STELLAã GAMES SIMULATION

Simple Game 1

To help students learn to modify, and hopefully create new, simulations, the teacher is encouraged to spend some time explaining how the simulation operates. If students have no experience in simulations, it may help to model a simulation by hand before the computer model is utilized.

This simulation models the situation of a simple Bernoulli event (repetitive binomial trials) . Propose the idea of two players playing any common game, tennis, checkers, etc. The probability that the first person (the student) wins is placed in the “Prob level” converter. This value should be in the interval from zero to one. The probability of a loss is then 1- this probability level. The number of games to be played is entered in the “Trials” stock and is preset to 25 games in this simulation. The “RANDOM GEN” is set to randomly produce a 1 (a win) in proportion to the value set in “Prob level”. This information is fed to the two “Pumps” which move a trial into the wins (if the value of Random Gen is one) or or losses stock holders until the Trials are completed. The two stock levels are reported in the presentations at the bottom of the window.

Worksheet 1

1) Students should simulate 20 repetitions of the 25 game trial and complete the worksheet down to the “additional questions”.

2) Using the Class worksheet make an overhead copy to project on the white board, or draw a graph similar to the class worksheet on the board to report class results.

3) Each group or student will enter a median value and the upper and lower interval values (highest remaining score and lowest remaining score from their worksheets) connected by a vertical bar. Suggest that they use a circle for the median, and horizontal bars for top and bottom values.

4) Ask the students to discuss the results they see. Try to help them see the following ideas:

a) The average value is usually about the same as the “expected value.

b) Most of the time, the “expected value” did not happen, but something close to it did.

c) The variability (how far apart the top and bottom of the intervals are) is wider in the middle values than at the ends.

After Each worksheet class discussion, if time permits, encourage students to explore and answer the “additional questions”. Also encourage them to ask questions they might want to answer about this type of event, and answer their own questions using the model.

Worksheet 2

This worksheet is similar to the first, expect each game is played as a best two-out-of-three event. To win one game you have to score two points.

The procedures are similar to the last. In addition to the other student observations, the following ideas are important issues for the class discussion following the collection of data:

1) How do the median values of the outcomes compare to the probability of success, and how does this compare to the last simulation.

2) Compare the variation about the median values for the two point game as opposed to the previous simulation; is there any difference?

Worksheet 3

This simulation is for a game similar to squash or volleyball. The idea is that you can only score if you have the advantage (serve?).

The procedure is similar to the last two examples and again, the following questions should be included in class discussions:

1) How do the median values of the outcomes compare to the probability of success, and how does this compare to the last two simulations.

2) Compare the variation about the median values for the advantage game as opposed to the previous simulations; is there any difference?