1. It might be argued that if we knew enough about the linear and angular velocities of the dice their inertia the rebounding characteristics of the dice and the table and so on we would be able to predict the outcome of any throw. However this is so impractical that the expressions “throw of the dice” and “crap shoot” have entered the language as synonyms for totally random events.
2. It should be noted that it is possible to apply Bayesian methods when probability is defined by relative frequency or classical methods to degree-of-belief probability. However to avoid excessive and extraneous complication the presentation follows the line that frequentist definitions of probability tend toward classical statistics while degree-of-belief approaches are more congenial with Bayesian approaches. This is also the historical distinction.
3. This database has been superceded by many more observations since the analyses were first carried out but the point about the meaning of the curves remains valid.
4. This is one instance of Stigler’s Law of Eponymy which states in its simplest form “No scientific discovery is named after its original discoverer” (Stigler 1999).
5. A similar analysis applies to many other exploration problems; the liquefiable zone problem is chosen for convenience.