Greedy Pig
Objectives: Students get a feel for the variation that occurs in random events
Students have to make and justify decisions, based on probability
Students learn how to construct stem-and-leaf plots
Materials
1 die
Preparation
All students make a table as follows:
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The Game
The match consists of 5 rounds. Each round consists of a number of games. Before each game, each student decides whether to stop (and retain the points they have earned in that round) or continue to play (and either win more points, or lose all points gained in that round, depending on the outcome).
All students get the first two throws for free. A die is tossed twice. The points are added together.
All students now stand up.
Each student now has two options.
They can quit, in which case their score is the total of the two dice. They sit down, and write this total in the Points column for round 1.
They can continue to play, and thus remain standing. The die is tossed. If the number is 1, 3, 4, 5 or 6, the student adds this number to their total for that round. But if the number is 2, the students that are still standing lose all points for that round, and record a score of 0 for that round.
The object of the game is to determine a strategy that in the long term will maximize the total points.
For each game, the student has the same option. They can decide to not risk their points, sit down and record the points they have earned in the Points column for round 1. Or they can continue to stand, the die is tossed and points are awarded (or lost) as before.
This continues until all students have sat down, or a 2 is rolled on the die. Then that round is over.
This process is continued for five rounds. The student then adds the points to get a TOTAL.
Record the Data in a Stem-And-Leaf Plot
While the students are adding their points, the teacher draws the stem of a stem-and-leaf plot on the board. Students are asked to come to the board and record their total points. The teacher explains the stem and leaf plot to the first few students, and then steps back and lets these students explain it to the others.
In a few minutes, the data is on the board, and the students have learned how to construct a stem-and-leaf plot!
Analyze the Outcome
Ask students what strategies they used to decide when to stop. Record these on the board as students speak. Discussion of the various strategies arises naturally. Some of the strategies are:
always quit after the first two throws (conservative strategy)
quit after n throws (eg I expect a 2 after six throws)
quit after n points
quit when n% of the class has sat down (don’t stand out in the crowd strategy)
never sit down, hoping for an enormous score (stand out from the crowd strategy)
Compare the strategies of the ‘winners’with those of the losers.
Play Again
Tell the students that they will play again, but this time they should choose a strategy first, and stick to it. Repeat the game.
Record the Data in a Back-to-Back Stem-And-Leaf Plot
Ask the students to record their result again. Show the first few students how to record their result on the left of the stem. The students have now learned how to construct a back-to-back stem-and-leaf plot!
Analyse the Outcome
In the second round, there is noticable improvement in the overall results of the class. Discuss how the back-to-back S&L plot displays this. With a senior class, you could start to discuss a theoretical approach to this problem.
Homework
Students toss a die until a 2 comes up. Record the number of throws and the total points. Repeat 20 times. Put each set of results into a frequency table.