Idea – Hind-sighted Monte Carlo Simulation

I calculated Pi from instructions using the Monte Carlo Method from the Wikipedia example. Looking at the result using recognition as a mental problem solver. I can see that there is a lot of unnecessary calculations going on. Let me explain.

MonteCarloRecognition2

Monte Carlo Method With Recognition?

From the calculations we can all can figure out what the resulting image would be. Maybe computer recognition could then be used to speed things up. So maybe in hind-sight a more advanced method could make a conclusion much earlier. I wonder if this could be applied to other Monte Carlo based problems.