A deck of cards is the best value object in any house with children in it. It costs almost nothing, it needs a second person, it fits in a coat pocket, and nothing on a screen has ever taught a child to lose gracefully.
Here is what to play, and roughly when.
From four: Snap
The whole game is noticing that two things are the same, which is exactly what a four-year-old is working on anyway. It is loud, it is fast, and it can be finished in four minutes, which suits an attention span of about that length.
From five: Go Fish
The first game with a hidden hand, which is a genuine cognitive step. The child has to hold information the other player cannot see and use it. Also the first game where they can be beaten fairly, which is worth more than the game.
From five: Memory or Pairs
Face down, find the matches. Children are much better at this than adults, which is not a myth, and letting a five-year-old destroy you at it three times running does more for them than any amount of praise.
From six: Uno
The first game with a strategy in it, and the first where a child can be cruel on purpose within the rules. That sounds like a warning and it is not. Learning that you can hurt someone's position without hurting them is a useful distinction to draw early, at a table, with an adult present.
From six: Spot It, or any speed-matching game
Pure pattern recognition under time pressure. Good for a child who thinks they are bad at games, because it does not reward patience or memory, only looking.
From seven: Rummy, or the beginning of a real card game
This is the age where an ordinary adult game becomes possible with simplified rules. And this is the moment a deck of cards changes from a children's toy to a thing the family does, which is the transition worth aiming for.
From seven: any game where you can be caught
Cheat, bluffing games, anything where lying is part of the rules. Children find this delicious and it is a much better place to explore deception than the real world.
And ours
The Sing Me a Fable deck is a real fifty-four card deck, so it plays every game on this list. What is different is the faces: each carries a fable animal, its flaw, and the virtue that answers it, plus a code that opens that fable's song. Eleven games come with it, and I wrote up ten more things to do with it that are not in the rulebook.
Its honest limitation: it comes with the storybook rather than on its own, so it is not the cheapest deck you can buy. If all you want is a deck, buy any deck. That advice costs me money and it is still the right advice.
The actual recommendation
Whatever you own, get it out this evening. The specific game matters far less than the fact of two people sitting at a table with a shared rule between them, which is a rarer thing in a house than it used to be.
If you want the fable animals without spending anything, the twenty-six colouring posters are free.