Advantage of the Monte Carlo method over a regular periodic sampling I am unclear on when to use the Monte Carlo random sampling method for algorithm design. The classic example that I keep seeing is using random points within some bounding rectangle to determine the area of some irregular figure. Wouldn't a regular periodic sampling provide more repeatable results for this application then using the Monte Carlo (random sampling) method?
If you use a fixed seed then Monte Carlo is also repeatable. Monte Carlo sampling has the advantage that the expected number of points inside your figure is proportional to the area, which is not necessarily the case for a grid &mdash; you can come up with a contrived figure in which the grid is off by a lot, whereas random points are impossible to "fool" this way.