  In quantum game theory, one of the most intriguing and important questions
is, "Is it possible to get quantum advantages without any modification of the
classical game?" The answer to this question so far has largely been negative.
So far, it has usually been thought that a change of the classical game setting
appears to be unavoidable for getting the quantum advantages. However, we give
an affirmative answer here, focusing on the decision-making process (we call
'reasoning') to generate the best strategy, which may occur internally, e.g.,
in the player's brain. To show this, we consider a classical guessing game. We
then define a one-player reasoning problem in the context of the
decision-making theory, where the machinery processes are designed to simulate
classical and quantum reasoning. In such settings, we present a scenario where
a rational player is able to make better use of his/her weak preferences due to
quantum reasoning, without any altering or resetting of the classically defined
game. We also argue in further analysis that the quantum reasoning may make the
player fail, and even make the situation worse, due to any inappropriate
preferences.
