  We give an estimate of the number of geometrically distinct open tours $\G$
for a knight on a chessboard. We use a randomization of Warnsdorff rule to
implement importance sampling in a backtracking scheme, correcting the observed
bias of the original rule, according to the proposed principle that ``most
solutions follow Warnsdorff rule most of the time''. After some experiments in
order to test this principle, and to calibrate a parameter, interpreted as a
distance of a general solution from a Warnsdorff solution, we conjecture that
$\G=1.22\times 10^{15}$.
