Ask HN: Insight Crucial to Play a Game?

I've recently started playing (tabletop) Scrabble. In the beginning, the game wasn't much fun for me. That changed with a crucial insight: you're not supposed to play for words, but for points.

Phrased like that, it may come across as trite. The point is that you shouldn't look at your own letterboard except to check for 7-letter words. Other than that, look at spots on the board that provide opportunity. This implies that there is little point in trying to construct nice long words on your letterboard.

I then recalled having read something about how to play the original Doom, which made me realise that I have never played that game the way it was intended. I always treated it as I would a survival horror: move slowly, eradicate everything. Apparently that's not what the game was designed for - which explains my lack of enjoyment.

Now I'm curious: are there any games where suddenly, something clicked and you are playing a completely different game from what you were doing before? If so, what was it that clicked?