  In this article, I will present a paradox whose purpose is to draw your
attention to an important topic in finance, concerning the non-independence of
the financial returns (non-ergodic hypothesis). In this paradox, we have two
people sitting at a table separated by a black sheet so that they cannot see
each other and are playing the following game: the person we call A flip a coin
and the person we'll call B tries to guess the outcome of the coin flip. At the
end of the game, both people are asked to estimate the compound probability of
the result obtained. The two people give two different answers, one estimates
the events as independent and the other one considers the events as dependent
therefore they calculate the conditional probability differently. This paradox
show how the erroneous estimation of conditional probability implies a strong
distortion of the forecasting skill that can lead us to bear excessive risks.
