I like wargames. Especially wargames of the card-driven game (“CDG”) sub genre. A couple of favourites among those are:
Empire of the Sun (2 players)
Paths of Glory (2 players)
Virgin Queen (6 players)
The famous cold war game “Twilight Struggle” is also in this genre, but significantly lighter than any of the above ones. I wouldn’t call Twilight Struggle a casual game either, but probably a good place to start if one wants to check out the CDGs. The others I mention takes quite a lot of effort to learn.
While not actually CDGs (or wargames), the COIN series of games are related to the above ones and excellent. Of those I have played, Cuba Libre (4 players) is relatively easy to learn and is a lot of fun.
Another wargame subgenre I enjoy a lot is wargames on a “tactical scale”. Think soldiers running from hedge to hedge, throwing grenades into buildings kind of gameplay. Two favourites in this genre are:
Advanced Squad Leader (INSANELY complex, but can be learned gradually via Starter Kits 1-4)
Combat Commander (much, much easier to learn and faster to play, but still a solid wargame experience)
I am currently in the middle of a Arkham Horror the Card Game campaign with some friends (but corona appears to have put that on hold for the time being). Love that game, despite the steep cost involved. My wife and I sometimes play Sherlock Holmes: Consulting Detective, a very challenging set of SH mysteries of varying quality. But at its best it is an excellent co-op experience suitable for an evening accompanied by wine and good food.