To extend the video game analogy, one activity that some video gamers have made a sport of is "speed running," or trying to completely a single-player game in as little time as possible. Sites like http://speeddemosarchive.com/ host videos, and people compete to get the lowest time.

There are two ways that one typically goes about improving on the existing record. The first is to look at the video posted by the current record holder, dissect the run, and find all of the small mistakes that the current record-holder made. Shave off a few seconds here, a few seconds there, and by the end of your run you've beaten a game in 4 hours and 57 minutes instead of 5 hours. That's playing harder.

The other way to break existing records is to start completely from scratch, map out the game and figure out if there's a different route to take that the previous runner didn't. Maybe it's doing the levels in a different order so you spend less time walking across the world map. Maybe you spend an extra 10 minutes picking up a stronger sword that allows you to save 20 minutes over the course of the game because you're killing enemies faster. These are the kinds of improvements that lead to people turning a 5 hour game into a 4 hour game. That's playing better, not harder.

Don't try to become faster or quantitatively better at something you're having enormous difficulty with; seek to become qualitatively better by trying different approaches to solving the same problem.