First Roll Results in a Game of Monopoly
Question: Players start the game of monopoly from Go
and throw two dice. The sum of the two
dice rolls ranges from 2 to 12. List
all squares that the player may land on after one roll of the two dice. What are the likelihoods of landing on each
property after one roll of the two dice?
Analysis: There are six numbers on each dice resulting
in 36 combinations of dice roll outcomes.
Not all dice throw outcomes are unique.
For instance (1,2) gives the same result as (2,1). Also, (1,3) (3,1) and (2,2) all give the sum
of 4.
In a previous post we calculated the unique outcomes from
the throws of two dice.
The outcomes are listed below.
Unique Outcomes From Two
Dice Throws


Outcome #

Unique Pair

Sum

Probability


1

1

1

2

0.027777778

2

1

2

3

0.055555556

3

1

3

4

0.055555556

4

1

4

5

0.055555556

5

1

5

6

0.055555556

6

1

6

7

0.055555556

7

2

2

4

0.027777778

8

2

3

5

0.055555556

9

2

4

6

0.055555556

10

2

5

7

0.055555556

11

2

6

8

0.055555556

12

3

3

6

0.027777778

13

3

4

7

0.055555556

14

3

5

8

0.055555556

15

3

6

9

0.055555556

16

4

4

8

0.027777778

17

4

5

9

0.055555556

18

4

6

10

0.055555556

19

5

5

10

0.027777778

20

5

6

11

0.055555556

21

6

6

12

0.027777778

I add probabilities of like outcomes to get the probability
that the sum of the two dice rolls are equal to k for all values of k ranging
from 2 to 12.
The table below lists the name of each square and the
probability of landing on each square after the first roll of two dice.
First Roll Results in a
Game of Monopoly


Dice Sum

Landing Spot

Probability

2

Community Chest

0.027777778

3

Baltic Ave.

0.055555556

4

Income Tax

0.083333333

5

Reading Railroad

0.111111111

6

Oriental Ave

0.138888889

7

Chance

0.166666667

8

Vermont Ave

0.138888889

9

Connecticut Ave

0.111111111

10

Just Visiting

0.083333333

11

St. Charles Place

0.055555556

12

Electric Company

0.027777778

1

The square that you are most likely to land on is Chance
because the most likely outcome for the sum of two dice rolls is 7.
The squares you are least likely to land on are Community
Chest and Electric Company. This occurs
because there is only one way to get on Community Chest (1,1) and only one way
to get on Electric Company (6,6). All
other possible sums formed by two dice rolls can be formed by more than one
combination.
Note: Readers might be interested in previous posts
on the game of Risk.
More Risk and Monopoly Problems will follow.
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