Activity 3.1.5
Spinners
Introduction: Game designers use probability to help them add randomness to game play. One way to add
randomness is by having each player use a spinner to determine the number of spaces to move or which item to
select. By varying the size and numbers of sections of a spinner, the game designer can control the possible
outcomes.
Materials: MS Excel, handout, calculator, spinner parts, cardboard, scissors, glue
Background information: Spinners play an important role in board games. Many board games have the
players flick a spinner to determine the number of spaces a player moves during a turn. Spinners are often used
in place of dice in games for young children because dice pose a danger of choking. During World War II, the
British version of Monopoly replaced the traditional dice with a cardboard spinner due to rationing. Spinner
probability can be predicted based on the area within the circle each section occupies. If you construct a spinner
with only 1 choice, the outcome will always be 100%. In a spinner with two equally sized sections, the
predicted outcome is 50:50. The values just stated are the theoretical outcomes.
In the real world, theoretical values often do not match the actual or empirical outcome. An actual outcome
would be what you got when you actually spun the spinner. There could be many different reasons why there
are differences between the theoretical and empirical values to do match. Thus Empirical Probability of an
event is an "estimate" that the event will happen based on how often the event occurs after collecting data or
running an experiment (in a large number of trials). It is based specifically on direct observations or
experiences.
Formula for probability of event E:
Theoretical Probability of an event is the number of ways that the event can occur, divided by the total
number of outcomes. It is finding the probability of events that come from a sample space of known equally
likely outcomes.
Formula for probability of event E (from sample space S):
Part 1:
With a partner, brainstorm two possible reasons to explain the difference between theoretical and empirical
outcomes of a spinner. As a game designer, you wish to include an improved spinner in your next game whose
empirical values more closely match its theoretical. Take each problem from your brainstorming session and
propose a possible solution to improve your spinner.
Reason 1:
Solution:
Reason 2:
Solution:
Part 2:
Working in pairs, use MS Excel to produce two different “Pie Chart” spinner backgrounds. One of the pie charts
should be from four equally sized values (25% each).
The other spinner background should contain between 5-8 sections of different sizes. The total of the all of the
values should still equal 100%. Use different values then those shown here.
Print each “pie chart” spinner. Cut the spinner background out with scissors and glue to cardboard. Use one of
the spinner kits to connect the plastic spinner to each of your spinners. Spin each spinner 50 times and record
the number of times the spinner lands on each section (actual outcome value). Compare your actual values to
the theoretical values (from your Excel spreadsheet).
Spinner #1:
Theoretical
Gray 1
25%
Gray 2
25%
Gray 3
25%
Gray 4
25%
Actual
Spinner #2:
Theoretical:
Gray 1
Gray 2
Gray 3
Gray 4
Black
Actual:
Essay Question:
You have created a new 2D board game. Included in the game is a spinner that players will use to determine
bonus points. Bonus points are valuable and should be scarce. Design a plan for the spinner and justify your
design with evidence from the data collected in this activity.