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:

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.


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.


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.

When comparing these first two examples, please note that when the goal is
moved to the right the center of the distribution moves down.
