This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results is that they are pointwise, their advantage over the algorithmic randomness results is that they are non-asymptotic, but the most important advantage over both is that they are very constructive, giving explicit and efficient strategies for players in a game of prediction.