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Blaise Pascal famously calculated the expected value of a risky lottery in the 1654 correspondence with Pierre de Fermat in the context of the so-called points problem. Pascal solved this problem by backward induction, whereas Fermat—by counting combinations. This paper analyzes a more complex version of the points problem from an anonymous XVth century Italian manuscript stored in the Vatican Apostolic Library. In this manuscript, the problem of points is solved by backward induction in a similar way to Pascal’s train of thought. In this light, Pascal’s pioneering contribution may be not as novel as it is traditionally believed.

Backward induction and expected value calculations in an anonymous XVth century Italian manuscript