On Fri, Jul 17, 2009 at 01:37:43PM -0500, 
travis+ml-cryptogra...@subspacefield.org wrote:
> I'm curious if there's a way to express this calculation as a
> mathematical formula, rather than an algorithm, but right now I'm just
> blanking on how I could do it.

This has been dubbed the "guesswork" of a distribution by some authors,
I think originating with:

        John O. Pliam. The disparity between work and entropy in
        cryptology. http://philby.ucsd.edu/cryptolib/1998/98-24.html,
        February 1999

It turns out that its asymoptic behaviour is bit like that of Renyi
entropy, see:

        E. Arikan. An inequality on guessing and its application
        to sequential decoding. IEEE Transactions on Information
        Theory, 42:99105, Janurary 1996.

I did an explanitory writeup of this with some experiments at:



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