  Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude as some vector in Hilbert space are given.
The games are macroscopic, no microscopic quantum agent is supposed. The reason
for the use of the quantum formalism is in breaking of the distributivity
property for the lattice of yes-no questions arising due to the special rules
of games. The rules of the games suppose two parts: the preparation and
measurement. In the first part due to use of the quantum logical
orthocomplemented non-distributive lattice the partners freely choose the wave
functions as descriptions of their strategies. The second part consists of
classical games described by Boolean sublattices of the initial non-Boolean
lattice with same strategies which were chosen in the first part. Examples of
games for spin one half are given. New Nash equilibria are found for some
cases. Heisenberg uncertainty relations without the Planck constant are written
for the "spin one half game".
