  An experimentally observed violation of Bell's inequality is supposed to show
the failure of local realism to deal with quantum reality. However, finite
statistics and the time sequential nature of real experiments still allow a
loophole for local realism, known as the memory loophole. We show that the
randomized design of the Aspect experiment closes this loophole. Our main tool
is van de Geer's (2000) supermartingale version of the classical Bernstein
(1924) inequality guaranteeing, at the root n scale, a
not-heavier-than-Gaussian tail of the distribution of a sum of bounded
supermartingale differences. The results are used to specify a protocol for a
public bet between the author and L. Accardi, who in recent papers (Accardi and
Regoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have
produced a suite of computer programmes, to be run on a network of computers,
which will simulate a violation of Bell's inequalites. At a sample size of
thirty thousand, both error probabilities are guaranteed smaller than one in a
million, provided we adhere to the sequential randomized design. The results
also show that Hess and Philipp's (2001a,b) recent claims are mistaken that
Bell's theorem fails because of time phenomena supposedly neglected by Bell.
