when ds1 was 3 we taught him snap with normal playing cards (on holiday when he had his 3rd birthday).
dominoes - we just got a normal cheap tesco set, not a kids one, he loved that and caught onto it quickly.
great game from elc, square wooden board with hedgehogs on it, and little wooden pegs, shake the dice and count the number of pegs into the holes on your hedgehog - 1st one to fill their hedgehog. It had a normal dice and a dice with just 1,2,3 on it, so you could start with the smaller one if they don't know their no's very well. You can then also progress to adding the two dice together.
orchard farm jigsaw train game - 6 carriages and a dice with colour spots and you had to get one of each colour to put the different animals into the carriages.
BUT ds1 has always had a very good concentration span and loves sitting playing these sort of games - NONE of his friends did and would get bored well before the game was anywhere near finished, so I am guessing that it is fairly unusual and tbh if your ds isn't interested I would go with what he IS interested in.
Cafe - I made a A4 menu with the names and pictures (clip art) of food and drink and prices (1-5p) and laminated it, and then printed a load of the menu's off with 4 to a page, cut the pages into 4 and stapled them together along the top and that gave him a little pad that he could take orders on (he just circled the items we wanted). He would then add them up on his till. He was a bit older when we did this, just 4yo I think - but the basic idea is still valid. I still have the template on Word if anyone wants it.