Nadal:Federer; 2 sets to 1, rain stopped play

I am presently reading Keith Devlin's 'The Language of Mathematics': or, if not reading, dipping into it, starting with the chapter on probability.

The book reminds me for how long probability was virgin territory, intractable and unknown to great mathematicians for centuries. Devlin suggests that this was perhaps due to the god-like nature of chance. Luca Pacioli, the father of double entry book-keeping which is the heart of my profession, posed the unfinished game problem, which took two centuries, for Pascal and Fermat to solve.

And yet, today, the problem seems fairly routine, almost obvious. It just shows how mental frameworks exist, how maths has been a stage by stage process.

Assume Nadal and Federer have played numerous times before, with precisely even scores, and no trends. They are now playing a five setter, when rain stops play, and, for special reasons, the tournament has to end, and the prize divided. Should it be split 2:1, or if not, how?

In fact, the prize should be split 3:1 to Nadal. For in only one of the four possible fourth and fifth set combinations does Federer win, and in the other three, Nadal gets the one further set he needs to win.

I suspect, though, in the real world, things have changed: in the fifteenth century, the dispute would have solved by a duel at dawn; and in the twenty first, I suspect the lawyers would have a field day.

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