Competition was the I think the biggest barrier for my youngest, she hates losing. Old Maid flips the equation a little because there's only 1 loser and many winners. Carcassonne can be played without keeping track of points, just rules for how you lay tiles. We recently got a game called Outfoxed! where you collectively hunt down a thief, it's great for kids because it exercises memory and deductive reasoning to eliminate suspects, and you have to strategize as a team.

We played pengaloo a lot. Its a matching game. We just work together to find the matching eggs. The kids enjoy the thrill of checking the eggs as well as the cute characters.