Chance: The Life of Games & the Game of Life
Our lives are immersed in a sea of chance. Everyone’s existence is a meeting point of a multitude of accidents. The origin of the word ‘chance’ is usually traced back to the vulgar Latin word ‘cadentia’, meaning a befalling by fortuitous circumstances, with no knowable or determinable causes. The Roman philosopher Cicero clearly expressed the idea of ‘chance’ in his work De Divinatione: For we do not apply the words ‘chance’, ‘luck’, ‘accident’ or ‘casualty’ except toanevent which hassooccurredorhappened that it either might not have occurred at all, or might have occurred in any other way. 2.VI.15. For if a thing that is going to happen, may happen in one way or another, indi?erently, chance is predominant; but things that happen by chance cannot be certain. 2.IX.24. Ina certain sensechance isthespiceoflife. Iftherewerenophenomena with unforeseeable outcomes, phenomena with an element of chance, all temporal cause–e?ect sequences would be completely deterministic.
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Abraham de Moivre approximately arithmetic mean assume average gain Bénard cells binary binomial binomial distribution bits Brownian motion chance phenomena chaotic Chap classifier coin-tossing computed confidence interval consider convergence correlation corresponding curve degree of certainty denote dice digit distribution elementary events entropy error estimate euros evolution example experiment face less fact formula frequency frequentist given graph heads heart rate histogram infinite initial instance interest rate large numbers law of large letters log2 logarithm mathematical expectation mathematician measure normal distribution normal numbers number of possible observations obtain orbits outcomes P(even face P(white ball photons player position prize probability density probability of winning problem produced quadratic iterator quantum random number random sequence random variables randomly reader result rounds Saint Petersburg paradox segment shown in Fig shows situation standard deviation Suppose symbols tails throws tossing training set turns two-envelope paradox
Page 3 - According to this principle, a division into "equally possible" cases is conceivable in any kind of observations, and the probability of an event is the ratio between the number of cases favorable to the event and the total number of possible cases. The weakness in this concept is apparent.