The more you play a game, the more you understand it. In fact, each time you play it, your understanding of the mechanics becomes closer and closer to perfect. With light games, this may take only 1 play. With heavier games this may take many.
The blue line shows an understanding of the game increasing over time.
But does it really feel that way to you with heavier games? I know with games line Princes of Florence or Amun-Re, it feels more like a "curve" with many unusual bumps in it.
The red line shows perceived depth over time. This is how deep the game feels to you over time after playing many times. When you are learning a game, the depth is more about putting the mechanics together. The more you play and observe the results of your choices, the more you appreciate the intricacies. You perceive a new plateau of depth. This may happen more than once.
The shaded area shows the difference between your understanding of the game and the depth you perceive. When you first learn a heavy game, it looks complicated. After a play or three, you start to settle in to the game. At some point, something clicks and you see more depth than you originally thought.
This graph shows the original 2 curves, and the difference between them represented as a line. This matches my experience in many heavier games, and is something I appreciate quite a bit--the notion that working to understand the game will yield a richer underlying game.
Do your experiences match mine at all? If not, please elaborate. In what games does this kind of thing happen for you?