You are exactly right you do need a different kind of strategy, I noticed this when I actually started getting better than "neighborhood fair", but then again, why would you be playing someone so much worse than you in the first place. You should as I have learned, only play those better than you, that way you can improve. But if everyone only played someone better than them, no one would play chess.
Observant vs. Oblivous - Predictability
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I've noticed that there seems to be two different ways to play chess: competing against a hard player that can see many moves into the future, and playing someone who's completely oblivious to the situation.
I was playing against my sister this afternoon. She's a fair player, but I mean that on a neighborhood standard. In otherwords, she falls into that second catagory.
I opened up a few diagnols so she could move her bishops deep into my territory. Some players would call that a stupid move, because it would have given her an easy mate in four. In reality, it was a ploy to get her pieces out of the way so I could checkmate her more quickly.
But you know what she did? She completely ignored it. So went on with a feeble attempt to capture a few pawns, but I easily repelled it and mated her a few moves later.
What I'm trying to say is that I can only think two moves ahead when facing inexperienced players. With masters, they always see the situation clearly and their moves are always going to be limited to the few best ones. With the oblivious opponents, it is very hard to predict whether they will do the best move, the worst move, or any possible move in between. They aren't too hard to defeat, but it requires a different kind of strategy.