Memo to Jaynes: please don't generalize beyond statistics. Cough... mixed strategy equilibria in game theory.

Game theory changes things because in many cases you are trying to reduce the effectiveness of an opponent, rather than increasing your own cleverness. Thus a "genuinely random" algorithm can be superior to a pseudo-random one, if you presume the opponent is clever enough to figure it out - and the math in game theory does. Certainly noise can act as an antidote to intelligence.

A good litmus test for whether your math is doing this, is to ask whether a fixed string of ones and zeroes is considered defective compared to a "random" generator that happens to produce exactly the same string.

Nancy, the quote is supposed to be from the book Seeker's Mask.

Cyan, there's numerous improvements on MCMC that are less random and more efficient (see e.g. the Wikipedia entry). I don't know if Jaynes would agree with this statement, but once you've used all of your prior knowledge about the structure of the problem, you should be able to use any generator you like for your remaining decision bits, including a "random" one. I think, though, that the main attractiveness of randomness is not knowing whether the resulting run will be flawed, a state of mind that is confused with a definite knowledge of the absence of flaws.