Sequential anytime-valid inference (SAVI) provides measures of statistical evidence and uncertainty --- e-values and e-processes for testing and confidence sequences for estimation --- that remain valid at all stopping times. These allow for continuous monitoring and analysis of accumulating data and optional stopping for any reason. These methods crucially rely on nonnegative martingales, which are wealth processes of a player in a betting game, thus yielding the area of "game-theoretic statistics". This tutorial will present the game-theoretic philosophy, intuition, language and mathematics behind SAVI, summarized in a recent a new book https://arxiv.org/pdf/2410.23614, to be published before ICML as the first edition of the new book series, Foundations and Trends in Statistics.