betting theory on tennis A bookmaker has quoted odds on a tennis match between players I and...

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betting theory on tennis
A bookmaker has quoted odds on a tennis match betweenplayers I and II. The match consists of the best two out of threesets, i.e., if a player wins the first two sets, the third set isnot played and the bet on it is canceled. The bookmaker is givingodds of 5 to 2 that player I will win the match and odds of 3 to 2that player I will win each set. A bettor has 100 dollars which hecan distribute by betting on either player I or II to win the matchand any of the sets. All bets are made before the match starts (ifthere are only two sets, all bets on the third set are returned tothe bettor).
(a) Find a way of placing bets so that no matter what happens thebettor is assured of winning an amount z where z is as large aspossible. Formulate this problem as a linear programming and solveit using AMPL.
(b) What if now we have best three out of five sets, i.e., once aplayer wins three sets, no more sets are played and theircorresponding bets are canceled, and everything else keeps thesame? Re-solve the problem and compare the answer with part(a).

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Heading into the 2014 Australian Open Rafael Nadal was the top seed in Melbourne and the world no1 Nadal was hotoff a sensational return to top form in 2013 that saw him come back from injury to take both the French and US Opens plus nine other titles After dismissing Roger Federer easily in the semifinals Nadal was a strong 118 favourite to defeat Stan Wawrinka in the final of the 2014 Australian Open At those odds if a bettor placed a 10 bet on Nadal to win they would win back a total of 1180 including the original 10 stake making a profit of just 180 As a probability there was an 8475 chance of a Nadal victory Despite playing the best tennis of his career and defeating See Answer

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