Right, the reason it seems noisy is shown on the slide. Are there established methods for running enough samples of rays until the scene meets a non-noise threshold? This could be done based on expectations (where a fixed number of rays is set) or by analyzing the currently rendered scene.
We actually implement adaptive sampling inside Project 3! Basically, we use an inequality revolving around variance, sample size, and mean which, when satisfied, means we have achieved a good estimate of the shading at that pixel. The 1.96 coefficient corresponds to a z-score with 95% confidence, meaning we are 95% confident in our estimate.