Sam2-who is matir scrabble? The Chachamim made a gezeira that you can’t do things that normally involve writing because it may lead to writing. In regular scrabble, you record the score. It’s assur miderabanon. In Scrabble, the pieces interlock, it’s really writing and it’s assur mideoraisa.
I would recommend to play on shabbos
risk- but that can get boring after awhile.
chess-some poskim say if you will have agmas nefesh if you lose, you shouldn’t play.
checkers
Quick Shtick (I don’t know if this game is around anymore.)
uno
battleship
Outburst (I’m not sure if that can be played on shabbos, but I think it’s fine)
Malarky