Part of what I do is study typical behavior of large combinatorial structures by looking at pseudorandom instances. But many commercially available pseudorandom number generators have known defects, which makes me wonder whether I should just use the digits (or bits) of $\pi$.

A colleague of mine says he "read somewhere" that the digits of $\pi$ don't make a good random number generator. Perhaps he's thinking of the article "A study on the randomness of the digits of $\pi$" by Shu-Ju Tu and Ephraim Fischbach. Does anyone know this article? Some of the press it got (see e.g. http://news.uns.purdue.edu/html4ever/2005/050426.Fischbach.pi.html ) made it sound like $\pi$ wasn't such a good source of randomness, but the abstract for the article itself (see http://adsabs.harvard.edu/abs/2005IJMPC..16..281T ) suggests the opposite.

Does anyone know of problems with using $\pi$ in this way? Of course if you use the digits of $\pi$ you should be careful not to re-use digits you've already used elsewhere in your experiment.

My feeling is, you should use the digits of $\pi$ for Monte Carlo simulations. If you use a commercial RNG and it leads you to publish false conclusions, you've wasted time and misled colleagues. If you use $\pi$ and it leads you to publish false conclusions, you've still wasted time and misled colleagues, but you've also found a pattern in the digits of $\pi$!