  Recent randomness expansion protocols have been proposed which are able to
generate an unbounded amount of randomness from a finite amount of truly random
initial seed. One such protocol, given by Miller and Shi, uses a pair of
non-signaling untrusted quantum mechanical devices. These play XOR games with
inputs given by the user in order to generate an output. Here we present an
analysis of the required seed size, giving explicit upper bounds for the number
of initial random bits needed to jump-start the protocol. The bits output from
such a protocol are $\varepsilon$-close to uniform even against quantum
adversaries. Our analysis yields that for a statistical distance of
$\varepsilon=10^{-1}$ and $\varepsilon=10^{-6}$ from uniformity, the number of
required bits is smaller than 225,000 and 715,000, respectively; in general it
grows as $O(\log\frac{1}{\varepsilon})$.
