A formal write-up of the simple proof (1995) of the existence of calibrated forecasts by the minimax theorem, which moreover shows that $N^3$ periods suffice to guarantee a calibration error of at most $1/N$.

翻译：关于极小极大定理存在性校准预测的简单证明（1995年）的正式阐述，该证明进一步表明只需$N^3$个周期即可确保校准误差不超过$1/N$。