I’ve been playing Angry Birds lately. I’m good at it, in the sense that I’m able to beat a game that was designed to be beaten by children. I get past every level, with one, two, or three stars. After I finish a group of levels this way, I go back and try and get 3 stars on all the levels where I didn’t the first time.
One thing I do to help with this is to pay attention to my points-per-bird average (good old PPB). If I need 100,000 points to pass a level, and I have 3 birds, I need 34,000 PPB. This matters, because if I only get 6,000 on the first bird, it is probably not worth my time to keep going on that level — I should hit restart. This is a good strategy, and gets me 3 stars often.
There’s a hidden assumption here: that throws are independent. This is not always true. Sometimes I need to take a lower PPB on the first bird to set me up for the next throw. If I get 6,000 on the first throw, but that exposes a box of TNT and I can get 90,000 on the second, then my standard of “6,000 PPB is too low” is flawed for that level (even though it’s a good idea for a starting point). If I don’t get 3 stars on a level with my PPB strategy within 15 minutes, I start looking for other openings.
Question hidden assumptions. It’s what Richard Feynman did, with his belief that all problems should be solved from first principles. He’d take even the most basic and widely accepted answers, strip them down, and re-derive the answers himself. I think it’s one of the things that led to him being so effective (a lot of people consider him a modern day Einstein, except his discoveries aren’t as consumer-friendly as e=mc^2, so he doesn’t have the same pop culture awareness). In doing this, he’d run into all sorts of assumptions that people were making (without realizing it), sometimes leading them away from a useful piece of information.