Defensive forecasting first identifies a betting strategy that succeeds if probabilistic forecasts are inaccurate and then makes forecasts that will defeat this strategy. Both the strategy and the forecasts are based on the similarity of the current situation to previous situations. The theory of defensive forecasting uses the game-theoretic framework for probability, in which game theory replaces measure theory. In this framework, a classical theorem such as the law of large numbers is proven by a betting strategy that multiplies the capital it risks by a large factor if the theorem’s prediction fails. Theorems proven in this way apply not only to the classical case where only point predictions are made. Defensive forecasting is possible because the strategies are specified explicitly.