Initial situation

At the first stage the answers to the questions are prompt and unanimous: we consider all boxes equally likely, thus assigning 1/6 probability to each of them; we consider Black and White equally likely too, with probabilities 1/2. Not satisfied with these answers, I also encourage `players' to express their confidence on the hypotheses of interest by means of a virtual lottery at zero entry cost.Specifically, I ask, if you are promised a large prize for making the correct prediction, which box or ball color would you choose? More precisely, is there any reason to prefer a particular color or a particular composition? Also, in this case there is a general consensus on the fact that any choice is equally good, in the sense that there is no reason to be blamed if we finally miss the prize.