7 February 2025, Preprint v1 · CC-BY 4.0 PREPRINT Research Article The Guessing Game and Its Implications for Sport Psychology Research — A Tale of Lotteries, Penalties, Mixed Strategies, and Nash Equilibria Kjetil Haugen 1 1. Molde University College, Norway This paper introduces the Guessing game, a game characterized by a single unique Nash equilibrium (NE) in mixed strategies. Furthermore, this game is shown to be important in most sports activities. Finally, central parts of sport psychology research are shown to neglect the existence of the Guessing game. The paper hence concludes by questioning the value of such research. 1. Introduction The two-player Guessing game may be dened as follows: Two players choose simultaneously strategies A or B. If both players choose the same strategy or , Player I wins. However, if they choose dierent strategies or , Player II wins. Clearly, the winning strategy in this game is for both players to try to guess what the other player does. For Player I, a correct guess implies choosing the same strategy as Player II, while Player II should choose the alternative strategy to his guess. Qeios qeios.com doi.org/10.32388/CJEKHU 1