  We fix the temperature $T$ and consider mean energy and
Boltzmann-Gibbs-Shannon entropy as two players of a game. As a result, basic
formulas for the ordinary quantum mean energy and the Boltzmann-Gibbs-Shannon
entropy are derived. We compare also the quantum and classical approaches
without a demand for Plank's constant being small. Important inequalities for
statistical sum, quantum energy, quantum entropy, and their classical analogs
follow.
