Dynamics of Gambling: Origins of Randomness in Mechanical Systems - Strzalko, Jaroslaw; Grabski, Juliusz; Perlikowski, Przemyslaw; Stefanski, Andrzej; Kapitaniak, Tomasz; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2009)
This monograph presents a concise discussion of the dynamics of mechanical randomizers (coin tossing, die throw and roulette). The authors derive the equations of motion, also describing collisions and body contacts. It is shown and emphasized that, from the dynamical point of view, outcomes are predictable, i.e. if an experienced player can reproduce initial conditions with a small finite uncertainty, there is a good chance that the desired final state will be obtained. Finally, readers learn why mechanical randomizers can approximate random processes and benefit from a discussion of the nature of randomness in mechanical systems. In summary, the book not only provides a general analysis of random effects in mechanical (engineering) systems, but addresses deep questions concerning the nature of randomness, and gives potentially useful tips for gamblers and the gaming industry.
Introduction -- Predictability in deterministic and random dynamical systems -- Mechanical randomizers - history, type of games, how fair they are -- Dynamical models -- Simulation results -- Why are mechanical randomizers predictable? -- Why can mechanical randomizers approximate random processes?- Nature of randomness in mechanical systems.
Keywords: Physics; Dynamics; Ergodic theory; Game theory; Mechanics; Statistics; Vibration; Dynamical systems; Physics; Theoretical, Mathematical and Computational Physics; Vibration, Dynamical Systems, Control; Mechanics; Dynamical Systems and Ergodic Theory; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Game Theory, Economics, Social and Behav. Sciences; Electronic books