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Tennis has become one of the most heavily traded sports online and particularly attractive for in-play traders. Horse racing and football have traditionally been popular among sports gamblers, however in recent years tennis has seen an enormous increase in bet volume, particularly on exchanges. The final match of Wimbledon 2008 was a perfect illustration of just how popular trading on tennis has become. During that one match between Roger Federer and Rafael Nadal, a total of £50 million worth of bets were matched on Betfair alone. More recently in the French Open 2011 final, over £40 million was matched, a figure routinely reached in Grand Slam finals and other high profile matches. From a trading point of view, tennis is a unique sport. The sequence of points are played within fixed intervals, usually no more than half a minute with rallies lasting roughly 10 seconds. As points are gained and lost regularly, in-play traders offer odds that vary with equal frequency. As we have mentioned, the greater the amplitude and frequency of odds changes, the more opportunity there is to profit. Another attraction lies in the availability of matches. Professional tennis is played in eleven months of a year with four major grand slam events; Wimbledon, the French, US and Australian Open as well as a series of prestigious tournaments including those of the Association of Tennis Professional (ATP) tour. This combination of profiting opportunity and availability of matches are the main contributing factors for the growing popularity of tennis trading.

A common assumption used in modeling a game of tennis is that each point is independent and identically distributed. That is, the chance of a player winning a point is not in any way dependent on the outcome of the point beforehand and the probability of a player winning a point on his serve can be assumed constant throughout the duration of a match. Based on this assumption we have developed a fast and reliable algorithm for calculating the winning probabilities of the two players for a tennis match of any type. User can specify the number of sets of the match (i.e. 3 setter or 5 setter) and the winning probability of each player's service. The other inputs are the current status: game scores, set scores, and overall match scores. Our command line functions, developed entirely in Matlab language, can be simply integrated in a tennis trading system for Betfair platform.

All results have been compared against a simple Monte Carlo-based tennis match simulator: we have simulated tennis matches under desired parameters and recorded the number of times each player wins over a total number of runs. The proportion of a player's wins compared to total simulation runs gives an estimation of their match-winning probability under those parameters. There is a perfect agreement between our approach and this tennis match simulator, moreover our algorithm results extremely fast and suitable for real-time applications, necessary for in-play trading on internet betting exchanges.

Index Terms: Matlab, source, code, tennis, match, winning, probability, calculator, BetFair, trading, system, betting, exchange.





Figure 1. Tennis

A simple and effective source code for Tennis Match-Winning Probability Calculator.

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The authors have no relationship or partnership with The Mathworks. All the code provided is written in Matlab language (M-files and/or M-functions), with no dll or other protected parts of code (P-files or executables). The code was developed with Matlab 14 SP1. Matlab is required. The code provided has to be considered "as is" and it is without any kind of warranty. The authors deny any kind of warranty concerning the code as well as any kind of responsibility for problems and damages which may be caused by the use of the code itself including all parts of the source code.

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