![]() ![]() Overall, if we think that mathematics can provide any sort of fix for problem gamblers, then we must be careful. We might say in this case that we have a poor model, due to interpretation and language, and it would be empirically invalidated when a one comes up twice in a row in a certain period of time. Moreover, it is the relative frequency (the ratio between the number of a variable’s occurrences and the number of experiments) that approaches that limit and not the absolute frequency (the total number of a variable’s occurrences), which seems to be the reference of the gambler’s words. Take the statement, “The relative frequency of the die showing a one will converge toward one in six with the number of throws.” One interpretation is the gambler’s expression that, “I expect a one to come up about once every six throws.” Here, about means on average or approximately-but this wording does not reflect the complete mathematical meaning of converge, which assumes an infinite series of experiments for the limit to be approached. When describing games or making predictions about bets, we use mathematical models, and any such model depends on language for interpretation and empirical validation. The same goes for the mathematics of gambling. ![]()
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