Many of you may be familiar with the three doors problem, aka the Monty Hall problem. (info on wikipedia).

Basically it states that you have three doors presented to you, one which holds a car behind it.  You pick one giving you 1/3 of a chance of having the right answer, but then you're presented what's behind one of the doors you didn't pick, and it's not the car. If you switch your pick, your chances of being right increases to 2/3, instead of your original chance of 1/3.

Here's the results of a simulation
http://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Monty_problem_monte_carlo.svg/583px-Monty_problem_monte_carlo.svg.png

So what if we give miners the monty hall problem? We could increase the chances of finding the right hash by a nice margin.

So in a pool you could effectively have it so 90% of miners ditch 1/3 of the hashes that need to be tested, and 10% of the miners work on the ditched ones.