Estimation and Limits -- A Descriptive Look -- Answers

1. W(2) = 0.2856
   L(2) = 0.2520
   T(2) = 0.4624
   

2. W(3) = 0.364208
   L(3) = 0.321360
   T(3) = 0.314432
   

3. The probability that you win is approximately 53.1%. The probability that your opponent wins is approximately 46.9%. The probability that the point goes on forever appears to be zero.

4. W(2) = 0.3360
   L(2) = 0.2016
   T(2) = 0.4624
   
   W(3) = 0.428480
   L(3) = 0.257088
   T(3) = 0.314432
   

   The probability that you win is approximately 62.5%. The probability that your opponent wins is approximately 37.5%. The probability that the point goes on forever appears to be zero.

5. Let your opponent make the first shot.

6. If you make the first shot then the probability that you win with this more aggressive strategy is roughly 48.3%.

   If your opponent makes the first shot then the probability that you win with this more aggressive strategy is roughly 58.6%.

   You should stay with your current strategy!