  The games of prediction with expert advice are considered in this paper. We
present some modification of Kalai and Vempala algorithm of following the
perturbed leader for the case of unrestrictedly large one-step gains. We show
that in general case the cumulative gain of any probabilistic prediction
algorithm can be much worse than the gain of some expert of the pool.
Nevertheless, we give the lower bound for this cumulative gain in general case
and construct a universal algorithm which has the optimal performance; we also
prove that in case when one-step gains of experts of the pool have ``limited
deviations'' the performance of our algorithm is close to the performance of
the best expert.
