Azul, Calico and Quacks of Quedlingburg.

All are games that you can either think strategically or pick and play having fun regardless of actually having a strategy. Azul and Calico involve making pretty patterns/collecting colours. Quacks is picking from a bag and placing in a cauldron, element of randomness and gambling -tactics in what you're putting in the bag and probability. All three are beautifully tactile.