Are there any positive sum board games?

Risk is positive sum as long as you all collectively agree that since Carl controls all of Asia, most of Europe, and most of North America, he's no longer welcome in the sum.

This is perhaps the wrong lesson.

You're looking for cooperative board games.

One of my favorites is Zombicide: https://www.zombicide.com/en/

Although I'm not sure it's suited for kids, when I start playing I always get hooked and then it's sleep time haha.

They're also known as cooperative games. A quick Google search gave me many top lists like this: https://coopboardgames.com/rankings/top-40-cooperative-board...

Do you mean a game where everyone wins together or all lose together?

Forbidden Island is a classic, probably best for slightly older kids

https://boardgamegeek.com/boardgame/65244/forbidden-island

Outfoxed is easier for younger kids: https://boardgamegeek.com/boardgame/172931/outfoxed

Many of the euro style games are positive sum - you add points at the end and see who had the most but each person built up during that time.

Powergrid and Agricola are two examples.

Pandemic is a decent team (all players) vs outbreak (board/chance) game.

Not quite positive sum, but there's a German board game called Max.

Players cooperate to get a bird, a chipmunk and a mouse safely to a tree while a cat named Max is chasing them. Players roll dice that decide how much the cat or other animals move, and they decide what order to move each, or whether to distract the cat with milk or catnip.

How about Acquire? The game ends with all players liquidating their built up equity. You cannot lose, only benefit in the tiled “marketplace”.

The original Monopoly, not sure how easy it is to get your hands on a modern version but it has two rulesets and you switch from classic Monopoly rules to Prosperity rules when a majority of players agree. The Prosperity rules are non-zero-sum.

https://en.m.wikipedia.org/wiki/The_Landlord's_Game

There's an indie board game company called TESA who makes cooperative educational board games, like Coopoly instead of Monopoly or Strike!.

my youngin is too young but I really want to buy stardew board game: https://www.youtube.com/watch?v=H9zhzoQPqLM

All players play together toward improving the farm.

I'm not sure I understand the question -- in a sense pretty much all games that have a single winner are "zero sum" in that only one person can be the winner. But maybe I'm misunderstanding -- could you provide some context?

A german card game called Bohnanza, though it may turn its players into communists lol.

https://en.wikipedia.org/wiki/Bohnanza