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Rock, Paper, Scissors 1
posted January 4, 2000 as
a Math
Forum EPoW
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Introduction: In the Rock,
Paper, Scissors problem series,
students investigate the concept
of probability through an investigation
of the fairness of games.
In this part of the series, students run a simulation where all of the outcomes are completely random.
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Where's the Math: Rock, Paper,
Scissors takes advatage of the computer's
ability to rapidly iterate a problem
, helping students visualize probability
over large sets of data. Graphs
facilitate identification of trends
as students experiment with problem
variations between random throws
and set throws in an even game.
Standards: Data
analysis & probability
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(The applet for this problem
is currently unavailable)
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Sample submitted
solution:
From: Richa,
age 13
School: Issaquah Middle School, Issaquah,
Washington
1. Do you think that this game is fair?
Please explain your answer.
Yes, I do think that this game is fair.
That's because, when you try the simulation
several times and compare the number of
times they win, it is about the same. I
tried the simulation about 6 times, and
found that Ed won three times and Vicky
won three times, if you exclude the number
of ties. The percentage of both of them
winning out of hundred is about the same
(there is not a huge difference).
2. Explain what happens to the graph
as the game goes on. What does this tell
you about the "fairness" of the game?
As the game goes on, the graph comes toward
the middle and levels out. The thing it
tells me about the fairness is that the
number of times each person wins becomes
a very close number (meaning that the number
of times each person wins out of hundred
excluding the ties is about the same).
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Reflections:
By running the simulation several times,
it was clear to most students that the total
number of Ed's wins, Vicky's wins and ties
were about the same. This means that the
game is fair since we can expect -- in the
long run -- Ed and Vicky to win the same
number of games. The graph provided, plotting
Ed's wins against the total number of wins,
is a visual interpretation of this. Though
it jumped around at the start of the simulation,
it eventually stettled into a straight line
at the halfway mark, meaning that Ed was
winning about 1/2 of the games and showing
that the game was fair. Most students were
able to see that the game is fair and seemed
to run the simulation successfully. They
found it more difficult to interpret the
graph and to explain how its long-term behavior
and placement related to the fairness of
the game.
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