A XIVth century approach to the points problem

The application of expected value as the first decision-theoretical criterion for evaluating risky lotteries is traditionally attributed to the 1654 correspondence between Pierre de Fermat and Blaise Pascal. However, an anonymous author of the XVth century Italian manuscript stored in the Vatican Apostolic Library calculated expected value by backward induction in a similar way to Pascal's approach. This note argues that an even earlier anonymous XIVth century Italian manuscript calculates expected value by a different method resembling the direct rule (regula recta) described in 1202 by Leonardo of Pisa (Fibonacci) in his Liber Abaci as borrowed from the Arabs.