Randomness and Simulation

Summary: In this laboratory, you will explore that random procedure using some fun Web services.

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Experimentation
  • Exercise 2: Improving Code
  • Exercise 3: Speeding Up the Game
  • Exercise 4: Favoring the House
  • Exercise 5: Seven or Eleven
  • Exercise 6: Or Doubles
  • Exercise 7: Changing Bets
  • Exercise 8: Flipping Coins

Exercises

Exercise 0: Preparation

a. Make a copy of dicegame.ss in your public_html directory.

b. Make the corresponding CGI script.

#!/bin/bash
/home/rebelsky/bin/schemeweb dicegame.ss

c. Share the CGI script and make it executable.

% share dicegame.ss
% share dicegame.cgi
% chmod a+x dicegame.cgi

d. Start DrScheme and load dicegame.ss.

e. Read through the procedures and make sure you understand what they do.

Exercise 1: Experimentation

Verify that the dicegame.cgi script works.

Exercise 2: Improving Code

Linda and Larry Leter have become addicted to the idea of putting lets around lambdas. Hence, they'd like to change the definition of pair-a-dice to

(define pair-a-dice
  (let ((dice (list (roll-a-die) (roll-a-die))))
    (lambda () dice)))

a. What do you think about their idea?

b. Test their change from within DrScheme by repeatedly rolling a pair of dice (using pair-a-dice). Do you notice anything interesting about the results?

c. Test their change on the Web. Do you notice the same change? Why or why not?

Exercise 3: Speeding Up the Game

Update dicegame.ss so that it reports the result of 10 rolls (or perhaps a user-selectable number of rolls) each time, rather than a single roll.

Exercise 4: Favoring the House

a. Update play-even-odd so that the house wins $2 rather than $1 if the dice are odd.

b. Can you foresee any problems that might occur with this change? If so, which ones?

c. Experiment ot see if your claim is correct.

Exercise 5: Seven or Eleven

Update dicegame.ss so that the player wins if the two dice total 7 or 11 rather than an odd number.

Exercise 6: Or Doubles

Update dicegame.ss so that the player wins if the two dice total 7 or 11 or if both dice have the same value.

Exercise 7: Changing Bets

Update dicegame.ss so that the player can choose the amount to bet.

Exercise 8: Flipping Coins

Update dicegame.ss so that the game is based on flipping coins, rather than rolling dice. (You can choose an appropriate game.)