The first game-theoretic zero-one law was announced by Akimichi Takemura in his talk at the 2006 Workshop on Game-theoretic Probability and Related Topics. Takemura's result, with some developments and an open problem, is described in [Takemura et al., 2008].
- Akimichi Takemura, Vladimir Vovk, and Glenn Shafer. The game-theoretic martingales behind the zero-one laws. arXiv technical report, March 2008.