The figure shows the 50 runs in different colors. Admittedly, the convergence is not great. We only managed one and a half excursions from one end to the other. Furthermore, it's clear that there is nothing wrong that running about 10 times as long won't cure. Of course, this is irrelevant because of the following Theorem.
All real applications are like the toy problems in which many short runs shines.
No real application is like the toy problems in which many short runs sucks. Left as an exercise for the many short runs enthusiasts. I do lots of runs. Generally, I've done dozens before the code is even debugged, even more in the testing after the last bug is found. Like everyone else, I generally am interested in many different related probability models.