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Rock, Paper, Scissors 2
posted January 11, 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 one of the
outcomes is fixed, but the other
is 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:
Scott, age 13
Josh, age 12
School: Issaquah Middle School, Issaquah,
Washington
1. What was your prediction?
That he would win because he'd catch on.
2. Do you think this simulation
represents a fair game? Why?
Yes it is fair, because he doesn't catch
on.
3. How would you compare
the fairness of this simulation to one in
which both players choose their throw at
random?
It is the same probability to win as
there was when they were random throws.
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Reflections:
Many students predicted that the new version
of this game would be unfair; it does seem
strange to mix random and nonrandom choices!
However, once they tried the simulation
a few times, they realized that since Ed
was continuing to choose randomly, the game
would remain fair. Ed and Vicky could be
expected to win the same number of games.
Many students correctly pointed out that
this game wasn't realistic since Ed, if
he were a real person, would certainly catch
on to Vicky's constant choice of Rock and
counteract with a constant choice of Paper.
Some students were hesitant to say that
this game was as fair as the previous one,
but most were convinced by the identical
behavior of the graph.
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