A new markovian model for tennis matches

In this paper we present a generalisation of previously considered Markovian models for Tennis that overcome the assumption that the points played are i.i.d. Indeed, we postulate that in any game there are two different situations: the first 6 points and the, possible, additional points after the first deuce, with different winning probabilities. We are able to compute the winning probabilities and the expected number of points played to complete a game and a set in this more general setting. We apply our results considering scores of matches between Novak Djokovic, Roger Federer and Rafael Nadal.