Here is for once a non f2p game. I'm actually not sue if the onkine multiplayer works but it is listed on the store page so I guess yes?
http://store.steampowered.com/app/270790/Etherlords 2. In my opinion one of the best card games for pc to exist.
Etherlords 2 is the sequel of Etherlords. Etherlords was a game similiar to the "Heroes of Migth and Magic" franchise, you had your city at the start and your hero. You move your hero through the world map and collect resources and conquer structures. Eventually you will come across monters and enemy heroes. Like HoM&M you initiated battle but instead of a tactical boardgame battle you played a card battle. You could get cards from special shops and spend your collected resources there.
The goal as to destroy/conquer the enemy city.
Apparently players liked the card game the most about Etherlords, so the developers designed an entire game centered around the card fights: Etherlords 2.
Etherlords removed the ciry building aspect and the need to conquer structures, you still needed resources but they reduced the amount of ten to three. It was a rpg game with card fights whenever you reached a monster. Instead of multiple champions that you could hire, you played one character the whole game. Etherlords 2 featured 5 campaigns, two to select for the start and two additonal once you've beaten any from the starting camapigns. If you've beaten any of the later campaigns, you've unlocked the final campaign where you could play as the antagonist of the series.
The game features 5 races/factions, I honestly don't remember any of the names anymore, so I just give an overview what card types they used.
There was a forest faction that played insects, plants and tree folks, a mechanical faction that played grotesque cyborg creatures, an angel faction that played mostly flying creatures and powerful dragons and a babarian faction that played aggressive creatures like goblins and orcs.
The last faction, the antagonist of the series, were the pale ones, a colorless faction that played creatures with two modes, a physical and a "spirit" mode. I think you could mix the pale creatures with any other faction because they lacked a color. The color is an important theme of the series since it is linked to the mana in this world (called Ether in the game).
The card game can be described as Magic the Gathering. It's not similiar to it, it is the exact same thing with the exception of lands. Etherlords does not feature lands, you get Mana/Ether at the start of your turn and that increases on each turn. Etherlords does not use actual Magic cards but the concept is pretty much the same, they just invented their own cards for this game. That was probably the main reason why I liked the game so much. Another change to the concept was Ether burn or something like that. After a lot of turns passed, the players start to get damage at the start of their round. This damage increases each round and will kill the player eventually. This was introduced to fix stalemates. If both players cannot kill each other because their defenses are two strong, ether burn will eventually kill one of them. So if you played better then your opponent until this point (have more hp) you will win. It's a better solution instead of waiting until your deck is empty.