Before revision:  Using results on the rate of convergence of supermartingales  we show that whenever the two experts' advice are sufficiently distinct  the proposed test will detect the informed expert in any desired degree of precision in some fixed finite time.
After revision:  Furthermore, using results on the rate of convergence of supermartingales we show that whenever the two experts' advice are sufficiently distinct the proposed test will detect the informed expert in any desired degree of precision in some fixed finite time.