For me, there's nothing better than Poker if we're talking about skills games, but there are other options. There's also blackjack and, I'm quite surprised no one mentioned Spades, it also includes a lot of strategic thinking, no less than Poker, perhaps. And, of course, there's Yahtzee. While it includes dice, which brings an element of luck to the game - a strategy should also be applied and you need to make a lot of decisions, evaluate your risks, which is why to play this game it's better to understand probabilities first.
I love Yahtzee but a computer can show you what all the best decisions are so it's not a game you could securely play for money. The OP is looking for PVP games that aren't solved by computers and can be +EV for players. Not easy criteria to fulfill.
I think Rock Paper Scissors is the purest and best PVP game but it's hard to call it a skill game since you can just let an RNG decide the throws to neutralize any advantage that might exist between the two players.
Any skilled player can outplay these calculators because it's not only about playing with the best odds, sometimes it's about knowing when to take the risk, which is also a skill.
I'm starting to think that what OP asked for is actually impossible because for any games that require skills the best option can be calculated (in one way or another), and the only games that can't be solved like this are those, which depend purely on luck
