[pawn]

One thing I'd be interested to learn is, how much of what makes the difference between an above average chess player and a Master or a Grandmaster can be tied to better decision making after looking 3 or 5 moves ahead, and how much is the Master/Grandmaster's ability to look 10+ moves ahead?

[quantdev]

The looking 10 or even just 5 moves ahead thing is overstated and this is not actually how it works most of the time. Most GMs only calculate that far in the endgame. Before that, often looking 2 or 3 moves ahead is sufficient based on strategic elements or opening theory (which can't easily be understood by 'looking moves ahead'; they're things like, "this pawn is passed" or "my light squares will become very weak" which are can be substitutes for looking 30+ moves ahead).

Often positions resemble historic or previous games, so pattern recognition here and the themes (e.g., "this particular structure will make it easier to get my rook on the 7th rank at some point") of the old game are important.

In fact, Capablanca, a former World Champion and endgame expert has a famous quote claiming to only look 1 move ahead.