### abstract ###
Using the game-theoretic framework for probability, Vovk and Shafer~ CITATION  have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests
This result generalizes work by other authors, who consider only tests of calbration
We complement this result with a lower bound
We show that Vovk and Shafer's result is valid only when the forecasts are computed with unrestrictedly increasing degree of accuracy
When some level of discreteness is fixed, we present a game-theoretic generalization of Oakes' example for randomized forecasting that is a test failing any given method of deferministic forecasting; originally, this example was presented for deterministic calibration
### introduction ###
Using the game-theoretic framework for probability~ CITATION , Vovk and Shafer have shown in~ CITATION  that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests
This result generalizes work by other authors, among them are Foster and Vohra~ CITATION , Kakade and Foster~ CITATION , Lehrer~ CITATION , Sandrony et al ~ CITATION , who consider only tests of calibration
We complement this result with a lower bound
We show that Vovk and Shafer's result is valid only when the forecasts are computed with unrestrictedly increasing degree of accuracy
When some level of discreteness is fixed, we present a game-theoretic version of Oakes' example for randomized forecasting that is a test failing any given method of deterministic forecasting; originally, this example was presented for deterministic calibration
To formulate this example, we use the forecasting game presented by Vovk and Shafer~ CITATION , namely Binary Forecasting Game II
We discuss details of the randomized forecasting algorithms in Section~
The Shafer and Vovk's~ CITATION  game-theoretic framework is considered in Section~
We present in this section the original Vovk and Shafer's~ CITATION  result on universal randomized forecasting and prove our result which gives the limits for such forecasting - a game-theoretic version of the Oakes' example for randomized forecasting
