We consider a setting where in a future known time, a certain continuous variable will be realized.There is a public prediction that converges to its value, and an expert has access to a more accurate prediction.Our goal is to study when should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log likelihood of the realized value).Our contributions are: (1) we show that the optimal expert policy is threshold based. (2) we analyze the expert's asymptotic optimal reward and show a tight connection to the law of the iterated logarithm, (3) we give an efficient dynamic programming algorithm to compute the optimal policy.