Rugby
The problem of the best position for "kicking a conversion" in rugby is solved with a probabilistic method instead of an analytic one.
For detailed instructions on using the program, take a look at the info window from the
Rugby model.
Download the StarLogoT source code for
the Rugby model:
Click on one of the pictures to see a quicktime movie
of the model:
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The left boundary of the goal is 0, the right boundary of the
goal is 20, and the kick line is at -20. There are 2000
kicks
occuring simultaneously.
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The left boundary of the goal is 20, the right boundary of the
goal is 40, and the kick line is at -20. There are 2000
kicks
occuring simultaneously.
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The left boundary of the goal is 0, the right boundary of the
goal is 35, and the kick line is at -30. There are 1000
kicks
occuring simultaneously.
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When comparing these first two examples, please note that when the goal is
moved to the right the center of the distribution moves down. 
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