Sim is a two-player game played with coloured pens and a piece of paper. The game starts with 6 points in the shape of a hexagon. Players choose a colour, then take turns to connect two unconnected points with a straight line each turn. The first person to form a triangle entirely in their colour loses. Triangles must have 3 corners at points of the hexagon, so corners formed by intersecting lines in the middle of the hexagon don't count. There's a helpful illustration of this game at http://www.papg.com/show?2UQ3, and the Wikipedia article on this game is also informative. It is known that the second player can always win with perfect play, but human players find it difficult to play perfectly. Your task is to estimate the probability that the second player wins in real game play. a) Specify a population of players for which you will estimate this probability. b) Perform an experiment to estimate the probability the second player wins. Clearly describe your experiment in sufficient detail that others could repeat it. c) Players in your selected population may differ in strategy and ability. Explain how your experiment takes this into account. STA1010 Statistical Methods for Science d) Players in your selected population may improve with practice. Explain how your experiment takes this into account. e) Report your results, and assess whether the second player has an advantage. Use numerical and/or graphical data summaries to support your answer, but do not use statistical tests that haven't been covered in lectures yet. For this experiment, you may pool results with other students, but you will need to ensure a common population and experimental conditions, and your report must be in your own words.
Sim is a two-player game played with coloured pens and a piece of paper. The game starts with 6 points in the shape of a hexagon. Players choose a colour, then take turns to connect two unconnected points with a straight line each turn. The first person to form a triangle entirely in their colour loses. Triangles must have 3 corners at points of the hexagon, so corners formed by intersecting lines in the middle of the hexagon don't count. There's a helpful illustration of this game at http://www.papg.com/show?2UQ3, and the Wikipedia article on this game is also informative. It is known that the second player can always win with perfect play, but human players find it difficult to play perfectly. Your task is to estimate the probability that the second player wins in real game play. a) Specify a population of players for which you will estimate this probability. b) Perform an experiment to estimate the probability the second player wins. Clearly describe your experiment in sufficient detail that others could repeat it. c) Players in your selected population may differ in strategy and ability. Explain how your experiment takes this into account. STA1010 Statistical Methods for Science d) Players in your selected population may improve with practice. Explain how your experiment takes this into account. e) Report your results, and assess whether the second player has an advantage. Use numerical and/or graphical data summaries to support your answer, but do not use statistical tests that haven't been covered in lectures yet. For this experiment, you may pool results with other students, but you will need to ensure a common population and experimental conditions, and your report must be in your own words.
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter10: Quadratic Equations
Section10.4: Solve Applications Modeled By Quadratic Equations
Problem 160E: A city planner wants to build a bridge across a lake in a park. To find the length of the bridge, he...
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Transcribed Image Text:Sim is a two-player game played with coloured pens and a piece of paper. The game
starts with 6 points in the shape of a hexagon. Players choose a colour, then take turns
to connect two unconnected points with a straight line each turn. The first person to
form a triangle entirely in their colour loses. Triangles must have 3 corners at points
of the hexagon, so corners formed by intersecting lines in the middle of the hexagon
don't count. There's a helpful illustration of this game at
http://www.papg.com/show?2UQ3, and the Wikipedia article on this game is also
informative.
It is known that the second player can always win with perfect play, but human
players find it difficult to play perfectly. Your task is to estimate the probability that
the second player wins in real game play.
a) Specify a population of players for which you will estimate this probability.
b) Perform an experiment to estimate the probability the second player wins.
Clearly describe your experiment in sufficient detail that others could repeat it.
c) Players in your selected population may differ in strategy and ability. Explain
how your experiment takes this into account.
STA1010 Statistical Methods for Science
d) Players in your selected population may improve with practice. Explain how
your experiment takes this into account.
e) Report your results, and assess whether the second player has an advantage.
Use numerical and/or graphical data summaries to support your answer, but do
not use statistical tests that haven't been covered in lectures yet.
For this experiment, you may pool results with other students, but you will need
to ensure a common population and experimental conditions, and your report
must be in your own words.
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