRPGs, board games or video games, a group of four players is the standard size.
DnD and adjacent systems balance their challenges around a party of four. Most boardgames come with four colours for players to choose from. Most video game consoles only can connect four controllers and most video games like Smash Bros and Mario Kart only have four slots? Why is that?
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My guess is it is a holdover from the arcades. 4 player cabs where crowded as heck, but you could just make it work if 1 or 2 of you where pretty small. Then consoles with more then 2 controller ports ( with an adapter *sold separately*) came and the geometry of the TV became the limiting factor, 4 way split, split it up any more then that and players either wont have an equal amount of screen space and/or no one will be able to see because the screen space they own is too small.
Makes for easy splitting into 2v2 should it be necessary, or just temporarily splitting the group in half for story reasons.
With a 2 man group, splitting would remove the cooperative element. With a 3 man group it would be 1v2, or the game/rules/dungeonmaster would have to enforce which split requires 2 players. 5 man group has much the same issue as 3. 6 would work, but the more players you require the harder it is to get a game going.
4 just makes sense. Enough for an even split. While still retaining cooperation if you need to split. Without the hurdle of gathering too many people.
For board games:
Game boards are historically square, tables are square, people sit around the games normally in a square, the average number of people sitting at a table is already close to 4, so 4 is just the least disrupting number in average.
The more people are required to participate in an activity, the least likely it is to gather the people necessary, so balancing a game for the “minimum viable player count” makes sense (most game allow for counts higher than 4, but are balanced for 4 players as you explained).
Why not 2? That “minimum number” also comes from the fact that board games are fundamentally a social activity (while there are plenty of very good and very popular 2 player games, they are somewhat of a different beast in terms of social dynamic).
Why not 3? I’d say in general symmetrical games are just easier to design and balance, in great part due to the fact that player interactions are normally 1 on 1, that’s also the reason why “team up” mechanics are easier to implement with a symmetrical player count.
Most board games are turn based (so are TTRPGS), so managing idle times is easier with 4 players.
Games that are essentially “multiplayer solitaire” scale great in terms of player count, but they are balanced for the expected average, in other words, it’s the norm because it’s common.
There is probably others that I’m missing but the comment is already long.
Regarding videogames I disagree about 4 being the standard, 2 players have always been and still remain a more popular count than 4 for couch multiplayer, while higher counts are much more common than 4 in online multiplayer.
I guess because of board games which were played on square or rectangle shaped boards. One guy can sit on each side and it won’t feel much crowded.
Likely self balancing but winnable.
1v1 will likely snowball. Winning player continues to win until they completely win the game.
1v1v1 players always work against the top player. Could be too strongly self balancing.
1v1v1v1 you now have potentially more complex interactions to try to balance and outwit opponents.
With 5 or more It’s not likely much better than 4.
Imagine you have a game in which you need 10 players to play it. What an absolute nightmare having to not only have 9 friends, but 9 friends who wants to play that specific game. Then set a date/dates to actually play it with all 10 of you able to show up. It’s just very inconvenient the more players you need to have.
For board games, this isn’t really true. Maybe it was Catan and Ludo that started this perception? Anyway, I have a collection of over 50 games, and just from a quick glance, it’s clear that the vast majority support 2-5 players
For games I always felt 5 was the standard, but maybe I’ve just been playing CS for 24 years…
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