Abstract

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.

摘要

布莱斯·帕斯卡 (Blaise Pascal) 在 1654 年与皮埃尔·德·费马 (Pierre de Fermat) 的通信中，在所谓的积分问题的背景下计算了有风险彩票的期望值，这一点颇为著名。帕斯卡通过逆向归纳法解决了这个问题，而费马则通过计算组合来解决这个问题。本文分析了梵蒂冈使徒图书馆保存的一份 15 世纪意大利匿名手稿中的积分问题的更复杂版本。在这篇手稿中，点的问题是通过逆向归纳法解决的，类似于帕斯卡的思路。从这个角度来看，帕斯卡的开创性贡献可能并不像传统认为的那么新颖。