There's a spectrum of strategy, from games that are mostly short-term tactics, to those with vast long-term strategy.
Chess and Scrabble are both excellent classic games, at different points on this spectrum.
In Scrabble, a good player is mostly trying to get a good score this turn, but they're also trying to retain good letters on their rack, and not give the opponent a nice spot for next turn. Scrabble play is more about the current turn than about the future.
In Chess, it's all about the long game. One move has no more value than a future move. The player always plans ahead, to the limit of their capacity.
But why do these games differ so much in this way? The answer is that, in Chess, you have perfect information. You know everything that's going on in the game, and can work everything out. It's only your limited ability that stops you working out the entire game, and making the perfect move. In Scrabble, you can't plan ahead with too much certainty, because the bag is full of random letters, and you could draw any of them. Also, you don't know what letters your opponent has.
This all leads me to a fundamental question about your game: what mental process are the players actually using, as they play the game?
In Chess, the player is largely calculating. In Scrabble, the player is largely intuiting. The Scrabble player can't calculate a huge amount, because they don't really know anything, other than what tiles they have right now. They must use their intuition to decide which move is best.
Most game players don't like high levels of calculation. Calculation is about "not messing up." Players generally find intuiting to be a much more enjoyable experience. Intuiting is also much faster than calculation.
Think about where the strategy horizon is, in your game. How far can you plan ahead? I like to be able to plan ahead, but not with too much certainty.
You remove the ability for forward planning by limiting the amount of information known to the player. Giving each player a secret hand of cards is the standard solution to this problem, but there are many ways to limit information.
Also, force players to re-intuit their strategy, by drip-feeding new information to them. Drawing a card every turn is a good way to do this.
Obviously, don't go too far in the direction of giving new information, or the game will be too chaotic, and it will be impossible to think ahead at all.
Consider the weight of your game, when you decide where the strategy horizon will be. Most games should be intuitive, not calculation-based.