Hands-On Reinforcement Learning for Games

Solving for

The standard introduction to Monte Carlo methods is to show how it can be used to solve for . Recall from geometry, represents half the circumference of a circle and 2π represents a full circle. To find this relationship and value, let's consider a unit circle with a radius of 1 unit. That unit could be feet, meters, parsecs, or whatever—it's not important. Then, if we place that circle within a square box with dimensions of 1 unit, we can see the following:

A unit circle inside a unit square

Given the preceding, we know that we ...