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).
