ABSTRACT
The initial assignment of the probabilities of the events in the sample space is fundamental. As Bertrand's paradox show, this is a serious matter since it affects the results obtained, and hence any future action taken. In physics experience has shown that the "natural variables" are usually the ones which enter into several mathematical formulas. In shuffling cards the uniformity is much less secure and more easily controlled by practiced hands. Indeed, the common habit of the shuffler letting someone else "cut the deck" before dealing is a tacit admission of the possibility of controlling the dealt cards. In the "chaos theory" it is constant folding and bifurcation that produces the unpredictable end result. A simple example of randomness in the ideal physical world of classical mechanics is the thought experiment of dropping an ideal ball down a chute as consistently as possible.
