Let me furnish you with a deep understanding of this monte carlo sampling technique; for the uninitiated, monte carlo sampling is a technique which takes a very complex data set, and samples it at random locations in order to build a probabilistic model for the truth of the underlying system, which may itself be intractable to process directly.

An example, here is a monte carlo rendering of a scene at an increasing number of samples:



The idea being that this sampling process is orders of magnitude faster than processing the full data set (in this image, it would be fully raytracing the entire scene, with multiple light bounces / radiosity etc).

In Iota, this technique is simply used to find the tips with the most cumulative weight (as I have been saying all along) but without having to process the entire set of transactions all the way back to genesis from every tip, which would be too slow. This is their game theoretically optimal choice as participants who want timely confirmation of their transactions.

TLDR; Iota uses monte carlo sampling to find the tips with the most cumulative weight in order to decide where to extend the DAG.