I want to talk about what I call "linkages". This is where parts and sub-parts of a game connect to each other in a big web. These are the key to interesting strategy in games. Let me explain.
If a mechanic is a self-contained mini-game, it can be easily solved by the players, or is random and no strategy is possible.
An example:
My orc attacks your orc. I roll a die, and if it's higher than your defence, your orc dies.
If you don't interlink, your systems are just self-contained, and either easily solvable, or just totally random. Or, you end up with scissors-paper-rock, prisoner's dilemma, or other known and basic problems. This means the rest of the game has to be that much more strategically interesting, because your boring core isn't pulling any weight. If you can't interlink, then your game probably doesn't have enough systems.
This is the key to creating strategy in games.
You also need to interlink out to something complex, or your puzzle will still be solvable.
That's boring.
It's boring and un-strategic because there's no interlink, and no strategy. Now, let's interlink.
My orc attacks your orc, and kills it. To do this, I must also discard two cards from my hand.
This interlinks combat into the game's card system. What's the value of those cards? It's an interesting trade-off.
My orc attacks your orc, and kills it. My attacking orc returns back to his home village, in a different part of the board.
This one interlinks combat into the game's spatial system. Maybe you need the orc in this part of the board, and there are other things for him to do. Again, this creates an interesting choice.
Many games revolve around a giant interlink between two systems, and it works. A typical combination is to have one part of the game be spatial, the other be a competitive resource-gathering area that isn't spatial.
In Agricola, the systems are the competitive central task board, and each player's own farm, which is spatial.
Eight-Minute Empire is a stark example of two interlinking systems. Players simply take a card from the card row on their turn, and follow its instructions. These cards move their armies around a board, or create new armies. Gaining control of the board gets the player points. However, these cards also have a colour, and picking many cards of the same colour awards lots of points at the end of the game. This simple interlink creates an unsolvable problem, and therefore an interesting game. Do I take a card, to help me take over the map, or to try to collect a certain colour?
Biblios is a good game, but it lacks proper interlinking at the start of the game. On your turn, you draw five cards, but one at a time. You choose one to keep, three to give the other players, and one to put into a future auction. The problem here is that the strategy is too simple, and solvable — as you go through the five cards, you just take a good one (or an average one if you're near the end of the five cards.) There's an interlink out to the game's coloured-card collecting system, but you don't have any other cards yet, so that interlink doesn't do anything.
Yahtzee has the same problem, early on. The moves are fairly obvious. However, the rerolling system in Yahtzee has a lot of internal complexity, so it can survive reasonably well without a proper interlink.
A properly-functioning core is essentially a mechanic or groups of mechanics that are too complex for the players to completely figure out. The play of the game is the players doing their best to figure this system out, as much as they can.
A core is usually composed of two or more systems, which are interlinked. Some games hide information (such as a hand of cards), creating a statistical calculation that's too complex to solve. One of the systems could be a complex human system, such as psychology, negotiation, or physical dexterity. Interlinking to these will create huge depth.
Scrabble interlinks a spatial system and the dictionary, both of which are highly complex. The result is a game I've now been playing for decades