In a repeated two-person zero-sum game with incomplete information on one side, the values upsilon(n) of the n-stage games converge to the value upsilon(infinity) of the infinite game with worst case error similar to (ln n/n)(1/3).
Mertens, J.-F. (1998). The speed of convergence in repeated games with incomplete information on one side. International Journal of Game Theory. https://doi.org/10.1007/s001820050077