We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10]. By studying the asymptotic behavior of its capital process, we prove a generalization of the strong law of large...

We give a general method for constructing a deterministic strategy of Reality from a randomized strategy in game-theoretic probability. The construction can be seen as derandomization in game-theoretic probability.

We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.

We derive some results on contrarian and one-sided strategies of Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [G. Shafer and V. Vovk. Probability and Finance -- It's Only a Game!, Wiley, New York, 2001]. In particular, as regards the rate...