Homework 1: Exercises with Dice, and Computing Fair Odds and the House Edge

Due Monday January 22 (send by email to pasquale at cs.ucsd.edu)


1. Using one die, a one should appear 1/6 of the time.  This means that if you
toss a die N times, a one should appear roughly N/6 times.  Test this by
conducting a set of experiments, the first consisting of 10, second of 30,
third of 100, trials (throws of the die).  Fill in the table:

Trials	Count	Frequency (count/trials)
 10
 30
100

2. As the number of trials increases, the frequencies should get closer to the
theoretical values.  Why do you think this should be?

3. Now, using two dice, determine (1) the probability of each number appearing
(for example, a seven should appear with probability 6/36), (2) the frequency
that each number after conducting 30 trails, and (3) the "fair odds" for that
number appearing.  Fill in the following table:

Number	Prob	Freq	Fair Odds
2
3
4
5
6
7
8
9
10
11
12

4. Say a casino offers 4 to 1 odds for throwing a 7.  What is the house edge?
How did you calculate this?

5. Say a casino offers 5 to 1 odds for throwing a 7 or 11 (i.e., throwing
either a 7 or 11 is a winner).  What is the house edge?  How did you calculate
this?

6. 4. Say a casino offers 19 to 1 odds for throwing a 7 or 11 followed by
throwing a 7 or 11 again.  What is the house edge?  How did you calculate
this?