1. Bridge
Bridge is very complex and in tournaments you can easily rely on skill giving you a 90 percent win rate. The only downside In my opinion is that it is a partnership game, but that can be a plus if your married. It takes a year before you can beat average players. You can pay professionals to be your partner in tournaments so you don't really have to worry about being stuck with novice players.
2. Magic the Gathering
Magic is a deep game. I checked out a list of the most consistent players and they have players who won 7 Grand Prix tournaments which can have thousands of participants.
3. Poker ( Texas Holdem)
Poker is very high skill but very high luck. There are some situations that are extremely complex, however it takes a high sample size of hands to get to those situations, so it can be hard to get some action. Poker has had successful tournament players but now the players are very skilled so the edges are small. Multi tabling online may be the best way to see if your a good player or not.
4. Yugioh
I believe Yugioh to also be a deep game. The game has many consistent players and even players with multiple YCS wins. I believe if the game had high buy ins like poker and cash prizes then the game would be profitable in the right format, (at least Until most of the player base gets really good). i think the best players can reliably make the top 10 percent of a tournament.
5. Gin Rummy
Gin rummy is probably the most skillful standard card deck game for 2 players. In this Game skill will help you have a 67 percent win rate but with Elite memory you can have about an 80 percent win rate.
6. Euchre
Similar to bridge but you can only win 2/3 of the time with skill.
7. Cribbage
Great game for 2 players with a standard deck
8. Canasta
9. Pokemon
10. Hearthstone
Can get more harder with more cards and mechanics
Overall Play what best for you and don't be too quick to jump to another game because in all the games listed i have noticed that players always have stuff to complain about. some are never satisfied so stick by your game regardless of the flaws