COME ON DOWN ... THE PRIZE IS RIGHT IN YOUR CLASSROOM

FURTHER QUESTIONS

Producing the information from Table 5 on a spreadsheet with formulas calculating the values in the body of the table has the advantage that when the dollar amounts in the various slots are changed, the other values are automatically re-computed to answer questions such as:

* If you were to "lose" $100 or $1000 instead of breaking even by landing in the $0 slots, would this change your strategy?

* How much would you have to lose by landing in those slots to make it worth aiming for some other slot?

* How would changing dollar values in the outer slots change your aiming strategy?

* What if the vertical border had a different shape with more or less intrusion into the grid?

STUDENT REACTIONS

Overall, the use of PLINKO has been successful and well-received in classes at both the upper and lower levels. Years later some returning graduates have fondly recalled analyzing this game. Because of the two-fold nature of the PLINKO discussion - first the ABRACADABRA problem, and then PLINKO - care must be taken to ensure that students follow each argument. For this reason, showing PLINKO video clips and using diagrams to help describe the game are essential. Students who tend to learn visually have remarked that the graphic depictions of the PLINKO board and the use of other graphic aids such as colored markers were imperative. Students have also suggested that the ABRACADABRA problem served as an excellent small-scale version of PLINKO and that it worked well as a lead-in to the game analysis. They like the way the assignments started small and got more involved - they felt they could handle this approach. In one rather unsuccessful experiment, the order of presenting ABRACADABRA and PLINKO was reversed, and students said they had a difficult time following both discussions. Another misstep was to have students view a clip of the game on their own outside of class, which disrupted the continuity of the entire solution process.

MONEY GAME

Another game we regularly use in class to illustrate analysis of pricing games is Money Game. Again, a video clip of the game is shown and the rules are explained to initiate discussion. In this game, the contestant's goal is to win a car by correctly guessing its five-digit price, the middle digit of which is given. The game is played on a board similar to that pictured in Figure 6. Nine cards with two-digit numbers are displayed. Hidden behind each card is a picture to be revealed when the card is selected: Behind the first two digits of the car being played for is the front half of the car; behind the last two digits, the back half. The remaining cards are marked "$." As cards are selected by the contestant, they are placed in the slots either over the two halves of the car at the bottom of the board or in the empty "$" slots to the left, as appropriate. The contestant wins the car and money if she can select both halves of the car before accumulating four "$" cards, in which case she wins only the money. Here it's not as crucial that an additional diagram be supplied. Discussion quickly leads to an important question: Assuming the contestant has no prior knowledge of the price of the car and picks at random, what proportion of time will she win the car?