Poker is a great game. There are so many aspects to it where you can go down a rabbit hole of strategy to improve your game - there's math, making decisions with incomplete information, deduction, reading people, all kinds of non-verbal communication, etc. Although there's chance involved, it is undoubtedly a skill game. The gambling is one of the unfortunate aspects, but it just doesn't play the same without some money involved. You can get around that a little bit with house games where everyone throws in $20 or small buy-in sit and go games at a casino.

Another game that's worth checking out if some of this sounds interesting but you really don't like gambling is "Blood on the Clocktower". It's a social logic and deduction party game. There's chance, bluffing, incomplete information, trying to figure out what other players have, etc. It's completely different, but it can scratch some of the same itches and it's a blast to play. My friends and I play it with our kids.