ECE194 S’02 Introduction to Engineering Design Arizona State University 1 Modeling #6 - Tennis Anyone? Begin with the end in mind  Deterministic model  Stochastic model  Simulation

ECE194 S’02 Introduction to Engineering Design Arizona State University 2 Modeling #6 - Tennis Anyone? Read the following problem statement:  Pat and John have dominated the world tennis scene for a number of years. They are to be found at every major tennis tournament, locked in battle and competing for titles. As an avid tennis fan, you and your friends have followed nearly every match between them.  Your best friend is an admirer of Pat - you think John has more style. However, even your friend concedes that John has an impressive service. You have been collecting all sorts of statistics on John and so you know how impressive it is. Your records show that John has served to Pat 230 times and won 154 of those points!

ECE194 S’02 Introduction to Engineering Design Arizona State University 3 Modeling #6 - Tennis Anyone?  Pat and John will be facing each other at Wimbledon next week. Your friend suggests that since you are so sure of John’s prowess, you should risk a wager. You craftily suggest that you will bet only on those games where John has the service. “Sure,” says your friend, “Each time John wins a game, I will give you $3, but each time Pat wins you will have to give me $10!” (It looks as though your friend has been collecting statistics, too.)  Is this a bet you should take?

ECE194 S’02 Introduction to Engineering Design Arizona State University 4 Modeling #6 - Tennis Anyone? Two possible approaches  An algorithm to simulate a tennis game  An analytic version of the tennis game

ECE194 S’02 Introduction to Engineering Design Arizona State University 5 Modeling #6 - Tennis Anyone? The simulation method (in Excel, for example)  Initialize the score at 0-0  Let John “serve” - use a random number generator to decide who wins the point  Update the score  Check the score to see whether the game is finished; if it is, record who has won  Repeat the serve and score process

ECE194 S’02 Introduction to Engineering Design Arizona State University 6 Modeling #6 - Tennis Anyone? The analytic approach First Serve

ECE194 S’02 Introduction to Engineering Design Arizona State University 7 Modeling #6 - Tennis Anyone? Second Serve

ECE194 S’02 Introduction to Engineering Design Arizona State University 8 Modeling #6 - Tennis Anyone? Third Serve

ECE194 S’02 Introduction to Engineering Design Arizona State University 9 Modeling #6 - Tennis Anyone? Entire game

ECE194 S’02 Introduction to Engineering Design Arizona State University 10 Modeling #6 - Tennis Anyone? And what happens at deuce?